Advanced Distributed Systems J urgen Sch onw alder - - PowerPoint PPT Presentation

Advanced Distributed Systems

J¨ urgen Sch¨

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http://www.faculty.jacobs-university.de/jschoenwae/ads-2007/

November 26, 2007

J¨ urgen Sch¨

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Part: Introduction

1

Definition and Applications

2

Wireless Sensor Network Motes

3

Research Topics

4

Motes on the Internet (6lowpan)

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Definition and Applications

1

Definition and Applications

2

Wireless Sensor Network Motes

3

Research Topics

4

Motes on the Internet (6lowpan)

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Wireless Sensor Networks

Definition A wireless sensor network is a wireless network consisting of spatially distributed autonomous devices using sensors to cooperatively monitor physical or environmental conditions, such as temperature, pressure, gases or motion.

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Applications of Wireless Sensor Networks

Applications Environmental monitoring Seismic detection Disaster situation monitoring and recovery Health and medical monitoring Inventory tracking and logistics Space monitoring (smart dust on mars) Smart spaces (home/office scenarios) Military surveillance

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Wireless Sensor Network Motes

1

Definition and Applications

2

Wireless Sensor Network Motes

3

Research Topics

4

Motes on the Internet (6lowpan)

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Wireless Sensor Network Motes

Definition Motes are small energy efficient computers with a wireless interface and several sensors, able to operate on battery power for months or years.

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Microcontroller — Atmel / TI / Intel

Atmel AVR ATmega 128 8 bit RISC at 16 MHz, 32 registers 4kB RAM, 128kB Flash, 4kB EEPROM TI MSP430 16 bit RISC at 8 MHz, 16 registers 10kB RAM, 48kB Flash, 16kB EEPROM Intel PXA271 XScale 32 bit RISC at 13-416MHz, 16 registers 256kB SRAM, 32MB SDRAM, 32MB Flash

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Microcontroller — Atmel / TI / Intel

Atmel AVR ATmega 128 8 bit RISC at 16 MHz, 32 registers 4kB RAM, 128kB Flash, 4kB EEPROM TI MSP430 16 bit RISC at 8 MHz, 16 registers 10kB RAM, 48kB Flash, 16kB EEPROM Intel PXA271 XScale 32 bit RISC at 13-416MHz, 16 registers 256kB SRAM, 32MB SDRAM, 32MB Flash

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Microcontroller — Atmel / TI / Intel

Atmel AVR ATmega 128 8 bit RISC at 16 MHz, 32 registers 4kB RAM, 128kB Flash, 4kB EEPROM TI MSP430 16 bit RISC at 8 MHz, 16 registers 10kB RAM, 48kB Flash, 16kB EEPROM Intel PXA271 XScale 32 bit RISC at 13-416MHz, 16 registers 256kB SRAM, 32MB SDRAM, 32MB Flash

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Microcontroller Power Consumption

MSP430 / ATmega 128 / PXA271 XScale MSP430 AVR 128 PXA271 design TI AVR Intel mote Telos-B Mica-Z Imote2 voltage 1.8V min 2.5V min 1.3V min active 1.8mA 8mA 44 − 66mA sleep 5.1µA < 15µA 390µA

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Radio — IEEE 802.15.4 (2003)

IEEE 802.15.4 20-250 kbps (2.4 GHz ISM band) Direct Sequence Spread Spectrum (DSSS) CSMA-CA medium access control Link encryption (AES) (no key management) Full / reduced function devices ChipCon CC2420 Popular 802.15.4 air interface 128byte TX/RX buffer

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Radio — IEEE 802.15.4 (2003)

IEEE 802.15.4 20-250 kbps (2.4 GHz ISM band) Direct Sequence Spread Spectrum (DSSS) CSMA-CA medium access control Link encryption (AES) (no key management) Full / reduced function devices ChipCon CC2420 Popular 802.15.4 air interface 128byte TX/RX buffer

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Radio — IEEE 802.15.4a (2007)

IEEE 802.15.4a 100 kbps up to 1 mbps (0.5, 2-3, 6-10 GHz) Impulse Radio Ultra Wide Band and Chirp ALOHA and CSMA-CA medium access control Link encryption (AES) (no key management) Full / reduced function devices Ranging support (!) Nanotron NanoLoc Chirp technology in the 2.4 GHz ISM band Enables real time location systems

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Radio — IEEE 802.15.4a (2007)

IEEE 802.15.4a 100 kbps up to 1 mbps (0.5, 2-3, 6-10 GHz) Impulse Radio Ultra Wide Band and Chirp ALOHA and CSMA-CA medium access control Link encryption (AES) (no key management) Full / reduced function devices Ranging support (!) Nanotron NanoLoc Chirp technology in the 2.4 GHz ISM band Enables real time location systems

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Radio Power Consumption

ChipCon CC 2420 / Nanotron Nanoloc CC 2420 NanoLoc standard 802.15.4 802.15.4a data rate 250 kbps 125 kbps / 1 Mbps voltage 2.1 − 3.9V 2.3 − 2.7V receive 19.7mA 33mA transmit 17.4mA 25 − 30mA idle ? ? sleep 20µA 2µA

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Research Topics

1

Definition and Applications

2

Wireless Sensor Network Motes

3

Research Topics

4

Motes on the Internet (6lowpan)

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Research Topics

Embedded systems and ad-hoc networking Energy-aware resource management Cross-layer design and optimization (Ad-hoc) mesh routing protocols Interworking and distributed algorithms Middleware for wireless sensor networks Localization, time synchronization, . . . Data fusion, control, actuation, . . . Security and novel applications

