Amortized random backtracking

Some nonsystematic search algorithms can deal with partial assignments of variables, and then can use constraint propagation techniques. Let us call them NSPA algorithms (Nonsystematic Search with Partial Assignments). For satisfiability or optimization problems, such NSPA algorithms scale a lot better than systematic algorithms. We show in this paper that naive NSPA algorithms have to pay a severe overhead due to the way they visit partial assignments. Amortizing the visits of partial assignments is an important feature which we introduce and analyze in this paper. We also propose a new NSPA algorithm that is amortized: it is called Amortized Random Backtracking, and performs a probabilistic exploration of the search space. It can be seen as an amortized version of iterative sampling and has given very good experimental results on a real life time-tabling problem.