Theory and Techniques for Synthesizing a Family of Graph Algorithms

Abstract

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

On Chinese and Western Family Trees: Mechanism and Performance

“…Also, there are a variety of ways to carry out the search, for example Depth-First (DFS), Breadth-First (BFS), Best-First, etc. While DFS is the most common, BFS actually has several advantages over DFS at the price of exponential space requirement (Nedunuri et al, 2012). BFS is one of the simplest algorithms for searching a tree or a graph and the archetype for many important graph algorithms (Cormen, 2009) (Horowitz et al, 1997).…”