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Motes on the Internet (6lowpan)

1

Definition and Applications

2

Wireless Sensor Network Motes

3

Research Topics

4

Motes on the Internet (6lowpan)

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Motes on the Internet

IPv6 over 802.15.4 (6lowpan) Talk IPv6 directly to 802.15.4 motes Supports header compression Requires link-layer fragmentation / reassembly Should support mesh networking Jacobs’ 6lowpan Implementation Based on the TinyOS 2.0 embedded OS Buffer management is major design issue Serial tunnel daemon / base station support Tested on Telos-B and Mica-Z motes

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Motes on the Internet

IPv6 over 802.15.4 (6lowpan) Talk IPv6 directly to 802.15.4 motes Supports header compression Requires link-layer fragmentation / reassembly Should support mesh networking Jacobs’ 6lowpan Implementation Based on the TinyOS 2.0 embedded OS Buffer management is major design issue Serial tunnel daemon / base station support Tested on Telos-B and Mica-Z motes

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Experimental Setup

serial_tunnel daemon tun(4) interface ethernet interface serial interface TinyOS mote running BaseStationCC2420 serial interface 802.15.4 interface 802.15.4 interface TinyOS mote with a IPv6/6lowpan stack USB 802.15.4 Linux kernel / IP stack 6lowpan-encapsulated IPv6 packets 6lowpan-encapsulated IPv6 packets IPv6 packets Internet IPv6 packets

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Try it yourself!

ping tests

$ ping6 mote-14.eecs.jacobs-university.de $ ping6 mote-18.eecs.jacobs-university.de

command line interface

$ nc6 -u mote-14.eecs.jacobs-university.de 1234 help

visual control (video streaming)

$ vlc http://rat.eecs.jacobs-university.de:8080

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References

• K. R¨
• mer and F. Mattern.

The Design Space of Wireless Sensor Networks. IEEE Wireless Communications, 11(6):54–61, December 2004.

• A. Wheeler.

Commercial Applications of Wireless Sensor Networks using ZigBee. IEEE Communications Magazine, 45(4):70–77, April 2007. L.D. Nardis and M.-G. Di Benedetto. Overview of the IEEE 802.15.4/4a standards for low data rate Wireless Personal Data Networks. In Proc. of the 4th IEEE Workshop on Positioning, Navigation and Communication 2007 (WPNC’07), Hannover, March 2007. IEEE.

• N. Kushalnagar, G. Montenegro, and C. Schumacher.

IPv6 over Low-Power Wireless Personal Area Networks (6LoWPANs): Overview, Assumptions, Problem Statement, and Goals. RFC 4919, Intel Corp, Microsoft Corporation, Danfoss A/S, August 2007.

• G. Montenegro, N. Kushalnagar, J. Hui, and D. Culler.

Transmission of IPv6 Packets over IEEE 802.15.4 Networks. RFC 4944, Microsoft Corporation, Intel Corp, Arch Rock Corp, September 2007.

• M. Harvan.

Connecting Wireless Sensor Networks to the Internet — a 6lowpan Implementation for TinyOS 2.0. Master’s thesis, Jacobs University Bremen, June 2007. J¨ urgen Sch¨

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Part: NesC and TinyOS

5

History

6

NesC Language Overview

7

TinyOS: Operating System for WSNs

8

Demonstration

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History

5

History

6

NesC Language Overview

7

TinyOS: Operating System for WSNs

8

Demonstration

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NesC and TinyOS History

developed by a consortium led by UC Berkeley two versions

TinyOS 1.1 TinyOS 2.0

2.0 not backwards compatible with 1.1

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NesC Language Overview

5

History

6

NesC Language Overview

7

TinyOS: Operating System for WSNs

8

Demonstration

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NesC: Programming Language for Embedded Systems

Programming language:

a dialect/extension of C static memory allocation only (no malloc/free) whole-program analysis, efficient optimization race condition detection

Implementation:

pre-processor – output is a C-program, that is compiled using gcc for the specific platform statically linking functions

For more details, see [?]

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NesC — Interfaces

commands

can be called by other modules think functions

events

signalled by other modules have to be handled by this module

Interface Example

interface Send { command error_t send(message_t* msg, uint8_t len); event void sendDone(message_t* msg, error_t error); ... }

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NesC — Components

a NesC application consists of components components provide and use interfaces components can be accessed only via interfaces (cannot call an arbitrary C-function from another module)

Figure: NesC Interface

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NesC — Components

modules – implement interfaces configurations – connect modules together via their interfaces (wiring)

Figure: NesC Configuration

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NesC — Concurrency — Tasks

Define a Task task void task_name() { ... } Post a Task post task_name(); posting a task – the task is placed on an internal task queue which is processed in FIFO order a task runs to completion before the next task is run, i.e. tasks do not preempt each other tasks can be preempted by hardware events

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TinyOS: Operating System for WSNs

5

History

6

NesC Language Overview

7

TinyOS: Operating System for WSNs

8

Demonstration

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TinyOS

written in nesC event-driven architecture no kernel/user space differentiation single shared stack no process or memory management no virtual memory multi-layer abstractions components statically linked together

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TinyOS — Functionality

hardware abstraction access to sensors access to actuators scheduler (tasks, hardware interrupts) timer radio interface Active Messages (networking) storage (using flash memory on the motes) . . .

