Kostas Stergiou

Domain filtering consistencies for non-binary constraints

In non-binary constraint satisfaction problems, the study of local consistencies that only prune values from domains has so far been largely limited to generalized arc consistency or weaker local consistency properties. This is in contrast with binary constraints where numerous such domain filtering consistencies have been proposed. In this paper we present a detailed theoretical, algorithmic and empirical study of domain filtering consistencies for non-binary problems. We study three domain filtering consistencies that are inspired by corresponding variable based domain filtering consistencies for binary problems. These consistencies are stronger than generalized arc consistency, but weaker than pairwise consistency, which is a strong consistency that removes tuples from constraint relations. Among other theoretical results, and contrary to expectations, we prove that these new consistencies do not reduce to the variable based definitions of their counterparts on binary constraints. We propose a number of algorithms to achieve the three consistencies. One of these algorithms has a time complexity comparable to that for generalized arc consistency despite performing more pruning. Experiments demonstrate that our new consistencies are promising as they can be more efficient than generalized arc consistency on certain non-binary problems.

Algorithms for Quantified Constraint Satisfaction Problems

Many propagation and search algorithms have been developed for constraint satisfaction problems (CSPs). In a standard CSP all variables are existentially quantified. The CSP formalism can be extended to allow universally quantified variables, in which case the complexity of the basic reasoning tasks rises from NP-complete to PSPACE-complete. Such problems have, so far, been studied mainly in the context of quantified Boolean formulae. Little work has been done on problems with discrete non-Boolean domains. We attempt to fill this gap by extending propagation and search algorithms from standard CSPs to the quantified case. We also show how the notion of value interchangeability can be exploited to break symmetries and speed up search by orders of magnitude. Finally, we test experimentally the algorithms and methods proposed.

Overlay networks for task allocation and coordination in dynamic large-scale networks of cooperative agents

This work proposes a method for allocating temporally interdependent tasks to homogeneous or heterogeneous cooperative agents in dynamic large-scale networks. This method views searching, task allocation and scheduling as an integrated problem that has to be efficiently solved in such networks. Solving the general problem optimally in a decentralized way is very hard and can only be solved by a centralized method, be approximated by means of heuristics, or by relaxations of the original problem. Our method facilitates effective searching through the dynamic assignment of gateway roles to agents and the exploitation of routing indices. In combination to searching, it exploits distributed constraint satisfaction techniques and dynamic re-organization of agent teams to efficiently handle the allocation of complex tasks with interdependent subtasks.

Heuristics for dynamically adapting propagation in constraint satisfaction problems

Building adaptive constraint solvers is a major challenge in constraint programming. An important line of research towards this goal is concerned with ways to dynamically adapt the propagation method applied on the constraints of the problem during search. In this paper we present a heuristic approach to this problem based on the monitoring of propagation events like value deletions and domain wipeouts. We develop a number of heuristics that allow the constraint solver to dynamically switch between a weaker and cheap local consistency and a stronger, but more expensive one, when certain conditions are met. The success of this approach is based on the observation that propagation events for individual constraints in structured problems mostly occur in clusters of nearby revisions. Hence, parts of the search space where certain constraints are highly active can be identified and exploited paving the way for the informed use of constraint propagation techniques. In this paper we first give some experimental results displaying the clustering of propagation events in structured binary CSPs. Then we present simple heuristics that exploit this clustering to efficiently switch between different local consistencies on individual constraints during search. Finally, we make an experimental study on various binary CSPs demonstrating the effectiveness of the proposed heuristics.

Capturing Semantics Towards Automatic Coordination of Domain Ontologies

Existing efforts on ontology mapping, alignment and merging vary from methodological and theoretical frameworks, to methods and tools that support the semi-automatic coordination of ontologies. However, only latest research efforts “touch” on the mapping /merging of ontologies using the whole breadth of available knowledge. Addressing this issue, the work presented in this paper is based on the HCONE-merge approach that makes use of the intended informal interpretations of concepts by mapping them to WordNet senses using lexical semantic indexing (LSI). Our aim is to explore the level of human involvement required for mapping concepts of the source ontologies to their intended interpretations. We propose a series of methods for ontology mapping/merging with varying degrees of human involvement and evaluate them experimentally. We conclude that, although an effective fully automated process is not attainable, we can reach a point where the process of ontology mapping/merging can be carried out efficiently with minimum human involvement.

