Dynamic Distributed BackJumping

Abstract

We consider Distributed Constraint Satisfaction Problems (DisCSP) when control of variables and constraints is distributed among a set of agents. This paper presents a distributed version of the centralized BackJumping algorithm, called the Dynamic Distributed BackJumping-DDBJ algorithm. The advantage is twofold: DDBJ inherits the strength of synchronous algorithms that enables it to easily combine with a powerful dynamic ordering of variables and values, and still it maintains some level of autonomy for the agents. Experimental results show that DDBJ outperforms the DiDB and AFC algorithms by a factor of one to two orders of magnitude on hard instances of randomly generated DisCSPs.

Asynchronous Forward-checking for DisCSPs

“…In [13], an elegant method for initializing the backtrack operation in AFC was proposed. Instead of sending Not_OK messages to all unassigned agents in the inconsistent partial assignment, the agent whose domain emptied and triggers a backtrack operation, sends a Backtrack message to the last agent assigned in the inconsistent partial assignment (Nogood).…”

“…The Not_OK message becomes obsolete when the partial assignment it carries is no longer a subset of the CPA. (Other options for initializing backtrack operations were suggested by [13] see Section 6).…”

“…Agents record the latest domain size they received from each agent and choose the smallest as the next agent to send the CPA to. -A heuristic for variable and value ordering was presented in [13] for the direct backtracking version of AFC. Each agent holds a counter for each of the values in its domain and for each of the other agents.…”

“…In order to evaluate the AFC algorithm with direct backjumping (AFC_DBJ) as presented in [13], it is compared to 'standard' AFC. Figures 8 and 9 compare AFC performing standard conflict based backjumping using the best ordering heuristic (Min_Domain) and AFC performing direct backjumping with the heuristic of [13].…”

Dynamic Ordering for Asynchronous Backtracking on DisCSPs

“…Dynamic ordering is a powerful heuristic used to improve the run-time of centralized CSP algorithms [6,8] and of distributed CSP algorithms with sequential assignments [5,17]. The results in the previous section, show that dynamic ordering must be combined with the right heuristic in order to improve the run-time and justify the overhead in message load of asynchronous backtracking.…”