Classical constraint satisfaction problems (CSPs) are commonly defined on finite domains. In real life, constrained variables can evolve over time. A variable can actually take an infinite sequence of values over discrete time points. In this paper, we propose constraint programming on infinite data streams, which provides a natural way to model constrained time-varying problems. In our framework, variable domains are specified by ω-regular languages. We introduce special stream operators as basis to form stream expressions and constraints. Stream CSPs have infinite search space. We propose a search procedure that can recognize and avoid infinite search over duplicate search space. The solution set of a stream CSP can be represented by a Büchi automaton allowing stream values to be non-periodic. Consistency notions are defined to reduce the search space early. We illustrate the feasibility of the framework by examples and experiments.

The number partitioning problem is to divide a given set of N positive integers into K subsets, so that the sum of the numbers in each subset are as nearly equal as possible. While effective algorithms for two-way partitioning exist, multi-way partitioning is much more challenging. We introduce an improved algorithm for optimal multi-way partitioning, by combining several existing algorithms with some new extensions. We test our algorithm for partitioning 31-bit integers from three to ten ways, and demonstrate orders of magnitude speedup over the previous state of the art.

Hash Distributed A* (HDA*) is a parallel A* algorithm that is proven to be effective in optimal sequential planning with unit edge costs. HDA* leverages the Zobrist function to almost uniformly distribute and schedule work among processors. This paper evaluates the performance of HDA* in optimal sequence alignment. We observe that with a large number of CPU cores HDA* suffers from an increase of search overhead caused by reexpansions of states in the closed list due to nonuniform edge costs in this domain. We therefore present a new work distribution strategy limiting processors to distribute work, thus increasing the possibility of detecting such duplicate search effort. We evaluate the performance of this approach on a cluster of multi-core machines and show that the approach scales well up to 384 CPU cores.

Heuristics used for solving hard real-time search problems have regions with depressions. Such regions are bounded areas of the search space in which the heuristic function is exceedingly low compared to the actual cost to reach a solution. Real-time search algorithms easily become trapped in those regions since the heuristic values of states in them may need to be updated multiple times, which results in costly solutions. State-of-the-art real-time search algorithms like LSS-LRTA*, LRTA*(k), etc., improve LRTA*'s mechanism to update the heuristic, resulting in improved performance. Those algorithms, however, do not guide search towards avoiding or escaping depressed regions. This paper presents depression avoidance, a simple real-time search principle to guide search towards avoiding states that have been marked as part of a heuristic depression. We apply the principle to LSS-LRTA* producing aLSS-LRTA*, a new real-time search algorithm whose search is guided towards exiting regions with heuristic depressions. We show our algorithm outperforms LSS-LRTA* in standard real-time benchmarks. In addition we prove aLSS-LRTA* has most of the good theoretical properties of LSS-LRTA*.

This paper proposes the integration of the resolution rule for Max-SAT with unsatisfiability-based Max-SAT solvers. First, we show that the resolution rule for Max-SAT can be safely applied as dictated by the resolution proof associated with an unsatisfiable core when such proof is read-once, that is, each clause is used at most once in the resolution process. Second, we study how this property can be integrated in an unsatisfiability-based solver. In particular, the resolution rule for Max-SAT is applied to read-once proofs or to read-once subparts of a general proof. Finally, we perform an empirical investigation on structured instances from recent Max-SAT evaluations. Preliminary results show that the use of read-once resolution substantially improves the performance of the solver.

The minimization problem for propositional formulas is an important optimization problem in the second level of the polynomial hierarchy. In general, the problem is Sigma-2-complete under Turing reductions, but restricted versions are tractable. We study the complexity of minimization for formulas in two established frameworks for restricted propositional logic: The Post framework allowing arbitrarily nested formulas over a set of Boolean connectors, and the constraint setting, allowing generalizations of CNF formulas. In the Post case, we obtain a dichotomy result: Minimization is solvable in polynomial time or coNP-hard. This result also applies to Boolean circuits. For CNF formulas, we obtain new minimization algorithms for a large class of formulas, and give strong evidence that we have covered all polynomial-time cases.

We address a dynamic decision problem in which decision makers must pay some costs when they change their decisions along the way. We formalize this problem as Dynamic SAT (DynSAT) with decision change costs, whose goal is to find a sequence of models that minimize the aggregation of the costs for changing variables. We provide two solutions to solve a specific case of this problem. The first uses a Weighted Partial MaxSAT solver after we encode the entire problem as a WeightedPartial MaxSAT problem. The second solution, which we believe is novel, uses the Lagrangian decomposition technique that divides the entire problem into sub-problems, each of which can be separately solved by an exact Weighted Partial MaxSATsolver, and produces both lower and upper bounds on the optimal in an anytime manner. To compare the performance of these solvers, we experimentedon the random problem and the target trackingproblem. The experimental results show that a solver based on Lagrangian decomposition performs better for the random problem and competitively for the target tracking problem.

ADOPT and BnB-ADOPT are two optimal DCOP search algorithms that are similar except for their search strategies: the former uses best-first search and the latter uses depth-first branch-and-bound search. In this paper, we present a new algorithm, called ADOPT( k ), that generalizes them. Its behavior depends on the k parameter. It behaves like ADOPT when k = 1, like BnB-ADOPT when k = ∞ and like a hybrid of ADOPT and BnB-ADOPT when 1 < k < ∞. We prove that ADOPT( k ) is a correct and complete algorithm and experimentally show that ADOPT( k ) outperforms ADOPT and BnB-ADOPT on several benchmarks across several metrics.

Bessiere et al. (AAAI'08) showed that several intractable global constraints can be efficiently propagated when certain natural problem parameters are small. In particular, the complete propagation of a global constraint is fixed-parameter tractable in k — the number of holes in domains — whenever bound consistency can be enforced in polynomial time; this applies to the global constraints AtMost-NValue and Extended Global Cardinality (EGC). In this paper we extend this line of research and introduce the concept of reduction to a problem kernel, a key concept of parameterized complexity, to the field of global constraints. In particular, we show that the consistency problem for AtMost-NValue constraints admits a linear time reduction to an equivalent instance on O(k 2 ) variables and domain values. This small kernel can be used to speed up the complete propagation of NValue constraints. We contrast this result by showing that the consistency problem for EGC constraints does not admit a reduction to a polynomial problem kernel unless the polynomial hierarchy collapses.

Transposition tables are a powerful tool in search domains for avoiding duplicate effort and for guiding node expansions. Traditionally, however, they have only been applicable when the current state is exactly the same as a previously explored state. We consider a generalized transposition table, whereby a similarity metric that exploits local structure is used to compare the current state with a neighbourhood of previously seen states. We illustrate this concept and forward pruning based on function approximation in the domain of Skat, and show that we can achieve speedups of 16+ over standard methods.