We define the concept of an internal symmetry. This is a symmety within a solution of a constraint satisfaction problem. We compare this to solution symmetry, which is a mapping between different solutions of the same problem. We argue that we may be able to exploit both types of symmetry when finding solutions. We illustrate the potential of exploiting internal symmetries on two benchmark domains: Van der Waerden numbers and graceful graphs. By identifying internal symmetries we are able to extend the state of the art in both cases.

Search based solvers for Quantified Boolean Formulas (QBF) have adapted the SAT solver techniques of unit propagation and clause learning to prune falsifying assignments. The technique of cube learning has been developed to help them prune satisfying assignments. Cubes, however, have not been able to achieve the same degree of effectiveness as clauses. In this paper we demonstrate how a circuit representation for QBF can support the propagation of dual truth values. The dual values support the identical techniques of unit propagation and clause learning, except now it is satisfying assignments rather than falsifying assignments that are pruned. Dual value propagation thus exploits the circuit representation and the duality of QBF formulas so that the same effective SAT techniques can now be used to prune both falsifying and satisfyingly assignments. We show empirically that dual propagation yields significantperformance improvements and advances the state of the art in QBF solving.

We present a fast local search algorithm that finds an improved solution (if there is any) in the k-exchange neighborhood of the given solutionto an instance of Weighted Feedback Arc Set in Tournaments. More precisely,given an arc weighted tournament T on n vertices and a feedback arc set F (a set of arcs whose deletion from T turns it into a directed acyclic graph), our algorithm decides in time O(2 o ( k ) n log n) if there is a feedback arc set of smaller weight and that differs from F in at most k arcs. To our knowledge this is the first algorithm searching the k -exchange neighborhood of an NP-complete problem that runs in (parameterized) subexponential time. Using this local search algorithm for Weighted Feedback Arc Set in Tournaments, we obtain subexponential time algorithms for a local search variant of Kemeny Ranking — a problem in social choice theory and of One-Sided Cross Minimization — a problem in graph drawing.

We consider the stochastic variant of the Canadian Traveler's Problem, a path planning problem where adverse weather can cause some roads to be untraversable. The agent does not initially know which roads can be used. However, it knows a probability distribution for the weather, and it can observe the status of roads incident to its location. The objective is to find a policy with low expected travel cost. We introduce and compare several algorithms for the stochastic CTP. Unlike the optimistic approach most commonly considered in the literature, the new approaches we propose take uncertainty into account explicitly. We show that this property enables them to generate policies of much higher quality than the optimistic one, both theoretically and experimentally.

We present a new technique to compress pattern databases to provide consistent heuristics without loss of information. We store the heuristic estimate modulo three, requiring only two bits per entry or in a more compact representation, only 1.6 bits. This allows us to store a pattern database with more entries in the same amount of memory as an uncompressed pattern database. These compression techniques are most useful where lossy compression using cliques or their generalization is not possible or where adjacent entries in the pattern database are not highly correlated. We compare both techniques to the best existing compression methods for the Top-Spin puzzle, Rubik's cube, the 4-peg Towers of Hanoi problem, and the 24 puzzle. Under certain conditions, our best implementations for the Top-Spin puzzle and Rubik's cube outperform the respective state of the art solvers by a factor of four.

This paper analyzes the performance of IDA* using additive heuristics. We show that the reduction in the number of nodes expanded using multiple independent additive heuristics is the product of the reductions achieved by the individual heuristics. First, we formally state and prove this result on unit edge-cost undirected graphs with a uniform branching factor. Then, we empirically verify it on a model of the 4-peg Towers of Hanoi problem. We also run experiments on the multiple sequence alignment problem showing more general applicability to non-unit edge-cost directed graphs. Then, we extend an existing model to predict the performance of IDA* with a single pattern database to independent additive disjoint pattern databases. This is the first analysis of the performance of independent additive heuristics.

We study propagation algorithms for the conjunction of two AllDifferent constraints. Solutions of an AllDifferent constraint can be seen as perfect matchings on the variable/value bipartite graph. Therefore, we investigate the problem of finding simultaneous bipartite matchings. We present an extension of the famous Hall theorem which characterizes when simultaneous bipartite matchings exists. Unfortunately, finding such matchings is NP-hard in general. However, we prove a surprising result that finding a simultaneous matching on a convex bipartite graph takes just polynomial time. Based on this theoretical result, we provide the first polynomial time bound consistency algorithm for the conjunction of two AllDifferent constraints. We identify a pathological problem on which this propagator is exponentially faster compared to existing propagators. Our experiments show that this new propagator can offer significant benefits over existing methods.

Within the electric power literature the transmission expansion planning problem (TNEP) refers to the problem of how to upgrade an electric power network to meet future demands. As this problem is a complex, non-linear, and non-convex optimization problem, researchers have traditionally focused on approximate models of power flows. Existing approaches are often tightly coupled to the approximation choice. Until recently, these approximations have produced results that are straight-forward to adapt to the more complex (real) problem. However, the power grid is evolving towards a state where the adaptations are no longer easy (e.g. large amounts of limited control, renewable generation) that necessitates new optimization techniques. In this paper, we propose a local search variation of the powerful Limited Discrepancy Search (LDLS) that encapsulates the complexity of power flows in a black box that may be queried for information about the quality of a proposed expansion. This allows the development of a new optimization algorithm that is independent of the underlying power model.

Modern complete SAT solvers almost uniformly implement variations of the clause learning framework introduced by Grasp and Chaff. The success of these solvers has been theoretically explained by showing that the clause learning framework is an implementation of a proof system which is as poweful as resolution. However, exponential lower bounds are known for resolution, which suggests that significant advances in SAT solving must come from implementations of more powerful proof systems. We present a clause learning SAT solver that uses extended resolution. It is based on a restriction of the application of the extension rule. This solver outperforms existing solvers on application instances from recent SAT competitions as well as on instances that are provably hard for resolution.

We propose in this paper a new interval constraint propagation algorithm, called MOnotonic Hull Consistency (Mohc), that exploits monotonicity of functions. The propagation is standard, but the Mohc-Revise procedure, used to filter/contract the variable domains w.r.t. an individual constraint, uses monotonic versions of the classical HC4-Revise and BoxNarrow procedures. Mohc-Revise appears to be the first adaptive revise procedure ever proposed in (interval) constraint programming.  Also, when a function is monotonic w.r.t. every variable, Mohc-Revise is proven to compute the optimal/sharpest box enclosing all the solutions of the corresponding constraint (hull consistency). Very promising experimental results suggest that Mohc has the potential to become an alternative to the state-of-the-art HC4 and Box algorithms.