Improved Distributed Approximate Matching

• Published in: Journal of the ACM Vol. 62; no. 5; pp. 1 - 17
• Main Authors: Lotker, Zvi, Patt-Shamir, Boaz, Pettie, Seth
• Format: Journal Article
• Language: English
• Published: New York Association for Computing Machinery 01.11.2015
• Subjects: Algorithms; Approximation; Communications networks; Complexity; Constants; Graph algorithms; Graphs; Matching; Mathematical analysis; Mathematical models; Network flow problem; Polynomials; Run time (computers); Studies
• ISSN: 0004-5411; 1557-735X
• DOI: 10.1145/2786753

We present distributed network algorithms to compute weighted and unweighted matchings with improved approximation ratios and running times. The computational model is a network of processors exchanging O (log n )-bit messages (the CONGEST model). For unweighted graphs, we give an algorithm providing (1-ϵ)-approximation in O (log n ) time for any constant ϵ>0, improving on the classical ½-approximation in O log n ) time of Israeli and Itai [1986]. The time complexity of the algorithm depends on 1⁃ϵ exponentially in the general case, and polynomially in bipartite graphs. For weighted graphs, we present another algorithm which provides (½-ϵ) approximation in general graphs in O (logϵ -1 log n ) time, improving on the previously known algorithms which attain (¼-ϵ)-approximation in O (log n ) time or ½-approximation in O ( n ) time. All our algorithms are randomized: the complexity bounds hold both with high probability and for the expected running time.