C ONSTRUCTING A L OAD -B ALANCED V IRTUAL B ACKBONE IN W IRELESS S - PowerPoint PPT Presentation

C ONSTRUCTING A L OAD -B ALANCED V IRTUAL B ACKBONE IN W IRELESS S ENSOR N ETWORKS Jing He * , Shouling Ji * , Pingzhi Fan ** , Yi Pan * , Yingshu Li * *Georgia State University **Southwest Jiaotong University Presenter: Dr. Kai Xiang

O UTLINE  Background & Motivation  Load-Balanced Virtual Backbones (LBVB) Construction Problem  Load-Balancedly Allocate Dominatees (LBAD) Problem  Simulation Results  Conclusions 2

Background & Motivation W H AT IS DS ?  A Dominating Set (DS) is a subset of all the nodes such that each node is either in the DS or adjacent to some node in the DS. 3

Background & Motivation W HAT IS CDS?  A Connected Dominating Set (CDS) is a subset of the nodes such that it forms a DS and all the nodes in the DS are connected. 4

Background & Motivation A PPLICATION OF CDS: V IRTUAL BACKBONE Virtual Backbone Flooding Reduction of communication Redundancy overhead Contention Collision Reliability Unreliability CDS is used as a virtual backbone in wireless networks. 5

Background & Motivation R ELATED W ORK  Constructing Minimum-sized CDS (MCDS) --- NP-hard  Subtraction-based : begin with the set of all nodes in the network, then systematically remove nodes by some rules to obtain the CDS.  Addition-based : start from a subset of nodes, then include additional nodes to form 6 the CDS.

Background & Motivation V ARIETY OF CDS o k -connected m -dominating Set --- fault tolerance • k -connectivity: between any pair of backbone nodes there exists at least k independent paths • m -domination: every dominatee has at least m adjacent dominator neighbors o Minimum Routing Cost CDS --- delivery delay • It can guarantee that each routing path between any pair of nodes is also the shortest path in the network. o D-Hop Dominating Sets • Minimum CDS with bounded Diameters 7

Background & Motivation O UR INTERESTS  Load-Balanced Virtual Backbone (LBVB) 1 2 1 2 3 4 3 4  5 6 7 8 5 6 7 8 LBVB MCDS 8

Background & Motivation O UR INTERESTS  Load-Balancedly Allocate Dominatees (LBAD) 1 2 1 2 3 4 3 4  5 6 7 8 5 6 7 8 LBAD Unbalanced Allocation 9

LBVB M EASURE LOAD BALANCE OF A V IRTUAL B ACKBONE 1 _ M    p p  VB p-norm : | | ( | | ) D d d p i  1 i where is the degree of each dominator; d i _ is the mean degree. d 1 2 2 1 3 4 3 4 5 6 7 8 5 6 7 8 10   2   2   2    2   2  | | ( 4 3 ) ( 4 3 ) ( 3 3 ) 2 | | ( 6 3 ) ( 3 3 ) 9 D D p p 10

LBVB P ROBLEM D EFINITION Load-balanced VB (LBVB) Problem: For a WSN represented by graph G = (V, E), the LBVB D  problem is to find a node set , D = {s 1 , s 2 , ..., s M } , V such that: '  1) The induced graph is connected, [ ] ( , ) G D D E '      { | ( , ), , , ( , ) } Where . E e e u v u D v D u v E  u   v   u  2) and , such that . ( , ) V D D u v E 1 _ 2     M 2 3) . 11 min | | ( | | ) D d d p 1 i i 11

LBVB G REEDY ALGORITHM 2 2 4 6 2 2 4 6 2 4 3 1 2 2 2 4 3 1 4 6   3 d  12  d min | | d i Greedy criterion: 2 4 3 1

LBAD L OAD -B ALANCEDLY A LLOCATE D OMINATEES  Allocated Dominatee Set: A(s i )  Valid Degree: d i ’ 1 _ _ M N - M   '   p p  Allocation p-norm : | | ( | | ) , where . D d p p p i M  1 i 1 1 1 1 3 1 2 1  _ 8 3 5   p 3 3 1 1 1 1 1 2 1 1 13 5 5 5 5 5 5 2 2 2          2   2   2  | | ( 3 ) ( 1 ) ( 1 ) 2.67 D | | ( 2 ) ( 2 ) ( 1 ) 0 . 67 D p p 3 3 3 3 3 3

LBAD P ROBLEM D EFINITION Load-balancedly Allocate Dominatees (LBAD) Problem: For a WSN represented by graph G = (V, E), and a VB D = {s 1 , s 2 , ..., s M } , the LBAD problem is to find M disjoint node sets on V , , such that: . ., ( ), ( ),......, ( ) i e A s A s A s 1 1 M   ( ) ( 1 ) A s i M 1) Each set contains exactly one dominator s i . i M         ( ) , ( ) ( ) (1 i j M) 2) . A s V A s A s i i j  1 i u  i      3) and , such that . ( , ) ) s u s E u A(s (1 i M) i i _ 1 2     M 2 min | | ( || ( ) | | ) D A s p 14 4) . p 1 i i 14

LBAD C ENTRALIZED ALGORITHM  Expected Allocation Probability (p ij ) : for each dominatee and dominator pair, there is an p ij , which represents the expected probability that the dominatee is allocated to the dominator.  Constrained non-linear programming 1 | ( ) | A s _ M j     p p Minimize : | | ( (| | ) , D p p p ij   1 1 j i | ( ) | N s i    Subject to : dominatee , 1 , s p i ij  1 j _  N M    where , 0 1, p p ij 15 M | ( ) | is the number of neighoring dominators of the dominatee . N s s i i 15

LBAD D ISTRIBUTED ALGORITHM  The distributed LBAD problem can be transformed to calculate the p ij value of each dominatee locally 1 1 1 1 1/4 1 5 3 3 2/7 3/8 3/8 5/7 1 2 2 1 1 2 2 1 ' ' '    ...... p d p d p d 1 1 2 2 | ( ) | | ( ) | i i i N s N s i i 16 16

Simulation S IMULATION SET UP  N nodes are randomly deployed in a fixed area of 100m *100m. All nodes have the same transmission range 10m.  VB -based broadcasting used as the communication mode  Four different schemes are implemented  LBCDS with LBAD, noted by LB-A  LBCDS with the smallest ID dominator selection, noted by LB-ID  MIS-based CDS with LBAD, noted by MIS-A  MIS-based CDS with the smallest ID dominator selection, noted by MIS-ID 17

Simulation S IMULATION R ESULTS 18 18

C ONCLUSIONS  For the LBVB problem, we design a greedy algorithm.  For the LBAD problem, we introduce a new term Expected Allocation Probability . Based on the probability, we formulate the LBAD problem into a constrained non-linear programming optimization problem.  For the LBAD problem, we also propose a probability-based distributed algorithm.  We conduct simulations to validate our proposed algorithms. 19

Q & A 20