fault tolerant subgraph for single source reachability
play

Fault-Tolerant Subgraph For Single-Source Reachability: General and - PowerPoint PPT Presentation

Dec 28, 2022 •539 likes •1.46k views

FMC-Properties Main Tools Construction of 2-FTRS Reference Fault-Tolerant Subgraph For Single-Source Reachability: General and Optimal Surender Baswana, Keerti Choudhary, Liam Roditty Presented by: Santhini K A and Sampriti Roy CS18D013

  1. FMC-Properties Main Tools Construction of 2-FTRS Reference Fault-Tolerant Subgraph For Single-Source Reachability: General and Optimal Surender Baswana, Keerti Choudhary, Liam Roditty Presented by: Santhini K A and Sampriti Roy CS18D013 CS18S007 Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 1 / 66

  2. FMC-Properties Main Tools Construction of 2-FTRS Reference Surender Baswana Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 2 / 66

  3. FMC-Properties Main Tools Construction of 2-FTRS Reference Surender Baswana Keerti Choudhary Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 2 / 66

  4. FMC-Properties Main Tools Construction of 2-FTRS Reference Surender Baswana Keerti Choudhary Liam Roditty Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 2 / 66

  5. FMC-Properties Main Tools Construction of 2-FTRS Reference Reachability? A fundamental problem of graph Is d reachable from s ? a c s t b d Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 3 / 66

  6. FMC-Properties Main Tools Construction of 2-FTRS Reference Is d reachable? Remove sa a c s t b d Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 4 / 66

  7. FMC-Properties Main Tools Construction of 2-FTRS Reference Is d reachable? Remove sb a c s t b d Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 5 / 66

  8. FMC-Properties Main Tools Construction of 2-FTRS Reference Is d reachable? Remove sa , sb . a c s t b d Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 6 / 66

  9. FMC-Properties Main Tools Construction of 2-FTRS Reference Is d reachable? Remove any 2 edges. Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 7 / 66

  10. FMC-Properties Main Tools Construction of 2-FTRS Reference Is d reachable? Remove any 2 edges. Can you conclude something?? . Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 7 / 66

  11. FMC-Properties Main Tools Construction of 2-FTRS Reference Is d reachable? Remove cb , bd a c s t b d Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 8 / 66

  12. FMC-Properties Main Tools Construction of 2-FTRS Reference Motivation Single source reachability in the presence of failures Any set of k vertex/edge failures Fault-tolerant reachability Previously known result only when k = 1 Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 9 / 66

  13. FMC-Properties Main Tools Construction of 2-FTRS Reference k - FTRS Input: G = ( V, E ) , k , and source s ∈ V Output: H ⊆ G Goal: construct a sparse subgraph H such that for every vertex v , for any set F of failure edges with | F | ≤ k , v is reachable from s in G \ F if and only if v is reachable from s in H \ F . H is k - FTRS ( k -fault tolerant reachability subgraph) for G Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 10 / 66

  14. FMC-Properties Main Tools Construction of 2-FTRS Reference Related Works k - FTTS (fault tolerant shortest path subgraph) 1- FTTS by Demetrescu et al., 1- FTTS by Parter and Peleg 2- FTTS by Parter Extension from 1- FTTS to 2- FTTS is complicated For every constant k , there is a k - FTRS Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 11 / 66

  15. FMC-Properties Main Tools Construction of 2-FTRS Reference Terminology E ( P )- edges lying on a path P Consider path P a c s t b d Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 12 / 66

  16. FMC-Properties Main Tools Construction of 2-FTRS Reference Terminology E ( P )- edges lying on a path P Consider path P P a c s t b d E ( P ) = { sa, ac, ct } Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 12 / 66

  17. FMC-Properties Main Tools Construction of 2-FTRS Reference Terminology E ( f )- edges of G carrying nonzero flow for a given flow f Consider the flow f from s to t a c s t b d Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 13 / 66

  18. FMC-Properties Main Tools Construction of 2-FTRS Reference Terminology E ( f )- edges of G carrying nonzero flow for a given flow f Consider the flow f from s to t f a c s t b d E ( f ) = { sa, ac, ct } Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 13 / 66

  19. FMC-Properties Main Tools Construction of 2-FTRS Reference Terminology E ( A )- edges of G whose end points both lie in set A , where A ⊆ V Consider set A = { s, a, b } a c s t b d Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 14 / 66

  20. FMC-Properties Main Tools Construction of 2-FTRS Reference Terminology E ( A )- edges of G whose end points both lie in set A , where A ⊆ V Consider set A = { s, a, b } a c s t b d E ( A ) = { sa, sb, ab, ba } Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 14 / 66

