Open AccessJournal Article
Linear Time 1/2-Approximation Algorithm for Maximum Weighted Matching in General Graphs
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TL;DR: In this article, a new algorithm for maximum weighted matching in general edge-weighted graphs is presented, which calculates a matching with an edge weight of at least one-half of the edge weight for a maximum weighted match.
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Abstract: A new approximation algorithm for maximum weighted matching in general edge-weighted graphs is presented. It calculates a matching with an edge weight of at least of the edge weight of a maximum weighted matching. Its time complexity is O(|E|), with |E| being the number of edges in the graph. This improves over the previously known -approximation algorithms for maximum weighted matching which require O(|E| log(|V|)) steps, where |V| is the number of vertices.
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Citations
Recent Advances in Graph Partitioning
Aydin Buluc,Henning Meyerhenke,Ilya Safro,Peter Sanders,Christian Schulz +4 more
- 01 Nov 2016
TL;DR: In this article, the authors survey recent trends in practical algorithms for balanced graph partitioning, point to applications, and discuss future research directions, and present a survey of the most popular algorithms.
Linear-Time Approximation for Maximum Weight Matching
Ran Duan,Seth Pettie +1 more
TL;DR: This article gives an algorithm that computes a (1 − 1 − 0))-approximate maximum weight matching in O(i) time, that is, optimal linear time for any fixed ε, and should be appealing in all applications that can tolerate a negligible relative error.
Thinking Like a Vertex: A Survey of Vertex-Centric Frameworks for Large-Scale Distributed Graph Processing
TL;DR: In this survey, the vertex-centric approach to graph processing is overviewed, TLAV frameworks are deconstructed into four main components and respectively analyzed, and TLAV implementations are reviewed and categorized.
Finding graph matchings in data streams
Andrew McGregor
- 22 Aug 2005
TL;DR: Algorithm for finding large graph matchings in the streaming model, applicable when dealing with massive graphs, edges are streamed-in in some arbitrary order rather than residing in randomly accessible memory, achieves a $\frac1{1+\epsilon}$ approximation for maximum cardinality matching and a $1+2$ approximation to maximum weighted matching.
Scheduling Efficiency of Distributed Greedy Scheduling Algorithms in Wireless Networks
Xinzhou Wu,R. Srikant +1 more
- 01 Dec 2006
TL;DR: This work proves a lower bound on the efficiency of a distributed scheduling algorithm by first assuming that all of the traffic only uses one hop of the network and proves that the lower bound is tight in the sense that, for any fraction larger than the lowerbound, it can find a topology and an arrival rate vector within the fraction of the capacity region such that the network is unstable under a greedy scheduling policy.
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References
An $n^{5/2} $ Algorithm for Maximum Matchings in Bipartite Graphs
John E. Hopcroft,Richard M. Karp +1 more
TL;DR: This paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to $(m + n)\sqrt n $.
3K
Some simplified NP-complete graph problems
TL;DR: This paper shows that a number of NP - complete problems remain NP -complete even when their domains are substantially restricted, and determines essentially the lowest possible upper bounds on node degree for which the problems remainNP -complete.
2.4K
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
Silvio Micali,Vijay V. Vazirani +1 more
- 13 Oct 1980
TL;DR: An 0(√|V|¿|E|) algorithm for finding a maximum matching in general graphs works in 'phases'.
1K
Recent Advances in Graph Partitioning
Aydin Buluc,Henning Meyerhenke,Ilya Safro,Peter Sanders,Christian Schulz +4 more
- 01 Nov 2016
TL;DR: In this article, the authors survey recent trends in practical algorithms for balanced graph partitioning, point to applications, and discuss future research directions, and present a survey of the most popular algorithms.
Data structures for weighted matching and nearest common ancestors with linking
Harold N. Gabow
- 01 Jan 1990
TL;DR: In this article, it was shown that the weighted matching problem on general graphs can be solved in O(n(m + n log n)), f or n and m the number of vertices and edges, respectively.
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