Many real world applications require managing both system requirements and user preferences where the latter are usually provided in a qualitative way. We introduce a new approach to handle these two aspects, in an efficient way, respectively through Constraint Satisfaction Problems (CSPs) and CP-nets. In particular, we use Arc Consistency (AC) in order to reduce the search space needed when looking for the optimal outcome in an acyclic CP-net. More precisely, assuming that there are always some shared variables between the CP-net and the CSP, our approach works by first applying AC to the CSP and then update the CP-net with the remaining variables values. The resulting simplified CP-net will then be used to look for the best outcome. Experimental tests conducted on randomly generated problem instances clearly show the effect of AC on the size of the search space and the time needed to find the best outcome.

In this paper we describe COLIN, a forward-chaining heuristic search planner, capable of reasoning with COntinuous LINear numeric change, in addition to the full temporal semantics of PDDL. Through this work we make two advances to the state-of-the-art in terms of expressive reasoning capabilities of planners: the handling of continuous linear change, and the handling of duration-dependent effects in combination with duration inequalities, both of which require tightly coupled temporal and numeric reasoning during planning. COLIN combines FF-style forward chaining search, with the use of a Linear Program (LP) to check the consistency of the interacting temporal and numeric constraints at each state. The LP is used to compute bounds on the values of variables in each state, reducing the range of actions that need to be considered for application. In addition, we develop an extension of the Temporal Relaxed Planning Graph heuristic of CRIKEY3, to support reasoning directly with continuous change. We extend the range of task variables considered to be suitable candidates for specifying the gradient of the continuous numeric change effected by an action. Finally, we explore the potential for employing mixed integer programming as a tool for optimising the timestamps of the actions in the plan, once a solution has been found. To support this, we further contribute a selection of extended benchmark domains that include continuous numeric effects. We present results for COLIN that demonstrate its scalability on a range of benchmarks, and compare to existing state-of-the-art planners.

We consider the task of obtaining the maximum a posteriori estimate of discrete pairwise random fields with arbitrary unary potentials and semimetric pairwise potentials. For this problem, we propose an accurate hierarchical move making strategy where each move is computed efficiently by solving an st-MINCUT problem. Unlike previous move making approaches, e.g. the widely used a-expansion algorithm, our method obtains the guarantees of the standard linear programming (LP) relaxation for the important special case of metric labeling. Unlike the existing LP relaxation solvers, e.g. interior-point algorithms or tree-reweighted message passing, our method is significantly faster as it uses only the efficient st-MINCUT algorithm in its design. Using both synthetic and real data experiments, we show that our technique outperforms several commonly used algorithms.

An important problem in computational social choice theory is the complexity of undesirable behavior among agents, such as control, manipulation, and bribery in election systems. These kinds of voting strategies are often tempting at the individual level but disastrous for the agents as a whole. Creating election systems where the determination of such strategies is difficult is thus an important goal. An interesting set of elections is that of scoring protocols. Previous work in this area has demonstrated the complexity of misuse in cases involving a fixed number of candidates, and of specific election systems on unbounded number of candidates such as Borda. In contrast, we take the first step in generalizing the results of computational complexity of election misuse to cases of infinitely many scoring protocols on an unbounded number of candidates. Interesting families of systems include $k$-approval and $k$-veto elections, in which voters distinguish $k$ candidates from the candidate set. Our main result is to partition the problems of these families based on their complexity. We do so by showing they are polynomial-time computable, NP-hard, or polynomial-time equivalent to another problem of interest. We also demonstrate a surprising connection between manipulation in election systems and some graph theory problems.

Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful cases: symmetry breaking constraints for row and column symmetry, and symmetry breaking constraints for eliminating value symmetry.

Some aspects of the result of applying unit resolution on a cnf formula can be formalized as functions with domain a set of partial truth assignments. We are interested in two ways for computing such functions, depending on whether the result is the production of the empty clause or the assignment of a variable with a given truth value. We show that these two models can compute the same functions with formulae of polynomially related sizes, and we explain how this result is related to the cnf encoding of Boolean constraints.

We introduce a new type of fully computable problems, for DSS dedicated to maximal spanning tree problems, based on deduction and choice: preferential consistency problems. To show its interest, we describe a new compact representation of preferences specific to spanning trees, identifying an efficient maximal spanning tree sub-problem. Next, we compare this problem with the Pareto-based multiobjective one. And at last, we propose an efficient algorithm solving the associated preferential consistency problem.

We present two new and efficient algorithms for computing all-pairs shortest paths. The algorithms operate on directed graphs with real (possibly negative) weights. They make use of directed path consistency along a vertex ordering d. Both algorithms run in O(n^2 w_d) time, where w_d is the graph width induced by this vertex ordering. For graphs of constant treewidth, this yields O(n^2) time, which is optimal. On chordal graphs, the algorithms run in O(nm) time. In addition, we present a variant that exploits graph separators to arrive at a run time of O(n w_d^2 + n^2 s_d) on general graphs, where s_d <= w_d is the size of the largest minimal separator induced by the vertex ordering d. We show empirically that on both constructed and realistic benchmarks, in many cases the algorithms outperform Floyd-Warshall's as well as Johnson's algorithm, which represent the current state of the art with a run time of O(n^3) and O(nm + n^2 log n), respectively. Our algorithms can be used for spatial and temporal reasoning, such as for the Simple Temporal Problem, which underlines their relevance to the planning and scheduling community.

Local consistency techniques such as k-consistency are a key component of specialised solvers for constraint satisfaction problems. In this paper we show that the power of using k-consistency techniques on a constraint satisfaction problem is precisely captured by using a particular inference rule, which we call negative-hyper-resolution, on the standard direct encoding of the problem into Boolean clauses. We also show that current clause-learning SAT-solvers will discover in expected polynomial time any inconsistency that can be deduced from a given set of clauses using negative-hyper-resolvents of a fixed size. We combine these two results to show that, without being explicitly designed to do so, current clause-learning SAT-solvers efficiently simulate k-consistency techniques, for all fixed values of k. We then give some experimental results to show that this feature allows clause-learning SAT-solvers to efficiently solve certain families of constraint problems which are challenging for conventional constraint-programming solvers.

Planning as satisfiability is a principal approach to planning with many eminent advantages. The existing planning as satisfiability techniques usually use encodings compiled from STRIPS. We introduce a novel SAT encoding scheme (SASE) based on the SAS+ formalism. The new scheme exploits the structural information in SAS+, resulting in an encoding that is both more compact and efficient for planning. We prove the correctness of the new encoding by establishing an isomorphism between the solution plans of SASE and that of STRIPS based encodings. We further analyze the transition variables newly introduced in SASE to explain why it accommodates modern SAT solving algorithms and improves performance. We give empirical statistical results to support our analysis. We also develop a number of techniques to further reduce the encoding size of SASE, and conduct experimental studies to show the strength of each individual technique. Finally, we report extensive experimental results to demonstrate significant improvements of SASE over the state-of-the-art STRIPS based encoding schemes in terms of both time and memory efficiency.