  21. FMC-Properties Main Tools Construction of 2-FTRS Reference Terminology G ( A )- subgraph of G induced by the vertices lying in a subset A of V Consider set A = { s, a, b } a c s t b d Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 15 / 66

  22. FMC-Properties Main Tools Construction of 2-FTRS Reference Terminology G ( A )- subgraph of G induced by the vertices lying in a subset A of V Consider set A = { s, a, b } a c s t b d Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 15 / 66

  23. FMC-Properties Main Tools Construction of 2-FTRS Reference Terminology P [ s, c ]- subpath of path P lying between s and c Q [ c, t ]- subpath of path Q lying between c and t a c s t b d Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 16 / 66

  24. FMC-Properties Main Tools Construction of 2-FTRS Reference Terminology P [ s, c ]- subpath of path P lying between s and c Q [ c, t ]- subpath of path Q lying between c and t P a c s t b d E ( P ) = { sa, ac } Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 16 / 66

  25. FMC-Properties Main Tools Construction of 2-FTRS Reference Terminology P [ s, c ]- subpath of path P lying between s and c Q [ c, t ]- subpath of path Q lying between c and t P a c Q s t b d E ( P ) = { sa, ac } E ( Q ) = { ct } Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 16 / 66

  26. FMC-Properties Main Tools Construction of 2-FTRS Reference Terminology P [ s, c ]- subpath of path P lying between s and c Q [ c, t ]- subpath of path Q lying between c and t P :: Q -path formed by concatenating paths P and Q in G P :: Q a c s t b d E ( P ) = { sa, ac } E ( Q ) = { ct } E ( P :: Q ) = { sa, ac, ct } Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 17 / 66

  27. FMC-Properties Main Tools Construction of 2-FTRS Reference Preliminaries Visualize graph G as network with unit edge capacities For any positive integer α , there is a flow from a source set S to a destination vertex t of α if and only if there are α edge disjoint paths from S to t . Farthest min-cut: -unique S - T min-cut for which the set containing source is of largest size Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 18 / 66

  28. FMC-Properties Main Tools Construction of 2-FTRS Reference What are the mincuts? a c f g s e t b d h Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 19 / 66

  29. FMC-Properties Main Tools Construction of 2-FTRS Reference What are the mincuts? a c f g s e t b d h Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 20 / 66

  30. FMC-Properties Main Tools Construction of 2-FTRS Reference What are the mincuts? a c f g s e t b d h Min-cuts { s, a, b, c } { d, e, f, g, h, t } { s, a, b, c, d } { e, f, g, h, t } Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 20 / 66

  31. FMC-Properties Main Tools Construction of 2-FTRS Reference Farthest min-cut a c f g s e t b d h Fault-Tolerant Subgraph For Single-Source Reachability: General Presented by: Santhini K A and Sampriti Roy 21 / 66

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Lecture 10: Fault Tolerance Fault Tolerant Concurrent Computing The main principles of fault

Lecture 10: Fault Tolerance Fault Tolerant Concurrent Computing The main principles of fault

Lecture 10: Fault Tolerance Fault Tolerant Concurrent Computing The main principles of fault tolerant programming are: Fault Detection - Knowing that a fault exists Fault Recovery - having atomic instructions that can be rolled back in

361 views • 18 slides
Fault-tolerant techniques Fault-tolerant techniques What causes component faults? What are the

Fault-tolerant techniques Fault-tolerant techniques What causes component faults? What are the

EDA421/DIT171 - Parallel and Distributed Real-Time Systems, Chalmers/GU, 2011/2012 Lecture #14 Updated May 2, 2012 Fault-tolerant techniques Fault-tolerant techniques What causes component faults? What are the effects if the

374 views • 9 slides
FAULT-TOLERANT CONTROL Is it possible? JAN MACIEJOWSKI Fault- tolerant control. DPS09,

FAULT-TOLERANT CONTROL Is it possible? JAN MACIEJOWSKI Fault- tolerant control. DPS09,

FAULT-TOLERANT CONTROL Is it possible? JAN MACIEJOWSKI Fault- tolerant control. DPS09, Gdask Canonical Control Engineering Problem Disturbance Controlled output Set-point Filter Controller Plant Sensor Noise This problem is

639 views • 29 slides
Adaptive Fault Tolerant Systems: Adaptive Fault Tolerant Systems: Reflective Design and

Adaptive Fault Tolerant Systems: Adaptive Fault Tolerant Systems: Reflective Design and

1 Adaptive Fault Tolerant Systems: Adaptive Fault Tolerant Systems: Reflective Design and Validation Reflective Design and Validation Marc-Olivier Killijian Dependable Computing and Fault Tolerance Research Group Toulouse - France 2

865 views • 50 slides
Mining Large Single Networks under Subgraph Mining Large Single Networks under Subgraph

