TY - GEN

T1 - Distributed maximum matching in bounded degree graphs

AU - Even, Guy

AU - Medina, Moti

AU - Ron, Dana

N1 - Publisher Copyright:
Copyright 2015 ACM.

PY - 2015/1/4

Y1 - 2015/1/4

N2 - We present deterministic distributed algorithms for computing approximate maximum cardinality matchings and approximate maximum weight matchings. Our algorithm for the unweighted case computes a matching whose size is at least (1 - ε) times the optimal in ΔO(1/ε) + O (1/ε2)·log∗(n) rounds where n is the number of vertices in the graph and Δ is the maximum degree. Our algorithm for the edge-weighted case computes a matching whose weight is at least (1 - ε) times the optimal in log(min{1/wmin, n/ε})O(1/ε)·(ΔO(1/ε) + log∗(n)) rounds for edge-weights in [wmin, 1]. The best previous algorithms for both the unweighted case and the weighted case are by Lotker, Patt-Shamir, and Pettie (SPAA 2008). For the unweighted case they give a randomized (1 - ε)-approximation algorithm that runs in O((log(n))/ε3) rounds. For the weighted case they give a randomized (1/2 - ε)-approximation algorithm that runs in O(log(ε-1)·log(n)) rounds. Hence, our results improve on the previous ones when the parameters Δ, ε and wmin are constants (where we reduce the number of runs from O(log(n)) to O(log∗(n))), and more generally when Δ, 1/ε and 1/wmin are sufficiently slowly increasing functions of n. Moreover, our algorithms are deterministic rather than randomized.

AB - We present deterministic distributed algorithms for computing approximate maximum cardinality matchings and approximate maximum weight matchings. Our algorithm for the unweighted case computes a matching whose size is at least (1 - ε) times the optimal in ΔO(1/ε) + O (1/ε2)·log∗(n) rounds where n is the number of vertices in the graph and Δ is the maximum degree. Our algorithm for the edge-weighted case computes a matching whose weight is at least (1 - ε) times the optimal in log(min{1/wmin, n/ε})O(1/ε)·(ΔO(1/ε) + log∗(n)) rounds for edge-weights in [wmin, 1]. The best previous algorithms for both the unweighted case and the weighted case are by Lotker, Patt-Shamir, and Pettie (SPAA 2008). For the unweighted case they give a randomized (1 - ε)-approximation algorithm that runs in O((log(n))/ε3) rounds. For the weighted case they give a randomized (1/2 - ε)-approximation algorithm that runs in O(log(ε-1)·log(n)) rounds. Hence, our results improve on the previous ones when the parameters Δ, ε and wmin are constants (where we reduce the number of runs from O(log(n)) to O(log∗(n))), and more generally when Δ, 1/ε and 1/wmin are sufficiently slowly increasing functions of n. Moreover, our algorithms are deterministic rather than randomized.

KW - Centralized local algorithms

KW - Distributed local algorithms

KW - Graph algorithms

KW - Maximum matching

KW - Maximum weighted matching

UR - http://www.scopus.com/inward/record.url?scp=84978695902&partnerID=8YFLogxK

U2 - 10.1145/2684464.2684469

DO - 10.1145/2684464.2684469

M3 - Conference contribution

AN - SCOPUS:84978695902

T3 - ACM International Conference Proceeding Series

BT - ICDCN 2015 - Proceedings of the 16th International Conference on Distributed Computing and Networking

PB - Association for Computing Machinery

T2 - 16th International Conference on Distributed Computing and Networking, ICDCN 2015

Y2 - 4 January 2015 through 7 January 2015

ER -