Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Fast algorithms for Maximum Subset Matching and All-Pairs Shortest Paths in graphs with a (not so) small vertex cover
 

Summary: Fast algorithms for Maximum Subset Matching and All-Pairs
Shortest Paths in graphs with a (not so) small vertex cover
Noga Alon
Raphael Yuster
Abstract
In the Maximum Subset Matching problem, which generalizes the maximum matching prob-
lem, we are given a graph G = (V, E) and S V . The goal is to determine the maximum number
of vertices of S that can be matched in a matching of G. Our first result is a new randomized
algorithm for the Maximum Subset Matching problem that improves upon the fastest known
algorithms for this problem. Our algorithm runs in ~O(ms(-1)/2
) time if m s(+1)/2
and in
~O(s
) time if m s(+1)/2
, where < 2.376 is the matrix multiplication exponent, m is the
number of edges from S to V \ S, and s = |S|. The algorithm is based, in part, on a method for
computing the rank of sparse rectangular integer matrices.
Our second result is a new algorithm for the All-Pairs Shortest Paths (APSP) problem. Given
an undirected graph with n vertices, and with integer weights from {1, . . . , W} assigned to its
edges, we present an algorithm that solves the APSP problem in ~O(Wn(1,1,)

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics