Big Step Greedy Algorithm for Maximum Coverage Problem

TL;DR

This paper introduces the Big step greedy heuristic for the maximum k-coverage problem, which generalizes classical greedy and exact algorithms by selecting multiple sets per step to improve solution quality.

Contribution

It proposes a novel greedy heuristic that evaluates multiple set combinations per step, bridging the gap between classical greedy and exact algorithms for maximum coverage.

Findings

The Big step greedy heuristic performs better than classical greedy in solution quality.

It reduces computational complexity compared to exact algorithms for large instances.

The algorithm adapts between greedy and exact solutions based on parameter p.

Abstract

This paper proposes a greedy heuristic named as Big step greedy heuristic and investigates the application of Big step greedy heuristic for maximum k-coverage problem. Greedy algorithms construct the solution in multiple steps, the classical greedy algorithm for maximum k-coverage problem, in each step selects one set that contains the greatest number of uncovered elements. The Big step greedy heuristic, in each step selects p (1 <= p <= k) sets such that the union of selected p sets contains the greatest number of uncovered elements by evaluating all possible p-combinations of given sets. When p=k Big step greedy algorithm behaves like exact algorithm that computes optimal solution by evaluating all possible k-combinations of given sets. When p=1 it behaves like the classical greedy algorithm.