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Open AccessJournal ArticleDOI

Deterministic and probabilistic algorithms for maximum bipartite matching via fast matrix multiplication

Oscar H. Ibarra, +1 more
- 27 Oct 1981 - 
- Vol. 13, Iss: 1, pp 12-15
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TLDR
A maximum matching is a matching of maximum cardinality and the set of nodes which take part in such amaximum matching is denoted by Nodes(G) and the cardinality of the matching isDenoted by Card(G).
About: 
This article is published in Information Processing Letters.The article was published on 1981-10-27 and is currently open access. It has received 29 citations till now. The article focuses on the topics: 3-dimensional matching & Blossom algorithm.

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Citations
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Proceedings ArticleDOI

Maximum matchings via Gaussian elimination

Marcin Mucha, +1 more
TL;DR: The results resolve a long-standing open question of whether Lovasz's randomized technique of testing graphs for perfect matching in time O(n/sup w/) can be extended to an algorithm that actually constructs a perfect matching.
Journal ArticleDOI

Linear-Time Approximation for Maximum Weight Matching

Ran Duan, +1 more
- 01 Jan 2014 - 
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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Optimal Covering Tours with Turn Costs

Esther M. Arkin, +5 more
- 09 Sep 2003 - 
TL;DR: In this article, the first algorithmic study of a class of covering tour problems related to the geometric Traveling Salesman Problem is presented, where the goal is to find a polygonal tour for a cutter so that it sweeps out a specified region (pocket) in order to minimize a cost that depends mainly on the number of em turns.
Journal ArticleDOI

Optimal Covering Tours with Turn Costs

Esther M. Arkin, +5 more
- 01 Sep 2005 - 
TL;DR: In this article, the authors give the first algorithmic study of a class of covering tour problems related to the geometric traveling salesman problem, and prove the NP-completeness of minimum-turn milling and give efficient approximation algorithms for several natural versions of the problem.
Posted Content

Towards Optimal Running Times for Optimal Transport

Jose Blanchet, +3 more
- 17 Oct 2018 - 
TL;DR: This work provides faster algorithms for approximating the optimal transport distance between two discrete probability distributions, e.g. earth mover's distance, and provides reductions from optimal transport to canonical optimization problems for which recent algorithmic efforts have provided nearly-linear time algorithms.
References
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Book

The Design and Analysis of Computer Algorithms

Alfred V. Aho, +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
Journal ArticleDOI

An $n^{5/2} $ Algorithm for Maximum Matchings in Bipartite Graphs

John E. Hopcroft, +1 more
- 01 Dec 1973 - 
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

Equivalence of free boolean graphs can be decided probabilistically in polynomial time

Manuel Blum, +2 more
- 18 Mar 1980 - 
Journal ArticleDOI

An algorithm for finding all shortest paths using N2.81 infinite-precision multiplications

Gideon Yuval
- 01 Mar 1976 - 
Journal ArticleDOI

New combinations of methods for the acceleration of matrix multiplications

V.Ya. Pan
- 01 Jan 1981 - 
TL;DR: The techniques of trilinear aggregating, uniting and canceling, AUC, due to the author, give the exponent < 2.77614 and a small constant defining an upper bounds on the both complexities, of MM and Boolean MM.
Frequently Asked Questions (1)
Q1. What are the contributions in this paper?

In this paper, a bipartite graph G = ( S, T, E ) is given, where S U T is the set of nodes ( S n T = 8 ), T = { VI, ..., vt } ( A t ), and 1 E I= e. The cardinality of a maximal matching in G is denoted by Card ( A ).