Practical Algorithms for Linear Boolean-width

TL;DR

This paper introduces new algorithms and heuristics for computing linear boolean decompositions, demonstrating significant runtime improvements and effective applications to vertex subset problems through experimental evaluation.

Contribution

It presents novel exact algorithms and heuristics for linear boolean decompositions, with extensive experimental validation showing improved efficiency and practical utility.

Findings

Significant reduction in running time without increasing decomposition width

Dynamic programming algorithms are often much faster than worst-case bounds

Effective application of algorithms to vertex subset problems

Abstract

In this paper, we give a number of new exact algorithms and heuristics to compute linear boolean decompositions, and experimentally evaluate these algorithms. The experimental evaluation shows that significant improvements can be made with respect to running time without increasing the width of the generated decompositions. We also evaluated dynamic programming algorithms on linear boolean decompositions for several vertex subset problems. This evaluation shows that such algorithms are often much faster (up to several orders of magnitude) compared to theoretical worst case bounds.