Counting the exact number of solutions of a Constraint Satisfaction Problem (CSP) is an important but difficult task. To overcome this difficulty, the techniques proposed in the literature organize the search process along a tree decomposition of the CSP, where all the extensions of a given partial solution over different branches of the tree are first independently counted in each branch before their numbers can be multiplied. We observe that this count is zero when any of the branches has no solution. We propose witnessbased search, which first ensures the existence of a solution (i.e., witness) in each branch before starting the counting. We empirically establish the benefits of our technique in the context of the BTD and AND/OR search graphs.

Constraint Satisfaction is a flexible paradigm for modeling many decision problems in Engineering, Computer Science, and Management. Constraint Satisfaction Problems (CSPs) are in general NP -complete and are usually solved with search. Research has identified various islands of tractability, which enable solving certain CSPs with backtrack-free search. For example, one sufficient condition for tractability relates the consistency level of a CSP to treewidth of the CSP's constraint network. However, enforcing higher levels of consistency on a CSP may require the addition of constraints, thus altering the topology of the constraint network and increasing its treewidth. This thesis addresses the following question: How close can we approach in practice the tractability guaranteed by the relationship between the level of consistency in a CSP and the treewidth of its constraint network? To achieve "practical tractability," this thesis proposes: (1) New local consistency properties and algorithms for enforcing them without adding constraints or altering the network's topology; (2) Methods to enforce these consistency properties on the clusters of a tree decomposition of the CSP; and (3) Schemes to bolster the propagation between the clusters of the tree decomposition. Our empirical evaluation shows that our techniques allow us to achieve practical tractability for a wide range of problems, and that they are both applicable (i.e., require acceptable time and space) and useful (i.e., outperform other consistency properties). We theoretically characterize the proposed consistency properties and empirically evaluate our techniques on benchmark problems. Our techniques for higher level consistency exhibit their best performances on difficult benchmark problems. They solve a larger number of difficult problem instances than algorithms enforcing weaker consistency properties, and moreover they solve them in an almost backtrack-free manner.

The tractability of a Constraint Satisfaction Problem (CSP)is guaranteed by a direct relationship between its consistencylevel and a structural parameter of its constraint network suchas the treewidth. This result is not widely exploited in practicebecause enforcing higher-level consistencies can be costlyand can change the structure of the constraint network andincrease its width. Recently, R(*,m)C was proposed as a relational consistency property that does not modify the structureof the graph and, thus, does not affect its width. In this paper,we explore two main strategies, based on a tree decomposition of the CSP, for improving the performance of enforcingR(*,m)C and getting closer to the above tractability condition. Those strategies are: a) localizing the application ofthe consistency algorithm to the clusters of the tree decomposition, and b) bolstering constraint propagation betweenclusters by adding redundant constraints at their separators,for which we propose three new schemes. We characterizethe resulting consistency properties by comparing them, theoretically and empirically, to the original R(*,m)C and thepopular GAC and maxRPWC, and establish the benefits ofour approach for solving difficult problems.

Computing the minimal network of a Constraint Satisfaction Problem (CSP) is a useful and difficult task. Two algorithms, PerTuple and AllSol, were proposed to this end. The performances of these algorithms vary with the problem instance. We use Machine Learning techniques to build a classifier that predicts which of the two algorithms is likely to be more effective.

Our goal is to investigate the definition and application of strong consistency properties on the dual graphs of binary Constraint Satisfaction Problems CSPs. As a first step in that direction, we study the structure of the dual graph of binary CSPs, and show how it can be arranged in a triangle-shaped grid. We then study, in this context, Relational Neighborhood Inverse Consistency RNIC, which is a consistency property that we had introduced for non-binary CSPs [17]. We discuss how the structure of the dual graph of binary CSPs affects the consistency level enforced by RNIC. Then, we compare, both theoretically and empirically, RNIC to Neighborhood Inverse Consistency NIC and strong Conservative Dual Consistency sCDC, which are higher-level consistency properties useful for solving difficult problem instances. We show that all three properties are pairwise incomparable.

Freuder and Elfe [1996] introduced Neighborhood Inverse Consistency (NIC) as a new local consistency property for Constraint Satisfaction Problems (CSPs) that filters the domains of variables. Two advantages of the algorithm for enforcing NIC is that it automatically adapts its filtering power to the local connectivity of the network and has insignificant space overhead. In this document, we discuss Relational Neighborhood Inverse Consistency (RNIC), which is an extension of NIC to filter relations introduced in [Woodward et al., 2011a], how we enhance the propagation effectiveness by reformulating the dual graph of the CSP. We also describe an automated selection policy that outperforms all approaches in a statistically significant manner.

