Parallelizing asymptotically optimal algorithms for large-scale dualization problems

TL;DR

This paper introduces a new static parallelization scheme for asymptotically optimal dualization algorithms, improving their efficiency on large-scale intractable problems through statistical estimation of subtask sizes.

Contribution

It presents a novel static parallelization scheme for dualization algorithms based on statistical estimations, enhancing their performance on large-scale problems.

Findings

The parallel scheme improves algorithm efficiency on large datasets.

Experimental results support the effectiveness of the parallelization approach.

Theoretical analysis justifies the average-case efficiency of the algorithms.

Abstract

Dualization is a key discrete enumeration problem. It is not known whether or not this problem is polynomial-time solvable. Asymptotically optimal dualization algorithms are the fastest among the known dualization algorithms, which is supported by new experiments with various data described in this paper. A theoretical justification of the efficiency of these algorithms on the average was given by E.V. Djukova more than 30 years ago. In this paper, new results on the construction of parallel algorithms for intractable enumeration problems are presented. A new static parallelization scheme for asymptotically optimal dualization algorithms is developed and tested. The scheme is based on statistical estimations of subtasks size.