Mining Large Single Networks under Subgraph Mining Large Single Networks under Subgraph

Mining Large Single Networks under Subgraph Mining Large Single Networks under Subgraph Homomorphism Homomorphism Mostafa H. Chehreghani Jan Ramon Thomas Fannes 12/13/13 Overview Introduction Problem definition and preliminaries

547 views • 13 slides
Design of a Single Event Effect fault tolerant microprocessor for space using commercial EDA

Design of a Single Event Effect fault tolerant microprocessor for space using commercial EDA

Design of a Single Event Effect fault tolerant microprocessor for space using commercial EDA tools Design Automation Conference DAC 2009 Roland Weigand European Space Agency Roland.Weigand[at]esa.int Jean Edelin Atmel Aerospace

704 views • 31 slides
Overview Introduction and basic concept ECE 753: FAULT-TOLERANT Fault model and fault

Overview Introduction and basic concept ECE 753: FAULT-TOLERANT Fault model and fault

4/1/2014 Overview Introduction and basic concept ECE 753: FAULT-TOLERANT Fault model and fault coverage COMPUTING Checkpointing and backward error recovery (rollback) Kewal K.Saluja General principles General principles

259 views • 3 slides
Fault-Tolerant Data Collection in Fault-Tolerant Data Collection in Heterogeneous Intelligent

Fault-Tolerant Data Collection in Fault-Tolerant Data Collection in Heterogeneous Intelligent

Fault-Tolerant Data Collection in Fault-Tolerant Data Collection in Heterogeneous Intelligent Monitoring Networks Networks Heterogeneous Intelligent Monitoring Jing Deng Department of Computer Science University of North Carolina at

335 views • 18 slides
A Fault-Tolerant Alternative to Lockstep Triple Modular Redundancy Andrew L. Baldwin, BS 09,

A Fault-Tolerant Alternative to Lockstep Triple Modular Redundancy Andrew L. Baldwin, BS 09,

A Fault-Tolerant Alternative to Lockstep Triple Modular Redundancy Andrew L. Baldwin, BS 09, MS 12 W. Robert Daasch, Professor Integrated Circuits Design and Test Laboratory Problem Statement In a fault tolerant system containing

478 views • 35 slides
Overview ECE 753: FAULT-TOLERANT Fault Modeling COMPUTING References Introduction

Overview ECE 753: FAULT-TOLERANT Fault Modeling COMPUTING References Introduction

1/21/2014 Overview ECE 753: FAULT-TOLERANT Fault Modeling COMPUTING References Introduction Kewal K.Saluja Kewal K Saluja Fault models at different levels (HW) Department of Electrical and Computer Engineering Error

304 views • 5 slides
4/22/2009 Designing highly available systems Incorporate elements of fault-tolerant design

4/22/2009 Designing highly available systems Incorporate elements of fault-tolerant design

4/22/2009 Designing highly available systems Incorporate elements of fault-tolerant design Replication, TMR Distributed Systems Fully fault tolerant system will offer non-stop availability Clusters You cant achieve this! Problem:

458 views • 11 slides
Verification and Validation of a Verification and Validation of a Fault- -Tolerant Architectural

Verification and Validation of a Verification and Validation of a Fault- -Tolerant Architectural

Verification and Validation of a Verification and Validation of a Fault- -Tolerant Architectural Abstraction Tolerant Architectural Abstraction Fault Patrick H. S. Brito - Unicamp, Brazil Rogrio de Lemos - University of Kent, UK Eliane

381 views • 21 slides
REVIEW OF FAULT TOLERANT TECHNIQUES FOR DIFFERENT TYPES OF GRAPHS BY- HATEM NASSRAT TARAK

REVIEW OF FAULT TOLERANT TECHNIQUES FOR DIFFERENT TYPES OF GRAPHS BY- HATEM NASSRAT TARAK

REVIEW OF FAULT TOLERANT TECHNIQUES FOR DIFFERENT TYPES OF GRAPHS BY- HATEM NASSRAT TARAK SHINGNE Outline General view of Fault Tolerance Ft-Design approaches Trees Meshes & Hypercubes conclusion Introduction Fault

584 views • 44 slides
outline introduction locality in fault-tolerant quantum comp. topological codes &

outline introduction locality in fault-tolerant quantum comp. topological codes &

outline introduction locality in fault-tolerant quantum comp. topological codes & local operations results single-shot error correction self-correction gauge color codes universality via gauge-fixing

687 views • 44 slides
Idealised Fault Tolerant Idealised Fault Tolerant Architectural Element Architectural Element

Idealised Fault Tolerant Idealised Fault Tolerant Architectural Element Architectural Element