Local consistency properties and algorithms for enforcing them are central to the success of Constraint Processing. Recently, we have demonstrated the importance of higher levels of consistency and the effectiveness of their algorithms for solving difficult problems (Karakashian et al. 2010; Woodward et al. 2011). In this paper, we introduce two reformulation techniques for improving the effectiveness of our algorithm for the relational consistency property R (*, m ) C (Karakashian et al. 2010). Both techniques exploit a tree decomposition of the constraint network of a Constraint Satisfaction Problem (CSP), which is a tree embedding of the network. Our first reformulation technique exploits the structure of the decomposition tree and the state of the backtrack search to omit unnecessary steps from our algorithm and improve its performance. Our second contribution is new relational consistency property called T-R (*, m, z ) C that is strictly stronger than R (*, m ) C. This property is achieved by modifying the structure of the constraint network and adding new redundant constraints to the CSP at the intersection of two vertices of the tree decomposition (Rollon and Dechter 2010). We demonstrate the advantages of the proposed two reformulations for finding all the solutions of a CSP using the technique known as Backtracking with Tree Decomposition (BTD) (Jegou and Terrioux 2003).

Freuder and Elfe (1996) introduced Neighborhood Inverse Consistency (NIC) as a strong local consistency property for binary CSPs. While enforcing NIC can significantly filter the variables domains, the proposed algorithm is too costly to be used on dense graphs or for lookahead during search. In this paper, we introduce and characterize Relational Neighborhood Inverse Consistency (RNIC) as a local consistency property that operates on the dual graph of a non-binary CSP. We describe and characterize a practical algorithm for enforcing it. We argue that defining RNIC on the dual graph unveils unsuspected opportunities to reduce the computational cost of our algorithm and increase its filtering effectiveness. We show how to achieve those effects by modifying the topology of the dual graph, yielding new variations the RNIC property. We also introduce an adaptive strategy to automatically select the appropriate property to enforce given the connectivity of the dual graph. We integrate the resulting techniques as full lookahead strategies in a backtrack search procedure for solving CSPs, and demonstrate the effectiveness of our approach for solving known difficult benchmark problems.

Freuder and Elfe (1996) introduced Neighborhood Inverse Consistency (NIC) as a new local consistency property for binary Constraint Satisfaction Problems (CSPs). Two advantages of the algorithm for enforcing NIC is that it automatically adapts its filtering power to the local connectivity of the network and has insignificant space overhead. However, studies on binary CSPs have shown that enforcing NIC is not effective on sparse graphs and too costly on dense graphs. In (Woodward et al. 2011), we introduced an algorithm for enforcing Relational Neighborhood Inverse Consistency (RNIC), which is an extension of NIC to non-binary CSPs. In this paper, we discuss how we enhance the propagation effectiveness of our algorithm and reduce its computational cost by reformulating the dual graph of the CSP. For that purpose, we describe two reformulation techniques that modify the topology of the dual graph without affecting the solution set of the problem. We present the two reformulations and their combinations, and discuss their effects on the consistency property enforced by the algorithm. We also describe a selection policy that nicely ties together the various components of our approach in a consistent, adaptive framework. Finally, we show that our automated selection policy outperforms all approaches in a statistically significant manner.

Freuder and Elfe (1996) introduced Neighborhood Inverse Consistency (NIC) for binary CSPs. In this paper, we introduce RNIC, the extension of NIC to non-binary CSPs, and describe a practical algorithm for enforcing it. We propose an adaptive strategy to weaken or strengthen this property based on the connectivity of the network. We demonstrate the effectiveness of RNIC as a full lookahead strategy during search for solving difficult benchmark problems.

Consistency properties and algorithms for achieving them are at the heart of the success of Constraint Programming. In this paper, we study the relational consistency property R(*,m)C, which is equivalent to m-wise consistency proposed in relational databases. We also define wR(*,m)C, a weaker variant of this property. We propose an algorithm for enforcing these properties on a Constraint Satisfaction Problem by tightening the existing relations and without introducing new ones. We empirically show that wR(*,m)C solves in a backtrack-free manner all the instances of some CSP benchmark classes, thus hinting at the tractability of those classes.

Substitutability, interchangeability and related concepts in Constraint Programming were introduced approximately twenty years ago and have given rise to considerable subsequent research. We survey this work, classify, and relate the different concepts, and indicate directions for future work, in particular with respect to making connections with research into symmetry breaking. This paper is a condensed version of a larger work in progress.

