Improved Greedy Algorithm for Set Covering Problem

TL;DR

This paper introduces a Big step greedy algorithm for the set covering problem, which selects multiple sets per iteration to improve approximation efficiency over the classical greedy approach.

Contribution

The paper presents a novel Big step greedy algorithm that generalizes the classical greedy method by selecting multiple sets simultaneously for better coverage.

Findings

The Big step greedy algorithm effectively reduces the number of steps needed for coverage.

It generalizes the classical greedy algorithm with p=1.

Potential for improved approximation ratios.

Abstract

This paper proposes a greedy algorithm named as Big step greedy set cover algorithm to compute approximate minimum set cover. The Big step greedy algorithm, in each step selects p sets such that the union of selected p sets contains greatest number of uncovered elements and adds the selected p sets to partial set cover. The process of adding p sets is repeated until all the elements are covered. When p=1 it behaves like the classical greedy algorithm.