A modified greedy algorithm to improve bounds for the vertex cover number

TL;DR

This paper introduces a modified greedy algorithm with improved bounds for the vertex cover number, providing both lower and upper bounds efficiently and ensuring minimal vertex covers, which enhances existing greedy approaches.

Contribution

A new modified greedy algorithm that computes tighter bounds for the vertex cover number and guarantees minimal vertex covers, improving upon existing greedy algorithms.

Findings

Algorithm has worst-case time complexity O(n^3)

Provides both lower and upper bounds for vertex cover number

Ensures the output vertex cover is always minimal

Abstract

In any attempt at designing an efficient algorithm for the minimum vertex cover problem, obtaining good upper and lower bounds for the vertex cover number could be crucial. In this article we present a modified greedy algorithm of worst-case time complexity O(n3) to obtain bounds for the vertex cover number of an input graph of order n. Using simple facts, the proposed algorithm computes a lower bound for the vertex cover number. Then using this lower bound it outputs a minimal vertex cover and hence gives an upper bound. The algorithm ensures the output vertex cover is always minimal, which feature is an improvement upon the existing greedy algorithms.