Abstract
In this paper, we study distributed algorithms to compute a weighted matching that have constant (or at least sub-logarithmic) running time and that achieve approximation ratio 2 + ε or better. In fact we present two such synchronous algorithms, that work on arbitrary weighted trees.
The first algorithm is a randomised distributed algorithm that computes a weighted matching of an arbitrary weighted tree, that approximates the maximum weighted matching by a factor 2 + ε. The running time is O(1). The second algorithm is deterministic, and approximates the maximum weighted matching by a factor 2 + ε, but has running time O(log* |V|). Our algorithms can also be used to compute maximum unweighted matchings on regular and almost regular graphs within a constant approximation.
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References
Avis, D.: A survey of heuristics for the weighted matching problem. Networks 13, 475–493 (1983)
Chattopadhyay, S., Higham, L., Seyffarth, K.: Dynamic and self-stabilizing distributed matching. In: 21st PODC, Monterey, CA, USA, pp. 290–297. ACM Press, New York (2002)
Gabow, H.: Data structures for weighted matching and nearest common ancestors with linking. In: 1st SODA, San Fransisco, Ca., USA, pp. 434–443. ACM Press, New York (1990)
Goldberg, A.V., Plotkin, S., Shannon, G.: Parallel symmetry breaking in sparse graphs. In: 19th STOC, New York City, NY, USA. ACM Press, New York (1987)
Hoepman, J.-H. Simple distributed weighted matchings, eprint cs.DC/0410047 (2004)
Israeli, A., Itai, A.: A fast and simple randomized parallel algorithm for maximal matching. Inf. Proc. Letters 22, 77–80 (1986)
Karaata, M., Saleh, K.: A distributed self-stabilizing algorithm for finding maximal matching. Computer Systems Science and Engineering 3, 175–180 (2000)
Kutten, S., Peleg, D.: Fast distributed construction of k-dominating sets and applications. Journal of Algorithms 28(1), 40–66 (1998)
Micali, S., Vazirani, V.: An \(O(\sqrt{V}E)\) algorithm for finding maximum matching in general graphs. In: 21st FOCS, Syracuse, NY, USA, pp. 17–27. IEEE Computer Society Press, Los Alamitos (1980)
Preis, R.: Linear time 1/2-approximation algorithm for maximum weighted matching in general graphs. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 259–269. Springer, Heidelberg (1999)
Uehara, R., Chen, Z.: Parallel approximation algorithms for maximum weighted matching in general graphs. Inf. Proc. Letters 76, 13–17 (2000)
Wattenhofer, M., Wattenhofer, R.: Distributed weighted matching. In: Guerraoui, R. (ed.) DISC 2004. LNCS, vol. 3274, pp. 335–348. Springer, Heidelberg (2004)
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Hoepman, JH., Kutten, S., Lotker, Z. (2006). Efficient Distributed Weighted Matchings on Trees. In: Flocchini, P., Gąsieniec, L. (eds) Structural Information and Communication Complexity. SIROCCO 2006. Lecture Notes in Computer Science, vol 4056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780823_10
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DOI: https://doi.org/10.1007/11780823_10
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