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Demonstration

5

History

6

NesC Language Overview

7

TinyOS: Operating System for WSNs

8

Demonstration

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TinyOS — Demo — Blink

no screen on which we could print “Hello World” let’s blink an led instead using a timer to blink an led 2 source files

BlinkC.nc BlinkAppC.nc

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BlinkC.nc

module BlinkC { uses interface Timer<TMilli> as Timer0; uses interface Leds; uses interface Boot; } implementation { event void Boot.booted() { call Timer0.startPeriodic(250); } event void Timer0.fired() { call Leds.led0Toggle(); } }

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BlinkAppC.nc

configuration BlinkAppC { } implementation { components MainC, BlinkC, LedsC; components new TimerMilliC() as Timer0; BlinkC -> MainC.Boot; BlinkC.Timer0 -> Timer0; BlinkC.Leds -> LedsC; }

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TinyOS — Demo — Blink

in reality using 3 timers

250 ms 500 ms 1000 ms

each timer toggling one led the result is a 3-bit counter

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TinyOS — Demo — Oscilloscope

motes – periodically get a sensor reading and broadcast

• ver the radio

BaseStation mote – forward packets between the radio and the serial interface PC - java application reading packets from the serial interface and plotting sensor readings

Figure: Oscilloscope Setup

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TinyOS — Demo — Oscilloscope

node ID sensor 7 light 8 light 18 temperature temperature = −38.4 + 0.0098 ∗ data

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References

• D. Gay, P. Levis, R. von Behren, M. Welsh, E. Brewer, and D. Culler.

The nesC Language: A Holistic Approach to Networked Embedded Systems. In PLDI03. ACM, June 2003.

• K. R¨
• mer and F. Mattern.

The Design Space of Wireless Sensor Networks. IEEE Wireless Communications, 11(6):54–61, December 2004.

• A. Wheeler.

Commercial Applications of Wireless Sensor Networks using ZigBee. IEEE Communications Magazine, 45(4):70–77, April 2007.

• L. D. Nardis and M.-G. Di Benedetto.

Overview of the IEEE 802.15.4/4a standards for low data rate Wireless Personal Data Networks. In Proc. of the 4th IEEE Workshop on Positioning, Navigation and Communication 2007 (WPNC’07), Hannover, March 2007. IEEE. J¨ urgen Sch¨

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Part: Distributed Algorithms

9

Transition System

10 Local and Distributed Algorithms 11 Induced Transition Systems 12 Events and Causal Order 13 Computations and Executions 14 Logical Clocks

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Transition System

9

Transition System

10 Local and Distributed Algorithms 11 Induced Transition Systems 12 Events and Causal Order 13 Computations and Executions 14 Logical Clocks

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Transition System

Definition (transition system) A transition system is a triple S = (C, →, I) where C is a set

• f configurations, → is a binary transition relation on C, and I

is a subset of C of initial configurations. Definition (execution) Let S = (C, →, I) be a transition system. An execution of S is a maximal sequence E = (γ0, γ1, . . .), where γ0 ∈ I and γi → γi+1 for all i ≥ 0. Notes A transition relation is a subset of C × C. The notation γ → δ is used for (γ, δ) ∈→,

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Transition System

Definition (reachability) Configuration δ is reachable from γ, notation γ δ, if there exists a sequence γ = γ0, γ1, . . . , γk = δ with γi → γi+1 for all 0 ≤ i < k. Notes A terminal configuration is a configuration γ for which there is no δ such that γ → δ A sequence E(γ0, γ1, . . .) with γi → γi+1 for all i is maximal if it is either infinite or ends in a terminal configuration Configuration δ is said to be reachable if it is reachable from an initial configuration.

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Local and Distributed Algorithms

9

Transition System

10 Local and Distributed Algorithms 11 Induced Transition Systems 12 Events and Causal Order 13 Computations and Executions 14 Logical Clocks

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Local Algorithm

Definition (local algorithm) The local algorithm of a process is a quintuple (Z, I, ⊢i, ⊢s, ⊢r), where Z is a set of states, I is a subset of Z

• f initial states, ⊢i is a relation on Z × Z, and ⊢s and ⊢r are

relations on Z × M × Z. The binary relation ⊢ on Z is defined by c ⊢ d ⇐ ⇒ (c, d) ∈⊢i ∨∃m ∈ M((c, m, d) ∈ (⊢s ∪ ⊢r)). Notes Let M be a set of possible messages. We denote the collection of multisets with elements from M with M(M). The relations ⊢i, ⊢s, and ⊢r correspond to state transitions related with internal, send, and receive events.

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Distributed Algorithm

Definition (distributed algorithm) A distributed algorithm for a collection P = {p1, . . . , pN} of processes is a collection of local algorithms, one for each process in P. Notes A configuration of a transition system consists of the state

• f each process and the collection of messages in transit

The transitions are the events of the processes, which do not only affect the state of the process, but can also affect (and be affected by) the collection of messages The initial configurations are the configurations where each process is in an initial state and the message collection is empty

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Induced Transition Systems

9

Transition System

10 Local and Distributed Algorithms 11 Induced Transition Systems 12 Events and Causal Order 13 Computations and Executions 14 Logical Clocks

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Induced Async. Transition System

Definition (Induced Async. Transition System) The transition system S = (C, →, I) is induced under asynchronous communication by a distributed algorithm for processes p1, . . . , pN, where the local algorithm for process pi is (Zpi, Ipi, ⊢i

pi, ⊢s pi, ⊢r pi), is given by

(1) C = {(cp1, . . . , cpN, M) : (∀p ∈ P : cp ∈ Zp)∧M ∈ M(M)} (2) → (see next slide) (3) I = {(cp1, . . . , cpN, M) : (∀p ∈ P : cp ∈ Ip) ∧ M = ∅}

