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Linear Time 1/2-Approximation Algorithm for Maximum Weighted Matching in General Graphs
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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.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.read more
Citations
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Cross-Layer Congestion Control, Routing and Scheduling Design in Ad Hoc Wireless Networks
TL;DR: A step toward a systematic way to carry out cross-layer design in the framework of “layering as optimization decomposition” for time-varying channel models for ad hoc wireless networks is presented.
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Recent Advances in Graph Partitioning
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.
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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.
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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.
Book ChapterDOI
Finding graph matchings in data streams
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.
References
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Journal ArticleDOI
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 $.
Journal ArticleDOI
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.
Proceedings ArticleDOI
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
Silvio Micali,Vijay V. Vazirani +1 more
TL;DR: An 0(√|V|¿|E|) algorithm for finding a maximum matching in general graphs works in 'phases'.
Proceedings ArticleDOI
Cross-Layer Congestion Control, Routing and Scheduling Design in Ad Hoc Wireless Networks
TL;DR: A step toward a systematic way to carry out cross-layer design in the framework of “layering as optimization decomposition” for time-varying channel models for ad hoc wireless networks is presented.
Book ChapterDOI
Recent Advances in Graph Partitioning
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.