Faster Deterministic Algorithms for Packing, Matching and $t$-Dominating Set Problems

TL;DR

This paper introduces three new deterministic algorithms for solving packing, matching, and dominating set problems with improved time bounds, advancing the efficiency of solutions compared to previous deterministic methods.

Contribution

The paper presents three deterministic algorithms with significantly improved time complexities for key combinatorial problems, surpassing prior deterministic bounds.

Findings

Algorithms run in time $O^*(5.44^{mk})$, $O^*(5.44^{(m-1)k})$, and $O^*(5.44^{t})$

Improves upon previous deterministic solutions for these problems

Provides a foundation for more efficient deterministic algorithms in combinatorial optimization

Abstract

In this paper, we devise three deterministic algorithms for solving the $m$-set $k$-packing, $m$-dimensional $k$-matching, and $t$-dominating set problems in time $O^*(5.44^{mk})$, $O^*(5.44^{(m-1)k})$ and $O^*(5.44^{t})$, respectively. Although recently there has been remarkable progress on randomized solutions to those problems, our bounds make good improvements on the best known bounds for deterministic solutions to those problems.