Theory and Techniques for Synthesizing a Family of Graph Algorithms

Srinivas Nedunuri
(The University of Texas at Austin)
William R. Cook
(The University of Texas at Austin)
Douglas R. Smith
(Kestrel Institute)

Although Breadth-First Search (BFS) has several advantages over Depth-First Search (DFS) its prohibitive space requirements have meant that algorithm designers often pass it over in favor of DFS. To address this shortcoming, we introduce a theory of Efficient BFS (EBFS) along with a simple recursive program schema for carrying out the search. The theory is based on dominance relations, a long standing technique from the field of search algorithms. We show how the theory can be used to systematically derive solutions to two graph algorithms, namely the Single Source Shortest Path problem and the Minimum Spanning Tree problem. The solutions are found by making small systematic changes to the derivation, revealing the connections between the two problems which are often obscured in textbook presentations of them.

In Doron Peled and Sven Schewe: Proceedings First Workshop on Synthesis (SYNT 2012), Berkeley, California, USA, 7th and 8th July 2012, Electronic Proceedings in Theoretical Computer Science 84, pp. 33–46.
Published: 3rd July 2012.

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