Abstract

We address the question of theoretical vs. practical behavior of algorithms for the minimum spanning tree problem. We review the factors that influence the actual running time of an algorithm, from choice of language, machine, and compiler, through low-level implementation choices, to purely algorithmic issues. We discuss how to design a careful experimental comparison between various alternatives. Finally, we present some results from an ongoing study in which we are using: multiple languages, compilers, and machines; all the major variants of the comparison-based algorithms; and eight varieties of graphs with sizes of up to 130,000 vertices (in sparse graphs) or 750,000 edges (in dense graphs). 1 Introduction Finding spanning trees of minimum weight (minimum spanning trees or MSTs) is one of the best known graph problems; algorithms for this problem have a long history, for which see the article of Graham and Hell [6]. The best comparison-based algorithm to date, due to Gabow...

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