In this paper, we propose a new algorithm for enforcing relational consistency on every set of k constraints of a finite Constraint Satisfaction Problem (CSP). This algorithm operates by filtering the constraint while leaving the topology of the graph unchanged. We study the resulting relational consistency property and compare it to existing ones. We evaluate the effectiveness of our algorithm in a search procedure for solving CSPs and demonstrate the applicability, effectiveness, and usefulness of enforcing high levels of consistency.

In this document, we describe two tree-based algorithms for computing all k-combinations and k-compositions of a finite set.

Consistency properties and algorithms for achieving them are at the heart of the success of Constraint Programming. For non-binary Constraint Satis- faction Problems (CSPs), the relational-consistency property R(i,j)C of (Dechter and van Beek 1997) may add new non-binary constraints to the constraint network, thus modifying its topology. The domain-filtering properties of (Bessiere et al. 2008) filter the domains of the variables and leave the constr aints un- changed but are restricted to combinations of two constraints. We restate the property of m-wise consistency (Gyssens 1986; Jegou 1993) as relational (∗,m)-consistency, R(∗,m)C. R(∗,m)C ensures that any tuple in a relation is consistent in every combination of m constraints. The main contributions of this document are the design of an algorithm for enforcing R(∗,m)C and the evaluation of its effectiveness in a search procedure so lving CSPs. This document thus establishes the usefulness in practice of higher consistency levels in non-binary CSPs.

We propose a new system that is able to handle the entire Personal Dataspace of a user. A Personal Dataspace includes all data pertaining to a user on all his disks and on remote servers such as network drives, email and web servers. This data is represented by a heterogeneous mix of files, emails, bookmarks, music, pictures, calendar data, personal information streams and so on. State-of-the-art tools such as desktop search engines and desktop operating systems (including the upcoming Vista) are not enough as they neither solve the problem of physical personal information independence (where is my data) nor format and data model independence (how is it stored and which application do I have to use in order to access that data). Our work builds on the visions presented in [DSKB05], which calls for a single system to manage the personal information jungle, and [FHM05], which advocates dataspaces as a new abstraction for information management. In contrast to [FHM05] this paper presents a concrete implementation of a Personal DataSpace Management System (PDSMS) termed iMeMex: integrated memex. We discuss the core architecture of iMeMex and services offered by our system. As we will show, a PDSMS can be seen as a system that occupies the middleground between a search engine, a database management system, and a traditional information integration system. A PDSMS has to bridge these separate worlds and requires: (1) no full control on data, i.e., data may be accessed bypassing the interfaces of a PDSMS, (2) simple keyword search on all data available in a dataspace without performing any semantic data integration, (3) rich querying able to mix structural, attribute, and content predicates, (4) pay-as-you-go integration capabilities, (5) the ability to define arbitrary logical views on all data, (6) durability and consistency guarantees to avoid loss of data assigned to a dataspace, and (7) update capabilities. iMeMex is the first implementation of a PDSMS we are aware of. This paper presents the architecture of iMeMex and reports on the current state of the iMeMex research project at ETH Zurich. ∗This work is partially supported by the Swiss National Science Foundation (SNF) under contract 200021112115.

A Personal Dataspace includes all data pertaining to a user on all his local disks and on remote servers such as network drives, email and web servers. This data is represented by a heterogeneous mix of files, emails, bookmarks, music, pictures, calendar, personal information streams and so on. We demonstrate a new breed of system that is able to handle the entire Personal Dataspace of a user. Our system, named iMeMex (integrated memex), is a first implementation of a Personal DataSpace Management System (PDSMS). Visions for this type of systems have been proposed recently [13, 10, 12, 17]. We showcase how iMeMex allows dataspace navigation across data source/file boundaries, how iMeMex offers rich contextual information on query results and how our system returns best-effort results.

Dataspace management has been recently identified as a new agenda for information management [17, 22] and information integration [23]. In sharp contrast to standard information integration architectures, a dataspace management system is a data-coexistence approach: it does not require any investments in semantic integration before querying services on the data are provided. Rather, a dataspace can be gradually enhanced over time by defining relationships among the data. Defining those integration semantics gradually is termed pay-as-you-go information integration [17], as time and effort (pay) are needed over time (go) to provide integration semantics. The benefits are better query results (gain). This paper is the first to explore pay-as-you-go information integration in dataspaces. We provide a technique for declarative pay-as-you-go information integration named iTrails. The core idea of our approach is to declaratively add lightweight 'hints' (trails) to a search engine thus allowing gradual enrichment of loosely integrated data sources. Our experiments confirm that iTrails can be efficiently implemented introducing only little overhead during query execution. At the same time iTrails strongly improves the quality of query results. Furthermore, we present rewriting and pruning techniques that allow us to scale iTrails to tens of thousands of trail definitions with minimal growth in the rewritten query size.