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Induced Async. Transition System

Definition (Induced Async. Transition System (cont.)) (2) →= (

p∈P →p), where the →p are the transitions

corresponding to the state changes of process p; →pi is the set of pairs (cp1, . . . , cpi, . . . , cpN, M1), (cp1, . . . , c′

pi, . . . , cpN, M2)

for which one of the following three conditions holds:

(cpi, c′

pi) ∈⊢i pi and M1 = M2

for some m ∈ M, (cpi, m, c′

pi) ∈⊢s pi and M2 = M1 ∪ {m}

for some m ∈ M, (cpi, m, c′

pi) ∈⊢r pi and M1 = M2 ∪ {m}

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Induced Sync. Transition System

Definition (Induced Sync. Transition System) The transition system S = (C, →, I) is induced under synchronous communication by a distributed algorithm for processes p1, . . . , pN, where the local algorithm for process pi is (Zpi, Ipi, ⊢i

pi, ⊢s pi, ⊢r pi), is given by

(1) C = {(cp1, . . . , cpN) : (∀p ∈ P : cp ∈ Zp)} (2) → (see next slide) (3) I = {(cp1, . . . , cpN) : (∀p ∈ P : cp ∈ Ip)}

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Induced Sync. Transition System

Definition (Induced Sync. Transition System (cont.)) (2) →= (

p∈P →p) ∪ ( p,q∈P:p=q →pq), where

→pi is the set of pairs (cp1, . . . , cpi, . . . , cpN), (cp1, . . . , c′

pi, . . . , cpN)

for which (cpi, c′

pi) ∈⊢i pi

→pipj is the set of pairs (. . . , cpi, . . . , cpj, . . .)(. . . , c′

pi, . . . , c′ pj, . . .)

for which there is a message m ∈ M such that (cpi, m, c′

pi) ∈⊢s pi and (cpj, m, c′ pj) ∈⊢r pj

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Events and Causal Order

9

Transition System

10 Local and Distributed Algorithms 11 Induced Transition Systems 12 Events and Causal Order 13 Computations and Executions 14 Logical Clocks

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Events and Causal Order

A transition a is said to occur earlier than transition b if a

• ccures in the sequence of transitions before b

An execution E = (γ0, γ1, . . .) can be associated with a sequence of events ¯ E = (e0, e1, . . .), where ei is the event by which the configuration changes from γi to γi+1 Events of a distributed execution can sometimes be interchanged without affecting the later configurations of the execution The notion of time as a total order on the events is not suitable and instead the notion of causal dependence is introduced

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Dependence of Events

Theorem Let γ be a configuration of a distributed system (with asynchronous message passing) and let ep and eq be events of different processes p and q, both applicable in γ. Then ep is applicable in eq(γ), eq is applicable in ep(γ), and ep(eq(γ)) = eq(ep(γ)). Let ep and eq be two events that occur consecutively in an execution. The premise of the theorem applies to these events except in the following two cases:

a) p = q or b) ep is a send event, and eq is the corresponding receive event

The fact that a particular pair of events cannot be exchanged is expressed by saying that there is a causal relation between these two events

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Causal Order

Definition (causal order) Let E be an execution. The relation ≺, called the causal

• rder, on the events of the execution is the smallest relation

that satisfies the following requirements: (1) If e and f are different events of the same process and e

• ccurs before f , then e ≺ f .

(2) If s is a send event and r the corresponding receive event, then s ≺ r. (3) ≺ is transitive. Write a b to denote (a ≺ b ∨ a = b) The relation is a partial order and there may be events a and b for which neither a ≺ b nor b ≺ a holds Such events are said to be concurrent, notation ab

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Computations and Executions

9

Transition System

10 Local and Distributed Algorithms 11 Induced Transition Systems 12 Events and Causal Order 13 Computations and Executions 14 Logical Clocks

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Computations

The events of an execution can be reordered in any order consistent with the causal order, without affecting the result of the execution Such a reordering of the events gives rise to a different sequence of configurations, but this execution will be regarded as equivalent to the original execution Let E = (γ0, γ1, . . .) be an execution with an associated sequence of events ¯ E = (e0, e1, . . .), and assume f is a permutation of ¯ E The permutation (f0, f1, . . .) of the events of E is consistent with the causal order if fi fj implies i ≤ j, i.e., if no event is preceded in the sequence by an event it causally precedes

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Equivalent Executions

Theorem Let f = (f0, f1, . . .) be a permutation of the events of E that is consistent with the causal order of E. Then f defines a unique execution F starting in the initial configuration of E. F has as many events as E, and if E is finite, the last configuration of F is the same as the last configuration of E. If the conditions of this theorem apply, we say that E and F are equivalent executions, denoted as E ∼ F A global observer, who has access to the actual sequence

• f events, may distinguish between two equivalent

executions The processes, however, cannot distinguish between two equivalent executions

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Computation

Definition (computation) A computation of a distributed algorithm is an equivalence class under ∼ of executions of the algorithm. It makes no sense to speak about the configurations of a computation, because different executions of the computation may not have the same configurations It does make sense to speak about the collection of events of a computation, because all executions if the computation consist of the same set of events The causal order of the events is defined for a computation

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Logical Clocks

9

Transition System

10 Local and Distributed Algorithms 11 Induced Transition Systems 12 Events and Causal Order 13 Computations and Executions 14 Logical Clocks

