Local, distributed weighted matching on general and wireless topologies

In this paper, we present and discuss a distributed algorithm for the local message passing communication model that constructs a (1-ε)-approximate Maximum Weight Matching in a graph (ε > 0). The approach has a deterministic runtime of O(1/ε2 log n. TMIS(nO(1/ε))), where TMIS(m) denotes the distributed time of computing a maximal independent set on a graph with m nodes. An immediate result of the presented approach is a local algorithm with expected O(log2 n) time complexity. If the given graph stems from a wireless ad-hoc network, characterized by the bounded growth property, we can further improve the algorithm by a preprocessing step that first locally constructs a colored clustering structure. This structure is then used in the matching algorithm to speed up the procedure significantly; we obtain a deterministic local algorithm that requires O(log n log* n) communication rounds. The main part of the algorithm works by repeatedly modifying and improving an existing matching in the network, and can thus be easily adapted to cope with changing and mobile topologies.