Publication
STOC 1977
Conference paper

Finding a minimum circuit in a graph

View publication

Abstract

Finding minimum circuits in graphs and digraphs is discussed. An almost minimum circuit is a circuit which may have only one edge more than the minimum. An 0(n2) algorithm is presented to find an almost minimum circuit. The straightforward algorithm for finding a minimum circuit has an 0(ne) behavior. It is refined to yield an O(n2) average time algorithm . An alternative method is to reduce the problem of finding a minimum circuit to that of finding a triangle in an auxiliary graph. Three methods for finding a triangle in a graph are presented. The first has an worst case bound (0(n) for planar graphs); the second takes 0(n5/3) time on the average; the third has an 0(nlog) worst case behavior. For digraphs, recent results of Bloniarz, Fisher and Meyer are used to obtain an algorithm with 0(n2logn) average behavior.

Date

Publication

STOC 1977

Authors

Share