Exact Algorithms for 0-1 Integer Programs with Linear Equality Constraints

TL;DR

This paper presents faster exact algorithms for 0-1 integer programs with linear equality constraints, achieving exponential time improvements over brute-force methods and extending to linear optimization problems.

Contribution

The authors develop $O(1.415^n)$-time and $O(1.190^n)$-space algorithms for these problems, significantly improving over previous methods and broadening applicability to linear optimization.

Findings

Algorithms are quadratically faster than exhaustive search.

Algorithms are nearly quadratically faster than previous inequality-based algorithms.

Extended algorithms to linear optimization problems.

Abstract

In this paper, we show $O(1.415^n)$-time and $O(1.190^n)$-space exact algorithms for 0-1 integer programs where constraints are linear equalities and coefficients are arbitrary real numbers. Our algorithms are quadratically faster than exhaustive search and almost quadratically faster than an algorithm for an inequality version of the problem by Impagliazzo, Lovett, Paturi and Schneider (arXiv:1401.5512), which motivated our work. Rather than improving the time and space complexity, we advance to a simple direction as inclusion of many NP-hard problems in terms of exact exponential algorithms. Specifically, we extend our algorithms to linear optimization problems.