An Expected-Cost Analysis of Backtracking and Non-Backtracking Algorithms

Abstract

Consider an infinite binary search tree in which the branches have independent random costs. Suppose that we must find an optimal (cheapest) or nearly optimal path from the root to a node at depth n. Karp and Pearl [1983] show that a bounded-lookahead backtracking algorithm A2 usually finds a nearly optimal path in linear expected time (when the costs take only the values 0 or 1). From this successful performance one might conclude that similar heuristics should be of more general use. But we find here equal success for a simpler non-backtracking bounded-lookahead algorithm, so the search model cannot support this conclusion. If, however, the search tree is generated by a branching process so that there is a possibility of nodes having no sons (or branches having prohibitive costs), then the non-backtracking algorithm is hopeless while the backtracking algorithm still performs very well. These results suggest the general guideline that backtracking becomes attractive when there is the possibility of "dead-ends" or prohibitively costly outcomes.