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Logical Clocks

Definition (clock) A clock is a function Θ from the set of events ¯ E to an ordered set (X, <) such that for a, b ∈ ¯ E a ≺ b ⇒ Θ(a) < Θ(b). Definition (lamport clock) A Lamport clock is a clock function ΘL which assigns to every event a the length k of the longest sequence (e1, . . . , ek) of events satisfying e1 ≺ e2 ≺ . . . ≺ ek = a. Note A clock function Θ expresses causal order, but does not necessarily express concurrency

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Lamport Clocks

The value of ΘL can be computed as follows:

ΘL(a) is 0 if a is the first event in a process If a is an internal event or send event, and a′ the previous event in the same process, then ΘL(a) = ΘL(a′) + 1 If a is a receive event, a′ the previous event in the same process, and b the send event corresponding to a, then ΘL(a) = max(ΘL(a′), ΘL(b)) + 1

The per process clock value may be combined with a process identifier to obtain a globally unique value

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Lamport Clock Example

e1,1 e1,2 e1,4 e1,3 e1,5 e2,1 e2,3 e2,2 e3,1 e3,2 e3,3 e3,5 e3,6 e3,4 P1: P2: P3:

2 5 6 7 1 2 1 1 3 4 5 6 7 7

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Vector Clocks

Definition (vector clocks) A vector clock for a set of N processes is a clock function ΘV which is defined by ΘV (a) = (a1, . . . , aN), where ai is the number of events e in process pi for which e ≺ a. Vectors are naturally ordered by the vector order: (a1, . . . an) ≤V (b1, . . . bn) ⇐ ⇒ ∀i (1 ≤ i ≤ b) : ai ≤ bi Vector clocks can express concurrency since concurrent events are labelled with incomparable clock values: a ≺ b ⇐ ⇒ ΘV (a) < ΘV (b) Vector clocks require more space in the messages, but element compression can reduce message overhead

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Vector Clock Example

e1,1 e1,2 e1,4 e1,3 e1,5 e2,1 e2,3 e2,2 e3,1 e3,2 e3,3 e3,5 e3,6 e3,4 P1: P2: P3:

(2,0,0) (3,2,3) (4,2,3) (5,2,3) (0,1,0) (0,2,0) (1,0,0) (0,0,1) (0,2,4) (0,2,5) (0,2,6) (4,3,3) (0,2,3) (0,2,2)

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References

• L. Lamport.

Time, Clocks, and the Ordering of Events in a Distributed System. Communications of the ACM, 21(7), July 1978.

• M. Raynal.

About logical clocks in distributed systems. Operating Systems Review, 26(1):41–48, 1992.

• G. Tel.

Introduction to Distributed Algorithms. Cambridge University Press, 2 edition, 2000. J¨ urgen Sch¨

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Part: Clock Synchronization in WSNs

15 Motivation and Introduction 16 Time-Stamp Synchronization (TSS) 17 Reachback Firefly Algorithm (RFA) 18 Reference Broadcast Synchronization (RBS) 19 Flooding Time Synchronization Protocol (FTSP)

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Motivation and Introduction

15 Motivation and Introduction 16 Time-Stamp Synchronization (TSS) 17 Reachback Firefly Algorithm (RFA) 18 Reference Broadcast Synchronization (RBS) 19 Flooding Time Synchronization Protocol (FTSP)

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Why Clock Synchronization in WSNs?

Motivation Time correlated sensor readings or time series data aggregation in the network Coordination of low duty cycles (power up hardware only when necessary) to increase overall network lifetime Transmission scheduling algorithms such as TDMA

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Clock Synchronization in WSNs

Approach #1 (external synchronization) All clocks are synchronized to a real time standard such as Coordinated Universal Time (UTC). Approach #2 (internal synchronization) Clocks are relatively synchronized to each other to provide

• rdering of events.

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Special Constraints in WSNs

Energy consumption: According to Hill et al., each transmitted bit consumes as much power as executing 800-1000 instructions. One goal is therefore to work with a minimum number of messages. Processing power: Sensor nodes usually use microcontrollers with limited computational power. Memory capacity: Sensor notes have limited amount of data and program memory, making it difficult to fit lengthy algorithms or to maintain larger data sets. Transmission range: The transmission range is a function

• f transmission power and since energy is a scarce

resource, the transmission range of sensor nodes is typically short. Depending on the application scenario, there might also be issues with noise.

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Sources of Synchronization Errors

Send time: Time spend at the sending node from creating a message until it reaches the network interface. Access time: Time spend getting access to the channel for transmission. Depending on the MAC, the access time can vary widely. Propagation time: Travel time of a message after leaving the sender node until it is received by a receiving node. Typically very small (in the order of nano seconds in LANs). Receive time: Time needed to process an incoming message and to notify the receiving application.

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Synchronization Metrics

1 Energy consumption 2 Synchronization precision 3 Scalability to support large networks with many nodes 4 Robustness against failures (self-organization) 5 Synchronization scope (local synchronization for some

nodes versus global synchronization of all nodes)

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Criteria and Classification

1 Master/slave vs. peer-to-peer synchronization 2 Clock correction vs. untethered clocks 3 Internal vs. external synchronization 4 Probabilistic vs. deterministic synchronization bounds 5 Sender to receiver vs. receiver to receiver synchronization 6 Single-hop vs. multi-hop networks 7 Stationary vs. dynamic network topologies J¨ urgen Sch¨

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Time-Stamp Synchronization (TSS)

15 Motivation and Introduction 16 Time-Stamp Synchronization (TSS) 17 Reachback Firefly Algorithm (RFA) 18 Reference Broadcast Synchronization (RBS) 19 Flooding Time Synchronization Protocol (FTSP)

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Time-Stamp Synchronization (TSS)

Focus on temporal relationships between events (x happened before y) Assumption that not all nodes can directly talk to each

• ther

. . .

