A simple parallel approximation algorithm for maximum weight matching

2009 ◽  
Author(s):  
Alicia Thorsen ◽  
Phillip Merkey ◽  
Fredrik Manne
Keyword(s):  
Approximation Algorithm ◽  
Maximum Weight ◽  
Maximum Weight Matching ◽  
Parallel Approximation ◽  
Parallel Approximation Algorithm

APPROXIMATING MAXIMUM 2-CNF SATISFIABILITY

1992 ◽  
Vol 02 (02n03) ◽  
pp. 181-187 ◽  
Author(s):  
DAVID J. HAGLIN
Keyword(s):  
Approximation Algorithm ◽  
Satisfiability Problem ◽  
Parallel Time ◽  
Performance Guarantees ◽  
Crew Pram ◽  
Parallel Approximation ◽  
Parallel Approximation Algorithm

A parallel approximation algorithm for the MAXIMUM 2-CNF SATISFIABILITY problem is presented. This algorithm runs in O( log 2(n + |F|)) parallel time on a CREW PRAM machine using O(n + |F|) processors, where n is the number of variables and |F| is the number of clauses. Performance guarantees are considered for three slightly differing definitions of this problem.

AN EFFICIENT NC ALGORITHM FOR APPROXIMATE MAXIMUM WEIGHT MATCHING

2013 ◽  
Vol 05 (03) ◽  
pp. 1350013
Author(s):  
SATYAJIT BANERJEE
Keyword(s):  
Approximation Algorithm ◽  
Execution Time ◽  
Maximum Weight ◽  
Model Of Computation ◽  
Erew Pram ◽  
Pram Model ◽  
Maximum Weight Matching

We present an alternative implementation of the (1 – ϵ) factor NC approximation algorithm for the maximum weight matching by Hougardy et al. [1]. Our implementation, on the EREW PRAM model of computation, achieves an [Formula: see text] factor improvement on both the execution time and the number of processors.

scholarly journals Stabilizing Weighted Graphs

2020 ◽  
Vol 45 (4) ◽  
pp. 1318-1341
Author(s):  
Zhuan Khye Koh ◽  
Laura Sanità
Keyword(s):  
Approximation Algorithm ◽  
Weighted Graph ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Constant Factor ◽  
Maximum Weight ◽  
Minimum Cardinality ◽  
Matching Games ◽  
Maximum Weight Matching ◽  
Network Bargaining

An edge-weighted graph [Formula: see text] is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in network bargaining games and cooperative matching games, because they characterize instances that admit stable outcomes. We give the first polynomial-time algorithm to find a minimum cardinality subset of vertices whose removal from G yields a stable graph, for any weighted graph G. The algorithm is combinatorial and exploits new structural properties of basic fractional matchings, which are of independent interest. In contrast, we show that the problem of finding a minimum cardinality subset of edges whose removal from a weighted graph G yields a stable graph, does not admit any constant-factor approximation algorithm, unless P = NP. In this setting, we develop an O(Δ)-approximation algorithm for the problem, where Δ is the maximum degree of a node in G.

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