Summary: A List Heuristic for Vertex Cover
School of Computer Science, McGill University #
Graduate School of Informatics, Kyoto University
We analyze a list heuristic for the vertex cover problem that han
dles the vertices in a given static order based on the degree sequence.
We prove an approximation ratio of at most # #/2 + 3/2 for a non
increasing degree sequence, and show that no ordering can achieve an
approximation ratio of less than # #/2.
Keywords: vertex cover, approximation algorithm, list heuristic
Let G = (V, E) be an undirected graph. The minimum vertex cover problem
for an undirected graph G is to find the smallest cardinality subset of ver
tices such that every edge is incident to at least one of the chosen vertices.
This is a well known NPhard optimization problem, and thus no polynomial
time algorithm is known. There are a number of approximation algorithms
that have been proposed for this problem with various performance guaran
tees. These are described in various textbooks, see for example Cormen et