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Time Transformation

Time Transformation The real-time time difference ∆t can be transformed into computer clock time difference ∆c as follows: (1 − ρ) ≤ ∆c ∆t ≤ (1 + ρ) (1) The parameter ρ is the bound of the computer clock drift. An equivalent notation is the following: (1 − ρ)∆t ≤ ∆c ≤ (1 + ρ)∆t (2) ∆c (1 + ρ) ≤ ∆t ≤ ∆c (1 − ρ) (3)

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Time Transformation

Example In order to transform a time difference ∆c from the local time

• f one node with upper bound ρ1 to the local time of another

node with upper bound ρ2, ∆t is first estimated by the real time interval

• ∆c

(1 + ρ1), ∆c (1 − ρ1)

• (4)

which in turn is estimated by the computer time interval

• ∆c (1 − ρ2)

(1 + ρ1), ∆c (1 + ρ2) (1 − ρ1)

• (5)

relative to the local time of the second node.

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Reachback Firefly Algorithm (RFA)

15 Motivation and Introduction 16 Time-Stamp Synchronization (TSS) 17 Reachback Firefly Algorithm (RFA) 18 Reference Broadcast Synchronization (RBS) 19 Flooding Time Synchronization Protocol (FTSP)

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Reference Broadcast Synchronization (RBS)

15 Motivation and Introduction 16 Time-Stamp Synchronization (TSS) 17 Reachback Firefly Algorithm (RFA) 18 Reference Broadcast Synchronization (RBS) 19 Flooding Time Synchronization Protocol (FTSP)

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Reference Broadcast Synchronization

NIC Sender Receiver Critical Path NIC Sender Receiver 1 Receiver 2 Critical Path Time

Idea Exploit the broadcast capability of wireless sensor networks Reduce the critical path by eliminating send time and access time Instead of synchronizing the sender with the receiver, synchronize a set of receivers with each other

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Reference Broadcast Synchronization

Algorithm Individual nodes broadcast reference beacons to their neighbors (beacons do not include timestamps). Receivers timestamp the arrival of the beacons using their local clocks Receivers exchange their timestamps. The only source of errors are different propagation delays (but usually very small) and receive time errors.

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Reference Broadcast Synchronization

Phase Offsets Errors mainly due to receive time variations since propagation time variation is usually negligible Calculate the offset over a number of received beacons Let m be the number of beacons and let Tr,b denote the time of receiver r’s clock when it receives broadcast b. Then the offset o[i, j] of the notes i and j is given by:

• [i, j] = 1

m

m

• k=1

(Tj,k − Ti,k) (6) By averaging the time differences, we take care of phase errors.

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Reference Broadcast Synchronization

Clock Skew Clocks typically have a bounded frequency error, i.e., the freqency is not precisely the expected frequency. The frequency of real-world clocks can change but it tends to stay in table over time periods.

Short-term instability is primarily due to environmental factors, such as variations in temperature, supply voltage, and shock. Long-term instability results from more subtle effects, such as oscillator aging.

Use linear regression to handle clock screw.

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Reference Broadcast Synchronization

Experiment Broacast a reference beacon in a network with 5 motes Every mote has a clock resolution of 2µs to timestamp the reception times of incoming broadcasts The following plot shows points (x, y) with (x, y) = (Tr1,k, Tr2,k − Tr1,k) (7) and the best linear fit. The vertical pulses visualize the distance from each point to the best-fit line.

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Reference Broacast Synchronization

Linear fit seems to be a “good enough” approximation for clock screw.

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Reference Broacast Synchronization

Comparision of RBS and NTP Implemented RBS on a Linux kernel in user space Each regression is based on a window of the 30 most recent pulse reception reports Outliers are automatically rejected based on an adaptive threshold equal to 3 times the median fit error of the set

• f points not yet rejected

Light network load: The 802.11 network had very little background traffic Heavy network load: Two additional machines generated traffic by sending a series of randomly-sized UDP datagrams, each picked uniformly between 500 and 15,000 bytes (IP fragmentation being required for larger packets). The inter-packet delay was 10msec.

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RBS Comparison to NTP

RBS outperforms NTP and also a modified version of NTP, which allows a fairer comparison to RBS.

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Flooding Time Synchronization Protocol (FTSP)

15 Motivation and Introduction 16 Time-Stamp Synchronization (TSS) 17 Reachback Firefly Algorithm (RFA) 18 Reference Broadcast Synchronization (RBS) 19 Flooding Time Synchronization Protocol (FTSP)

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Flooding Time Synchronization Protocol

Goals Achieve high precision clock synchronization Support sparse multi-hop network topologies Must run with limited resources (Mica2 / TinyOS) Approach Advanced MAC layer time stamping Linear regression of clock skew Flooding protocol with a dynamically elected root Graceful handling of election / join phases

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Flooding Time Synchronization Protocol

Clock Skew Time synchronization error between two motes. After 30 minutes, time synchronization is stopped and the initially small error results in increasing synchronization error over time.