Idealised Fault Tolerant Idealised Fault Tolerant Architectural Element Architectural Element Rog rio rio de Lemos de Lemos Rog University of Kent, UK University of Kent, UK Motivation architectural fault tolerance; iFTE

350 views • 16 slides
Fault-Tolerant Distributed Optimization Lili Su, Arun Padakandla, Qiong Hu, Seyyed A. Fatemi,

Fault-Tolerant Distributed Optimization Lili Su, Arun Padakandla, Qiong Hu, Seyyed A. Fatemi,

Fault-Tolerant Distributed Optimization Lili Su, Arun Padakandla, Qiong Hu, Seyyed A. Fatemi, Rehana Mahfuz, Vidyasagar Sadhu CSOI-Data Science Workshop May 27th, 2016 Lili Su et al. (SOI-DSWKSP) Fault-tolerant distributed optimization May

854 views • 6 slides
Fault Tolerance via the State Machine Replication Approach Favian Contreras Implementing

Fault Tolerance via the State Machine Replication Approach Favian Contreras Implementing

Fault Tolerance via the State Machine Replication Approach Favian Contreras Implementing Fault-Tolerant Services Using the State Machine Approach: A Tutorial Written by Fred Schneider Why a Tutorial? The State Machine Approach was

743 views • 52 slides
Wonderful Counselor Wonderful Counselor He made us. Wonderful Counselor He made us.

Wonderful Counselor Wonderful Counselor He made us. Wonderful Counselor He made us.

Wonderful Counselor Wonderful Counselor He made us. Wonderful Counselor He made us. He knows everything about us. Wonderful Counselor He made us. He knows everything about us. He can relate to us. Mighty God

200 views • 15 slides
What is DNA? D eoxyribo n ucleic A cid A molecule composed of two chains that wrap

What is DNA? D eoxyribo n ucleic A cid A molecule composed of two chains that wrap

What is DNA? D eoxyribo n ucleic A cid A molecule composed of two chains that wrap around each other consisting of sugars, phosphates, and nucleotide bases (adenine, guanine, thyamine, and cytosine) Acts as the store of genetic

397 views • 3 slides
Virtual file system 1. VFS basic concepts 2. VFS design approach and architecture 3. Device

Virtual file system 1. VFS basic concepts 2. VFS design approach and architecture 3. Device

Advanced Operating Systems MS degree in Computer Engineering University of Rome Tor Vergata Lecturer: Francesco Quaglia Virtual file system 1. VFS basic concepts 2. VFS design approach and architecture 3. Device drivers 4. The Linux case

2.15k views • 90 slides
Statistical Ineffective Fault Attacks on Masked AES with Fault Countermeasures Christoph

Statistical Ineffective Fault Attacks on Masked AES with Fault Countermeasures Christoph

Statistical Ineffective Fault Attacks on Masked AES with Fault Countermeasures Christoph Dobraunig, Maria Eichlseder, Hannes Gross, Stefan Mangard, Florian Mendel, Robert Primas ASIACRYPT 2018 IAIK - Graz University of Technology www.tugraz.at

1.01k views • 78 slides
MPLS TP Ring Fault Detection and Localization draft-jiang-mpls-tp-ring-fd Authors Albert

MPLS TP Ring Fault Detection and Localization draft-jiang-mpls-tp-ring-fd Authors Albert

MPLS TP Ring Fault Detection and Localization draft-jiang-mpls-tp-ring-fd Authors Albert Jiang Guoman Liu Xuehui Dai (ZTE) Purpose & Overview MPLS TP Ring Optimized Node/Link Fault Detection & Localization Mechanism 1)

405 views • 21 slides
VLSI Testing Sequential ATPG Virendra Singh Associate Professor C omputer A rchitecture and D

VLSI Testing Sequential ATPG Virendra Singh Associate Professor C omputer A rchitecture and D

VLSI Testing Sequential ATPG Virendra Singh Associate Professor C omputer A rchitecture and D ependable S ystems L ab Department of Electrical Engineering Indian Institute of Technology Bombay http://www.ee.iitb.ac.in/~viren/ E-mail:

1.05k views • 15 slides
Nonlinear Autoregressive with Exogenous Wathiq R Abed #UDT2019 Outline Aim of Fault

Nonlinear Autoregressive with Exogenous Wathiq R Abed #UDT2019 Outline Aim of Fault

Unmanned Marine Vehicles Motor Fault Classifier Based on Nonlinear Autoregressive with Exogenous Wathiq R Abed #UDT2019 Outline Aim of Fault diagnosis and condition monitoring Task Major Faults in electrical Machines Fault

274 views • 9 slides

More recommend