Theory and Techniques for Synthesizing a Family of Graph Algorithms
This work addresses a space efficiency bottleneck for algorithm designers in graph theory, though it appears incremental as it builds on dominance relations from existing search techniques.
The paper tackles the prohibitive space requirements of Breadth-First Search (BFS) by introducing Efficient BFS (EBFS) theory and a recursive program schema, resulting in derived solutions for Single Source Shortest Path and Minimum Spanning Tree problems through systematic changes.
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.