(PDF) Peter van Beek. Backtracking search algorithms. Chapter 4 in Handbook of Constraint Programming, F. Rossi, P. van Beek, T. Walsh (eds.), Elsevier, 2006.


Since the first formal statements of backtracking algorithms over 40 years ago, many techniques for improving the efficiency of a backtracking search algorithm have been suggested and evaluated. In this chapter, I survey some of the most important techniques including branching strategies, constraint propagation, nogood recording, backjumping, heuristics for variable and value ordering, randomization and restart strategies, and alternatives to depth-first search. The techniques are not always orthogonal and sometimes combining two or more techniques into one algorithm has a multiplicative effect (such as combining restarts with nogood recording) and sometimes it has a degradation effect (such as increased constraint propagation versus backjumping). Given the many possible ways that these techniques can be combined together into one algorithm, I also survey work on comparing backtracking algorithms. The best combinations of these techniques result in robust backtracking algorithms that can now routinely solve large, hard instances that are of practical importance.

Return to Publications