Counting Linear Extensions in Practice: MCMC Versus Exponential Monte Carlo

Authors

  • Topi Talvitie University of Helsinki
  • Kustaa Kangas Aalto University
  • Teppo Niinimäki Aalto University
  • Mikko Koivisto University of Helsinki

Keywords:

partial order, linear extension, counting, Monte Carlo, MCMC, practice

Abstract

Counting the linear extensions of a given partial order is a #P-complete problem that arises in numerous applications. For polynomial-time approximation, several Markov chain Monte Carlo schemes have been proposed; however, little is known of their efficiency in practice. This work presents an empirical evaluation of the state-of-the-art schemes and investigates a number of ideas to enhance their performance. In addition, we introduce a novel approximation scheme, adaptive relaxation Monte Carlo (ARMC), that leverages exact exponential-time counting algorithms. We show that approximate counting is feasible up to a few hundred elements on various classes of partial orders, and within this range ARMC typically outperforms the other schemes.

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Published

2018-04-25

How to Cite

Talvitie, T., Kangas, K., Niinimäki, T., & Koivisto, M. (2018). Counting Linear Extensions in Practice: MCMC Versus Exponential Monte Carlo. Proceedings of the AAAI Conference on Artificial Intelligence, 32(1). Retrieved from https://ojs.aaai.org/index.php/AAAI/article/view/11528

Issue

Section

AAAI Technical Track: Heuristic Search and Optimization