Most work in heuristic search considers problems where a low cost solution is preferred (MIN problems). In this paper, we investigate the complementary setting where a solution of high reward is preferred (MAX problems). Example MAX problems include finding a longest simple path in a graph, maximal coverage, and various constraint optimization problems. We examine several popular search algorithms for MIN problems and discover the curious ways in which they misbehave on MAX problems. We propose modifications that preserve the original intentions behind the algorithms but allow them to solve MAX problems, and compare them theoretically and empirically. Interesting results include the failure of bidirectional search and close relationships between Dijkstra's algorithm, weighted A*, and depth-first search.

Most work in heuristic search considers problems where a low cost solution is preferred (MIN problems). In this paper, we investigate the complementary setting where a solution of high reward is preferred (MAX problems). Example MAX problems include finding a longest simple path in a graph, maximal coverage, and various constraint optimization problems. We examine several popular search algorithms for MIN problems and discover the curious ways in which they misbehave on MAX problems. We propose modifications that preserve the original intentions behind the algorithms but allow them to solve MAX problems, and compare them theoretically and empirically. Interesting results include the failure of bidirectional search and close relationships between Dijkstra's algorithm, weighted A*, and depth-first search.

Snake in the Box (SIB) is the problem of finding the longest simple path along the edges of an n -dimensional cube, subject to certain constraints. SIB has important applications in coding theory and communications. State of the art algorithms for solving SIB apply uninformed search with symmetry breaking techniques. We formalize this problem as a search problem and propose several admissible heuristics to solve it. Using the proposed heuristics is shown to have a huge impact on the number of nodes expanded and, in some configurations, on runtime. These results encourage further research in using heuristic search to solve SIB, and to solve maximization problems more generally.