Abstract

Depth-first search is the key to a wide variety of graph algorithms. In this paper we express depth-first search in a lazy functional language, obtaining a linear-time implementation. Unlike traditional imperative presentations, we use the structuring methods of functional languages to construct algorithms from individual reusable components. This style of algorithm construction turns out to be quite amenable to formal proof, which we exemplify through a calculationalstyle proof of a far from obvious strongly-connected components algorithm. 1 Introduction The importance of depth-first search (DFS) for graph algorithms was established twenty years ago by Tarjan (1972) and Hopcroft and Tarjan (1973) in their seminal work. They demonstrated how depth-first search could be used to construct a variety of efficient graph algorithms. In practice, this is done by embedding code-fragments necessary for a particular algorithm into a DFS procedure skeleton in order to compute relevant informati...

Citations