Run-Time Analysis of Classical Path-Planning Algorithms
Run-time analysis is a type of empirical tool that studies the time consumed by running an algorithm. This type of analysis has been successfully used in some Artificial Intelligence (AI) fields, in paticular in Metaheuristics. This paper is an attempt to bring this tool to the path-planning community. In particular, we analyse the statistical properties of the run-time of the A*, Theta* and S-Theta* algorithms with a variety of problems of different degrees of complexity. Traditionally, the path-planning literature has compared run-times just comparing their mean values. This practice, which unfortunately is quite common in the literature, raises serious concerns from a methodological and statistical point of view. Simple mean comparison provides poorly supported conclusions, and, in general, it can be said that this practice should be avoided.
After our analysis, we conclude that the time required by these three algorithms follows a lognormal distribution. In low complexity problems, the lognormal distribution looses some accuracy to describe the algorithm run-times. The lognormality of the run-times opens the use of powerful parametric statistics to compare execution times, which could lead to stronger empirical methods.
KeywordsMobile Robot Lognormal Distribution Path Planning Problem Hardness Timetabling Problem
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