TY - GEN

T1 - Approximating maximum integral flows in wireless sensor networks via weighted-degree constrained k-flows

AU - Nutov, Zeev

N1 - Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.

PY - 2008

Y1 - 2008

N2 - We consider the Maximum Integral Flow with Energy Constraints problem: given a directed graph G = (V, E) with edge-weights {w(e) : e G E} and node battery capacities {b(v) : v G V}, and two nodes r, s G V, find a maximum integral rs-flow f so that for every node v its energy consumption P vueEf(vu)w(vu) is at most b(v). Let k be the maximum integral flow value. We give a polynomial time algorithm that computes a flow of value at least [k/16\. As checking whether k > 1 can be done in polynomial time, this gives an approximation algorithm with ratio that approaches 1/16 when k is large, and is not worse than 1/31. This is the first constant ratio approximation algorithm for this problem, which solves an open question from [2]. This result is based on a bicriteria approximation algorithm for a more general problem, in which we seek a minimum cost set of k pairwise edge-disjoint rs-paths (that is, a k-flow) subject to weighted degree constraints. We give a polynomial time algorithm that computes a flow of value k and violates the weighted degrees by a factor at most 4. This result is of independent interest.

AB - We consider the Maximum Integral Flow with Energy Constraints problem: given a directed graph G = (V, E) with edge-weights {w(e) : e G E} and node battery capacities {b(v) : v G V}, and two nodes r, s G V, find a maximum integral rs-flow f so that for every node v its energy consumption P vueEf(vu)w(vu) is at most b(v). Let k be the maximum integral flow value. We give a polynomial time algorithm that computes a flow of value at least [k/16\. As checking whether k > 1 can be done in polynomial time, this gives an approximation algorithm with ratio that approaches 1/16 when k is large, and is not worse than 1/31. This is the first constant ratio approximation algorithm for this problem, which solves an open question from [2]. This result is based on a bicriteria approximation algorithm for a more general problem, in which we seek a minimum cost set of k pairwise edge-disjoint rs-paths (that is, a k-flow) subject to weighted degree constraints. We give a polynomial time algorithm that computes a flow of value k and violates the weighted degrees by a factor at most 4. This result is of independent interest.

KW - Integral flow

KW - Maximum flow

KW - Network design

KW - Weighted degree

KW - Wireless sensor networks

UR - http://www.scopus.com/inward/record.url?scp=65249162194&partnerID=8YFLogxK

U2 - 10.1145/1400863.1400871

DO - 10.1145/1400863.1400871

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AN - SCOPUS:65249162194

SN - 9781605582443

T3 - DIALM-POMC'08: Proceedings of the ACM 5th International Workshop on Foundations of Mobile Computing

SP - 29

EP - 33

BT - DIALM-POMC'08

T2 - 5th ACM SIGACT-SIGOPS International Workshop on Foundations of Mobile Computing, DIALM-POMC

Y2 - 22 August 2008 through 22 August 2008

ER -