{"type":"ScholarlyArticle","title":"An Expected-Cost Analysis of Backtracking and Non-Backtracking Algorithms","authors":[{"name":"Colin J. H. McDiarmid","slug":"colin-j-h-mcdiarmid","given":"Colin J. H.","family":"McDiarmid","affiliation":""},{"name":"Gregory M. Provan","slug":"gregory-m-provan","given":"Gregory M.","family":"Provan","affiliation":""}],"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.","doi":null,"url":"https://ijcai.org/proceedings/1991/26","pdf":"https://ijcai.org/proceedings/1991/0026.pdf","markdown":"https://ijcai.org/proceedings/1991/26.md","bibtex":"https://ijcai.org/proceedings/1991/bibtex/26","volume":{"slug":"1991","title":"Proceedings of the Twelfth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1991","url":"https://ijcai.org/proceedings/1991/","year":1991,"location":"Sydney, New South Wales, Australia","dates":"24-30 August 1991","editors":"John Mylopoulos and Ray Reiter","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Automated Reasoning","track":"Automated Reasoning","number":26,"pages":{"first":172,"last":176},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}