Even Faster Exact Bandwidth

TL;DR

This paper introduces a significantly faster exact algorithm for the NP-hard Bandwidth problem, reducing the time complexity from previous bests and applying Measure & Conquer analysis for the first time in this context.

Contribution

It presents a new algorithm with improved exponential time complexity and novel analysis techniques for the Bandwidth problem.

Findings

Achieved O(4.83^n) time complexity for exact Bandwidth algorithm

Introduced Measure & Conquer analysis to this problem class

Reduced space complexity to O*(4^n)

Abstract

We deal with exact algorithms for Bandwidth, a long studied NP-hard problem. For a long time nothing better than the trivial O*(n!) exhaustive search was known. In 2000, Feige an Kilian came up with a O*(10^n)-time algorithm. Recently we presented algorithm that runs in O*(5^n) time and O*(2^n) space.. In this paper we present a major modification to our algorithm which makes it run in O(4.83^n) time with the cost of O*(4^n) space complexity. This modification allowed us to perform Measure & Conquer analysis for the time complexity which was not used for such types of problems before.