Incremental Symmetry Breaking Constraints for Graph Search Problems

Avraham Itzhakov, Michael Codish
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
This paper introduces incremental symmetry breaking constraints for graph search problems which are complete and compact. We show that these constraints can be computed incrementally: A symmetry breaking constraint for order n graphs can be extended to one for order n + 1 graphs. Moreover, these constraints induce a special property on their canonical solutions: An order n canonical graph contains a canonical subgraph on the first k vertices for every 1 ≤ k ≤ n. This facilitates a "generate and
more » ... extend" paradigm for parallel graph search problem solving: To solve a graph search problem φ on order n graphs, first generate the canonical graphs of some order k < n. Then, compute canonical solutions for φ by extending, in parallel, each canonical order k graph together with suitable symmetry breaking constraints. The contribution is that the proposed symmetry breaking constraints enable us to extend the order k canonical graphs to order n canonical solutions. We demonstrate our approach through its application on two hard graph search problems.
doi:10.1609/aaai.v34i02.5513 fatcat:5xzcxod4wvdhpju3pgb2s2bg7q