The depth first proof number search (df-pn) is an effective and popular algorithm for solving and-or tree problems by using proof and disproof numbers. This paper presents a simple but effective parallelization of the df-pn search algorithm for a shared-memory system. In this parallelization, multiple agents autonomously conduct the df-pn with a shared transposition table. For effective cooperation of agents, virtual proof and disproof numbers are introduced for each node, which is an estimation of future proof and disproof numbers by using the number of agents working on the node's descendants as a possible increase. Experimental results on large checkmate problems in shogi, which is a popular chess variant in Japan, show that reasonable increases in speed were achieved with small overheads in memory.

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.

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 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.

We present and implement a Weighted Partial MaxSAT solver based on successive calls to a SAT solver. We prove the correctness of our algorithm and compare our solver with other Weighted Partial MaxSAT solvers.

Density modeling is notoriously difficult for high dimensional data. One approach to the problem is to search for a lower dimensional manifold which captures the main characteristics of the data. Recently, the Gaussian Process Latent Variable Model (GPLVM) has successfully been used to find low dimensional manifolds in a variety of complex data. The GPLVM consists of a set of points in a low dimensional latent space, and a stochastic map to the observed space. We show how it can be interpreted as a density model in the observed space. However, the GPLVM is not trained as a density model and therefore yields bad density estimates. We propose a new training strategy and obtain improved generalisation performance and better density estimates in comparative evaluations on several benchmark data sets.