Technical Communications of ICLP

Abstract Dynamic programming (DP) on tree decompositions is a well studied approach for solving hard problems efficiently. State-of-the-art implementations usually rely on tables for storing information, and algorithms specify how the tuples are manipulated during traversal of the decomposition. However, a major bottleneck of such table-based algorithms is relatively high memory consumption. The goal of the doctoral thesis herein discussed is to mitigate performance and memory shortcomings of such algorithms. The idea is to replace tables with an efficient data structure that no longer requires to enumerate intermediate results explicitly during the computation. To this end, Binary Decision Diagrams (BDDs) and related concepts are studied with respect to their applicability in this setting. Besides native support for efficient storage, from a conceptual point of view BDDs give rise to an alternative approach of how DP algorithms are specified. Instead of tuple-based manipulation operations, the algorithms are specified on a logical level, where sets of models can be conjointly updated. The goal of the thesis is to provide a general tool-set for problems that can be solved efficiently via DP on tree decompositions

Bounded Search and Symbolic Inference for Constraint Optimization

Constraint optimization underlies many problems in AI. We present a novel algorithm for finite domain constraint optimization that generalizes branch-and-bound search by reasoning about sets of assignments rather than individual assignments. Because in many practical cases, sets of assignments can be represented implicitly and compactly using symbolic techniques such as decision diagrams, the set-based algorithm can compute bounds faster than explicitly searching over individual assignments, while memory explosion can be avoided by limiting the size of the sets. Varying the size of the sets yields a family of algorithms that includes known search and inference algorithms as special cases. Furthermore, experiments on random problems indicate that the approach can lead to significant performance improvements.