Theory and Techniques for Synthesizing a Family of Graph Algorithms by Srinivas Nedunuri, William R. Cook, and Douglas R. Smith.
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.
I don’t think it would satisfy the formal derivation requirements of the authors but am curious why the dominance relationships are derived? Wouldn’t it be easier to ask a user at each node, go/no-go as far as dominance relationship? Allowing an interactive application of the search algorithms based upon the users dominance judgement?
I say that because the derivation strategy depends upon the developer’s interpretation of dominance from a field that may be unfamiliar or incorrectly communicated by a user. To be sure the derivation and results may be formally correct but not produce an answer that is “correct” in the view of a user.
Not to mention that once a derivation is formally “correct,” there would be resistance to changing a “correct” derivation.
A interactive, dynamic, symbiotic search experience between users and their search systems is more likely to produce results thought to be “correct” by users. (What other measure of “correctness” comes to mind?)
PS: Srinivas Nedunuri‘s homepage promises a copy of his PhD dissertation, which formed the basis for this paper, soon!