Russian Doll Search with Tree Decomposition

Optimization in graphical models is an important problem which has been studied in many AI frameworks such as weighted CSP, maximum satisfiability or probabilistic networks. By identifying conditionally independent subproblems, which are solved independently and whose optimum is cached, recent Branch and Bound algorithms offer better asymptotic time complexity. But the locality of bounds induced by decomposition often hampers the practical effects of this result because subproblems are often uselessly solved to optimality. Following the Russian Doll Search (RDS) algorithm, a possible approach to overcome this weakness is to (inductively) solve a relaxation of each subproblem to strengthen bounds. The algorithm obtained generalizes both RDS and treedecomposition based algorithms such as BTD or AND-OR Branch and Bound. We study its efficiency on different problems, closing a very hard frequency assignment instance which has been open for more than 10 years.

TagSNP selection using Weighted CSP and Russian Doll Search with Tree Decomposition

Abstract. The TagSNP problem is a specific form of compression problem arising in genetics. Given a very large set of SNP (genomic positions where polymorphism is observed in a given population), the aim is to select a smallest subset of SNPs which represents the complete set of tagSNP reliably. This is possible because strong correlations existing between neighboring SNPs. Typically, besides minimizing the tagSNP set size (mostly for economical reasons), one also seek a maximally informative subset for the given size, generating different secondary criteria. This problem, which is also closely related to a set covering problem, can be simply described as a weighted CSP. We report here our experiments with human tag SNP data using a recently designed WCSP algorithm combining the “Russian Doll Search ” algorithm with local consistency for cost functions and an active exploitation of the problem structure, through a tree decomposition of the problem