Solving quantified constraint satisfaction problems

We make a number of contributions to the study of the Quantified Constraint Satisfaction Problem (QCSP). The QCSP is an extension of the constraint satisfaction problem that can be used to model combinatorial problems containing contingency or uncertainty. It allows for universally quantified variables that can model uncertain actions and events, such as the unknown weather for a future party, or an opponents next move in a game. In this paper we report significant contributions to two very different methods for solving QCSPs. The first approach is to implement special purpose algorithms for QCSPs; and the second is to encode QCSPs as Quantified Boolean Formulas and then use specialized QBF solvers. The discovery of particularly effective encodings influenced the design of more effective algorithms: by analyzing the properties of these encodings, we identify the features in QBF solvers responsible for their efficiency. This enables us to devise analogues of these features in QCSPs, and implement them in special purpose algorithms, yielding an effective special purpose solver, QCSP-Solve. Experiments show that this solver and a highly optimized QBF encoding are several orders of magnitude more efficient than the initially developed algorithms. A final, but significant, contribution is the identification of flaws in simple methods of generating random QCSP instances, and a means of generating instances which are not known to be flawed.

Learning How to Propagate Using Random Probing

In constraint programming there are often many choices regarding the propagation method to be used on the constraints of a problem. However, simple constraint solvers usually only apply a standard method, typically (generalized) arc consistency, on all constraints throughout search. Advanced solvers additionally allow for the modeler to choose among an array of propagators for certain (global) constraints. Since complex interactions exist among constraints, deciding in the modelling phase which propagation method to use on given constraints can be a hard task that ideally we would like to free the user from. In this paper we propose a simple technique towards the automation of this task. Our approach exploits information gathered from a random probing preprocessing phase to automatically decide on the propagation method to be used on each constraint. As we demonstrate, data gathered though probing allows for the solver to accurately differentiate between constraints that offer little pruning as opposed to ones that achieve many domain reductions, and also to detect constraints and variables that are amenable to certain propagation methods. Experimental results from an initial evaluation of the proposed method on binary CSPs demonstrate the benefits of our approach.

Repair-based methods for Quantified CSPs

The Quantified CSP (QCSP) is a generalization of the CSP which allows for universally quantified variables. For each possible sequence of assignments to such variables, we have to find a way to set the values of the remaining, existentially quantified, variables so that all the constraints are satisfied. Such problems arise in areas such as planning under uncertainty, model checking, and adversary game playing. QCSPs are starting to attract interest following the development of numerous efficient solvers for the closely related area of QBF. Two approaches have been studied so far; the encoding of QCSPs into QBF, and the generalization of well-known search procedures for CSPs, like FC and MAC, to the quantified case. In this paper we introduce a new approach which utilizes repair-based techniques. We describe a framework for a QCSP solver in which complete and incomplete repair-based methods can be incorporated. We also evaluate such a solver that applies backtracking and local search methods based on the min-conflicts heuristic. Experimental results demonstrate that even simple repair-based techniques can outperform the state-of-the-art solver QCSP-Solve.

Strong Inverse Consistencies for Non-Binary CSPs

Domain filtering local consistencies, such as inverse consistencies, that only delete values and do not add new constraints are particularly useful in constraint programming. Although many such consistencies for binary constraints have been proposed and evaluated, the situation with non-binary constraints is quite different. Only very recently have domain filtering consistencies stronger than GAC started to attract interest. Following this line of research, we define a number of strong inverse consistencies for non-binary constraints and compare their pruning power. We show that three of these consistencies are equivalent to maxRPC in binary CSPs while another is equivalent to PIC. We also describe a generic algorithm for inverse consistencies in non-binary CSPs and show how it can be instantiated to enforce some of the proposed consistencies. Finally, we make a preliminary empirical study that demonstrates the potential of strong inverse consistencies.

Restricted Path Consistency Revisited

Restricted path consistency RPC is a strong local consistency for binary constraints that was proposed 20 years ago and was identified as a promising alternative to arc consistency AC in an early experimental study of local consistencies for binary constraints. However, and in contrast to other strong local consistencies such as SAC and maxRPC, it has been neglected since then. In this paper we revisit RPC. First, we propose RPC3, a new lightweight RPC algorithm that is very easy to implement and can be efficiently applied throughout search. Then we perform a wide experimental study of RPC3 and a light version that achieves an approximation of RPC, comparing them to state-of-the-art AC and maxRPC algorithms. Experimental results clearly show that restricted RPC is by far more efficient than both AC and maxRPC when applied throughout search. These results strongly suggest that it is time to reconsider the established perception that MAC is the best general purpose method for solving binary CSPs.