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Flooding Time Synchronization Protocol

Linear Regression Distribution of error of linear regression on Mica2 motes: T = 30s time sync interval results in an average absolute error of 1.48µs and a maximum absolute error of 6.48µs T = 300s time sync interval results in an average absolute error of 2.24µs and a maximum absolute error of 8.64µs

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Flooding Time Synchronization Protocol

Protocol Idea Every synchronized node periodically broadcasts a synchronization message A node is synchronized if it has collected sufficient reference points Only synchronization messages from an elected synchronization root node are taken into account Message Format The synchronization message contains timeStamp — synchronization timestamp rootID — ID of the synchronization root seqNum — sequence number (assigned by sync. root)

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Flooding Time Synchronization Protocol

Protocol Details Nodes must ignore messages which are from an invalid synchronization root or have an old sequence number Nodes must collect sufficient reference points before they are allowed to broadcast Protocol must keep stability when a sync. root fails and a new one is elected with a different clock drift Need to handle partitions and (massive) joins gracefully

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Flooding Time Synchronization Protocol

event Radio.receive(TimeSync *msg) { if (msg->rootID < myRootID) myRootID = msg->rootID; else if (msg->rootID > myID || msg->seqNum <= highestSeqNum) return; highestSeqNum = msg->seqNum; if (myRootID < myID) heartBeats = 0; if (numEntries >= NUMENTRIES_LIMIT && getError(msg) > TIME_ERROR_LIMIT) clearRegressionTable(); else addEntryAndEstimateDrift(msg); }

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Flooding Time Synchronization Protocol

event Timer.fired() { ++heartBeats; if (myRootID != myID) && heartBeats >= ROOT_TIMEOUT) myRootID = myID; if (numEntries >= NUMENTRIES_LIMIT || myRootID == myID) { msg.rootID = myRootID; msg.seqNum = highestSeqNum; Radio.send(msg); if (myRootID == myID) ++highestSeqNum; } }

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Flooding Time Synchronization Protocol

Experiment Evaluation on a 5 × 12 grid of Mica / Mica2 nodes Nodes only communicate with their direct neighbors Topology enforced by software

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Flooding Time Synchronization Protocol

Experiment Goal: measure average pairwise error, maximum pairwise error, percentage of synchonized motes Test plan:

A: at 00:04 all motes were turned on B: at 01:00 the root ID1 was switched off and ID2 becomes root eventually C: between 02:00 and 02:15, randomly selected nodes were reset one by one (30 seconds period) D: at 02:30 all motes with odd node IDs were switched off E: at 03:01 all motes with odd node IDs were switched on F: at 04:02 experiment ended

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Flooding Time Synchronization Protocol

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References

• K. R¨
• mer.

Time Synchronization in Ad Hoc Networks. In Proc. ACM Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc 2001), pages 173–182, October 2001.

• K. R¨
• mer.

Time Synchronization and Localization in Sensor Networks. PhD thesis, ETH Zurich, 2005.

• J. Elson, L. Girod, and D. Estrin.

Fine-Grained Network Time Synchronization using Reference Broadcasts. In Proc. Fifth Symposium on Operating Systems Design and Implementation (OSDI 2002), pages 147–163, December 2002.

• J. E. Elson.

Time Synchronization in Wireless Sensor Networks. PhD thesis, University of California Los Angeles, 2003.

• M. Mar´
• ti, B. Kusy, G. Simon, and A. L´

edeczi. The Flooding Time Synchronization Protocol. In Proc. of the ACM Conference on Embedded Networked Sensor Systems (SenSys’04), November 2004.

• G. Werner-Allen, G. Tewari, A. Patel, M. Welsh, and R. Nagpal.

Firefly-Inspired Sensor Network Synchronicity with Realistic Radio Effects. In Proc. of the ACM Conference on Embedded Networked Sensor Systems (SenSys’05), November 2005. J¨ urgen Sch¨

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Part: Wave and Traversal Algorithms

20 Wave Algorithms and their Properties 21 Equivalence with Related Problems

Propagation of Information with Feedback Synchronization Infimum Functions

22 Wave Algorithms

Ring Algorithm Tree Algorithm Echo Algorithm Polling Algorithm

23 Traversal Algorithms

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Wave Algorithms and their Properties

20 Wave Algorithms and their Properties 21 Equivalence with Related Problems

Propagation of Information with Feedback Synchronization Infimum Functions

22 Wave Algorithms

Ring Algorithm Tree Algorithm Echo Algorithm Polling Algorithm

23 Traversal Algorithms

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Motivation

Message passing schemes which involve all processes are common subroutines in more specific algorithms. So called wave algorithms exchange a finite number of messages and then they make a decision, which depends causally on some event in each process. Considering wave algorithms first and in isolation will make it easier to understand more detailed algorithms. Certain problems in distributed computations can be solved by generic constructions that yield a specific algorithm.

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Preliminaries

We consider distributed systems where

the network topology is fixed, the channels are bidrectional, the topology is free of partitions, and the system is asynchronous and there is no notion of global time.

The set of all processes is denoted as P, and the set of channels by E. The number of events of computation C is denoted |C| and the subset of events that occur in process p is denoted Cp. There is a special type of internal event called decide event (represented by the statement decide).

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Wave Algorithm

Definition A wave algorithm is a distributed algorithm that satisfies the following three requirements. (1) Each computation is finite: ∀C : |C| < ∞ (2) Each computation contains at least one decide event: ∀C : ∃e ∈ C : e is a decide event (3) In each computation each decide event is causally preceded by an event in each process: ∀C : ∀e ∈ C : (e is decide event ⇒ ∀q ∈ P : ∃f ∈ Cq : f ≺ e)

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Terminology

The computation of a wave algorithm is called a wave. A process is called an initiator if it starts the execution of its local algorithm spontaneously. A non-initiator becomes involved only when a message of the algorithm arrives and triggers the execution of the local algorithm. As a consequence, the first event of an initiator is an internal or send event while the first event of a non-initiator is a receive event. An algorithm is called centralized if there must be exactly

• ne initiator in each computation, and decentralized if

the algorithm can be started spontaneously by an arbitrary subset of the processes.

