An efficient distributed algorithm for maximum matching in general graphs

Algorithmica ◽  
1990 ◽  
Vol 5 (1-4) ◽  
pp. 383-406 ◽  
Author(s):  
Michael M. Wu ◽  
Michael C. Loui
Keyword(s):  
Distributed Algorithm ◽  
Maximum Matching ◽  
General Graphs

scholarly journals THE FIRST APPROXIMATED DISTRIBUTED ALGORITHM FOR THE MINIMUM DEGREE SPANNING TREE PROBLEM ON GENERAL GRAPHS

2004 ◽  
Vol 15 (03) ◽  
pp. 507-516 ◽  
Author(s):  
LÉLIA BLIN ◽  
FRANCK BUTELLE
Keyword(s):  
Distributed Algorithm ◽  
Spanning Tree ◽  
Time Complexity ◽  
Minimum Degree ◽  
Np Hard ◽  
Message Complexity ◽  
General Graphs

In this paper we present the first distributed algorithm on general graphs for the Minimum Degree Spanning Tree problem. The problem is NP-hard in sequential. Our algorithm give a Spanning Tree of a degree at most 1 from the optimal. The resulting distributed algorithm is asynchronous, it works for named asynchronous arbitrary networks and achieves O(|V|) time complexity and O(|V||E|) message complexity.

scholarly journals The Power of Linear-Time Data Reduction for Maximum Matching

Algorithmica ◽  
2020 ◽  
Vol 82 (12) ◽  
pp. 3521-3565
Author(s):  
George B. Mertzios ◽  
André Nichterlein ◽  
Rolf Niedermeier
Keyword(s):  
Systematic Study ◽  
Data Reduction ◽  
Linear Time ◽  
Maximum Matching ◽  
Maximum Cardinality ◽  
Solution Strategy ◽  
Time Data ◽  
Undirected Graphs ◽  
Running Time ◽  
General Graphs

Abstract Finding maximum-cardinality matchings in undirected graphs is arguably one of the most central graph primitives. For m-edge and n-vertex graphs, it is well-known to be solvable in $$O(m\sqrt{n})$$ O ( m n )  time; however, for several applications this running time is still too slow. We investigate how linear-time (and almost linear-time) data reduction (used as preprocessing) can alleviate the situation. More specifically, we focus on linear-time kernelization. We start a deeper and systematic study both for general graphs and for bipartite graphs. Our data reduction algorithms easily comply (in form of preprocessing) with every solution strategy (exact, approximate, heuristic), thus making them attractive in various settings.

A Fast Distributed Algorithm for Approximating the Maximum Matching

2004 ◽  
pp. 252-263 ◽  
Author(s):  
Andrzej Czygrinow ◽  
Michał Hańćkowiak ◽  
Edyta Szymańska
Keyword(s):  
Distributed Algorithm ◽  
Maximum Matching

scholarly journals Distributed algorithm for approximating the maximum matching

2004 ◽  
Vol 143 (1-3) ◽  
pp. 62-71 ◽  
Author(s):  
A. Czygrinow ◽  
M. Hańćkowiak ◽  
E. Szymańska
Keyword(s):  
Distributed Algorithm ◽  
Maximum Matching
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