Min-domain retroactive ordering for Asynchronous Backtracking

Ordering heuristics are a powerful tool in CSP search algorithms. Among the most successful ordering heuristics are heuristics which enforce a fail first strategy by using the Min-domain property (Haralick and Elliott, Artif Intel 14:263-313, 1980; Bessiere and Regin, Mac and combined heuristics: two reasons to forsake FC (and CBJ?) on hard problems. In Proc. CP 96, pp. 61-75, Cambridge, MA, 1996; Smith and Grant, Trying harder to fail first. In European Conference on Artificial Intelligence, pp. 249-253, 1998; Dechter, Constraint Processing. Morgan Kaufman, 2003). Ordering heuristics have been introduced recently to asynchronous backtracking (ABT), for distributed constraints satisfaction (DisCSP) (Zivan and Meisels, Dynamic ordering for asynchronous backtracking on discsps. In CP-2005, pp. 32-46, Sigtes (Barcelona), Spain, 2005). However, the pioneering study of dynamically ordered ABT, ABT-DO, has shown that a straightforward implementation of the Min-domain heuristic does not produce the expected improvement over a static ordering. The present paper proposes an asynchronous dynamic ordering which does not follow the standard restrictions on the position of reordered agents in ABT-DO. Agents can be moved to a position that is higher than that of the target of the backtrack. Combining the Nogood-triggered heuristic and the Min-domain property in this new class of heuristics results in the best performing version of ABT-DO. The new version of retroactively ordered ABT is faster by a large factor than the best form of ABT.