An exact algorithm with the time complexity of $O^*(1.299^m)$ for the weighed mutually exclusive set cover problem

TL;DR

This paper presents an exact algorithm with a time complexity of $O^*(1.299^m)$ for solving the weighted mutually exclusive set cover problem, which is relevant in cancer gene mutation analysis.

Contribution

The paper introduces a novel exact algorithm with improved exponential time complexity for the weighted mutually exclusive set cover problem.

Findings

Algorithm achieves $O^*(1.299^m)$ time complexity.

Applicable to cancer gene mutation recognition.

Provides exact solutions for the problem.

Abstract

In this paper, we will introduce an exact algorithm with a time complexity of $O^*(1.299^m)$ for the {\sc weighted mutually exclusive set cover} problem, where $m$ is the number of subsets in the problem. This problem has important applications in recognizing mutation genes that cause different cancer diseases.