Evaluating Las Vegas Algorithms - Pitfalls and Remedies

TL;DR

This paper introduces a new methodology for evaluating Las Vegas Algorithms by analyzing empirical run-time distributions, demonstrated on stochastic local search algorithms for SAT, highlighting pitfalls of improper methods and benefits of the proposed approach.

Contribution

It presents a novel methodology for assessing LVAs through empirical run-time distributions, improving evaluation accuracy for stochastic algorithms.

Findings

Identifies pitfalls in current empirical evaluation methods.

Demonstrates the methodology on SAT stochastic local search algorithms.

Highlights benefits of proper run-time distribution analysis.

Abstract

Stochastic search algorithms are among the most sucessful approaches for solving hard combinatorial problems. A large class of stochastic search approaches can be cast into the framework of Las Vegas Algorithms (LVAs). As the run-time behavior of LVAs is characterized by random variables, the detailed knowledge of run-time distributions provides important information for the analysis of these algorithms. In this paper we propose a novel methodology for evaluating the performance of LVAs, based on the identification of empirical run-time distributions. We exemplify our approach by applying it to Stochastic Local Search (SLS) algorithms for the satisfiability problem (SAT) in propositional logic. We point out pitfalls arising from the use of improper empirical methods and discuss the benefits of the proposed methodology for evaluating and comparing LVAs.