A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
On the Distributed Complexity of Computing Maximal Matchings
SIAM Journal on Discrete Mathematics
Approximating weighted matchings in parallel
Information Processing Letters
Fast deterministic distributed maximal independent set computation on growth-bounded graphs
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Distributed fractional packing and maximum weighted b-matching via tail-recursive duality
DISC'09 Proceedings of the 23rd international conference on Distributed computing
A new analysis of a self-stabilizing maximum weight matching algorithm with approximation ratio 2
Theoretical Computer Science
Optimizing social welfare for network bargaining games in the face of unstability, greed and spite
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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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.