Theory and Techniques for Synthesizing Space-efficient Breadth-first Search Algorithms

Although Breadth-First Search (BFS) has several advantages over DepthFirst 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 space-e cient BFS (SEBFS) 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 eld of search algorithms. We also show that greedy and greedy-like algorithms form a very useful and important sub-category of SEBFS. Finally, we show how the SEBFS class can be used for semi-automated program synthesis by introducing some techniques for demonstrating that a given problem is solvable by SEBFS. We illustrate our approach on several examples.