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Wave Properties

Lemma For each event e ∈ C there exists an initiator p and an event f in Cp such that f ≺ e. Lemma Let C be a wave with one initiator p and, foreach non-initiator q, let fatherq be the neighbor of q from which q received a message in its first event. Then the graph T = (P, ET), with ET = {qr : q = p ∧ r = fatherq} is a spanning tree directed towards p. Lemma Let C be a wave and dp ∈ C a decide event in process p. Then ∀q = p : ∃f ∈ Cq : (f dp ∧ f is a send event)

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Wave Properties (cont.)

Theorem Let C be a wave with one initiator p, such that a decide event dp occurs in p. Then at least N messages are exchanged in C. Theorem Let A be a wave algorithm for arbitrary networks without initial knowledge of the neighbors’ identities. Then A exchanges at least |E| messages in each computation.

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Equivalence with Related Problems

20 Wave Algorithms and their Properties 21 Equivalence with Related Problems

Propagation of Information with Feedback Synchronization Infimum Functions

22 Wave Algorithms

Ring Algorithm Tree Algorithm Echo Algorithm Polling Algorithm

23 Traversal Algorithms

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Propagation of Information with Feedback

Propagation of Information with Feedback (PIF) A subset of processes is formed by those that have a message M (all of these have the same message), which must be broadcasted, i.e., all processes must receive and accept M. Certain processes must be notified of termination of the broadcast; that is, they must execute a special notify event, with the requirement that a notify event may be executed only when all processes have already received the message M. Notification by the PIF algorithm is considered as a decide event.

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PIF and Wave Algorithms

Theorem Every PIF algorithm is a wave algorithm. Theorem Every wave algorithm can be employed as a PIF algorithm. The constructed PIF algorithm has the same message complexity as A but has a different bit complexity.

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Synchronization

Synchronization Problem In each process q an event aq must be executed, and in some processes an event bp must be executed, such that the execution of all aq events must have taken place temporally before any of the bp events is executed. In a synchronization algorithm (SYN) the bp events will be considered as decide events.

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Synchronization and Wave Algorithms

Theorem Every SYN algorithm is a wave algorithm. Theorem Every wave algorithm can be employed as a SYN algorithm.

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Infimum Functions

Definition If (X, <) is a partial order, then c is called the infimum of a and b if c ≤ a, c ≤ b, and ∀d : (d ≤ a ∧ d ≤ b ⇒ d ≤ c). Let a △ b denote the infimum of a and b. The binary

• perator △ is cummutative and associative and can be

generalized to finite sets: inf {j1, . . . , jk} = j1 △ . . . △ jk Infimum Problem Each process q holds and input jq, which is an element of a partially ordered set X. It is required that certain processes compute the value of inf jq : q ∈ P and that these processes know when the computation is terminated.

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Infimum Functions and Wave Algorithms

Theorem Every INF algorithm is a wave algorithm. Theorem Every wave algorithm can be employed as a INF algorithm.

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Infimum Theorem

Theorem If ⋆ is a binary operator on a set X such that (1) ⋆ is commutative, i.e., a ⋆ b = b ⋆ a, (2) ⋆ is associative, i.e., (a ⋆ b) ⋆ c = a ⋆ (b ⋆ c), and (3) ⋆ is idempotent, i.e., a ⋆ a = a then there is a partial order ≤ on X such that ⋆ is the infimum function. Corollary ∧, ∨, min, max, gcd, lcm, ∩, and cup of values local to the processes can be computed in a single wave.

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Wave Algorithms

20 Wave Algorithms and their Properties 21 Equivalence with Related Problems

Propagation of Information with Feedback Synchronization Infimum Functions

22 Wave Algorithms

Ring Algorithm Tree Algorithm Echo Algorithm Polling Algorithm

23 Traversal Algorithms

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Ring Algorithm

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Tree Algorithm

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Echo Algorithm

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Polling Algorithm

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Traversal Algorithms

20 Wave Algorithms and their Properties 21 Equivalence with Related Problems

Propagation of Information with Feedback Synchronization Infimum Functions

22 Wave Algorithms

Ring Algorithm Tree Algorithm Echo Algorithm Polling Algorithm

23 Traversal Algorithms

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Traversal Algorithm

Definition A traversal algorithm is an algorithm with the following properties: (1) In each computation there is one initiator, which starts the algorithm by sending exactly one message. (2) A process, upon receipt of a message, either sends out

• ne message or decides.

(3) The algorithm terminates in the initiator and when this happens, each process has sent a message at least once.

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Ring and Polling Algorithms

Theorem The Ring Algorithm is a traversal algorithm. Theorem The sequential polling algorithm is a traversal algorithm.

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Computing Sums

Observation A large number of functions are not computable using general wave algorithms, e.g., the sum over all inputs, because the sum operator is not idempotent. Computing sums is possible in special cases, e.g., when the wave algorithm is a traversal algorithm, when the processes have identities, or when the algorithm induces a spanning tree.

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Tarry’s Traversal Algorithm

A traversal algorithm for arbitrary connected networks was given by Tarry in 1895. The algorithm is formulated in the following two rules:

R1 A process never forwards the token twice through the same channel. R2 A non-initiator forwards the token to its father (the neighbor from which it first received the token) only if there is no other channel possible according to rule R1.

Theorem Tarry’s algorithm is a traversal algorithm.

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References

• G. Tel.

Introduction to Distributed Algorithms. Cambridge University Press, 2 edition, 2000. J¨ urgen Sch¨

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Part:

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