Learning Bayesian networks is often cast as an optimization problem, where the computational task is to find a structure that maximizes a statistically motivated score. By and large, existing learning tools address this optimization problem using standard heuristic search techniques. Since the search space is extremely large, such search procedures can spend most of the time examining candidates that are extremely unreasonable. This problem becomes critical when we deal with data sets that are large either in the number of instances, or the number of attributes. In this paper, we introduce an algorithm that achieves faster learning by restricting the search space. This iterative algorithm restricts the parents of each variable to belong to a small subset of candidates. We then search for a network that satisfies these constraints. The learned network is then used for selecting better candidates for the next iteration. We evaluate this algorithm both on synthetic and real-life data. Our results show that it is significantly faster than alternative search procedures without loss of quality in the learned structures. 1

Conjunctive-query containment is recognized as a fundamental problem in database query evaluation and optimization. At the same time, constraint satisfaction is recognized as a fundamental problem in artificial intelligence. What do conjunctive-query containment and constraint satisfaction have in common? Our main conceptual contribution in this paper is to point out that, despite their very different formulation, conjunctive-query containment and constraint satisfaction are essentially the same problem. The reason is that they can be recast as the following fundamental algebraic problem: given two finite relational structures A and B, is there a homomorphism h : A ! B? As formulated above, the homomorphism problem is uniform in the sense that both relational structures A and B are part of the input. By fixing the structure B, one obtains the following non-uniform problem: given a finite relational structure A, is there a homomorphism h : A ! B? In general, non-uniform tractability results do not uniformize. Thus, it is natural to ask: which tractable cases of non-uniform tractability results for constraint satisfaction and conjunctive-query containment do uniformize? Our main technical contribution in this paper is to show that several cases of tractable non-uniform constraint satisfaction problems do indeed uniformize. We exhibit three non-uniform tractability results that uniformize and, thus, give rise to polynomial-time solvable cases of constraint satisfaction and conjunctive-query containment.

A number of efficient methods for evaluating first-order and monadic-second order queries on finite relational structures are based on tree-decompositions of structures or queries. We systematically study these methods. In the first part of the paper we consider arbitrary formulas on tree-like structures. We generalize a theorem of Courcelle [8] by showing that on structures of bounded tree-width a monadic second-order formula (with free first- and second-order variables) can be evaluated in time linear in the structure size plus the size of the output. In the second part we study tree-like formulas on arbitrary structures. We generalize the notions of acyclicity and bounded tree-width from conjunctive queries to arbitrary first-order formulas in a straightforward way and analyze the complexity of evaluating formulas of these fragments. Moreover, we show that the acyclic and bounded tree-width fragments have the same expressive power as the wellknown guarded fragment and the finite-variable fragments of first-order logic, respectively.

. We introduce the concept of a class of graphs being locally tree-decomposable. There are numerous examples of locally treedecomposable classes, among them the class of planar graphs and all classes of bounded valence or of bounded tree-width. We show that for each locally tree-decomposable class C of graphs and for each property ' of graphs that is denable in rst-order logic, there is a linear time algorithm deciding whether a given graph G 2 C has property '. 1 Introduction It is an important task in the theory of algorithms to nd feasible instances of otherwise intractable algorithmic problems. A notion that has turned out to be extremely useful in this context is that of tree-width of a graph. 3-Colorability, Hamiltonicity, and many other NP-complete properties of graphs can be decided in linear time when restricted to graphs whose tree-width is bounded by a xed constant (see [Bod97] for a survey). Courcelle [Cou90] proved a meta-theorem, which easily implies numer...

An information retrieval (IR) engine can rank documents based on textual proximityofkeywords within each document. In this paper we apply this notion to search across an entire database for objects that are \near " other relevant objects. Proximity search enables simple \focusing " queries based on general relationships among objects, helpful for interactive query sessions. We view the database as a graph, with data in vertices (objects) and relationships indicated by edges. Proximity is dened based on shortest paths between objects. We have implemented a prototype search engine that uses this model to enable keyword searches over databases, and we have found it very e ective for quickly nding relevant information. Computing the distance between objects in a graph stored on disk can be very expensive. Hence, we show how to build compact indexes that allow us to quickly nd the distance between objects at search time. Experiments show that our algorithms are e-cient and scale well. 1

We construct a polynomial-time algorithm to approximate the branch-width of certain symmetric submodular functions, and give two applications. The first is to graph “clique-width”. Clique-width is a measure of the difficulty of decomposing a graph in a kind of tree-structure, and if a graph has clique-width at most k then the corresponding decomposition of the graph is called a “k-expression”. We find (for fixed k) an O(n 9 log n)-time algorithm that, with input an n-vertex graph, outputs either a (2 3k+2 − 1)expression for the graph, or a true statement that the graph has clique-width at least k + 1. (The best earlier algorithm algorithm, by Johansson [13], constructed a k log n-expression for graphs of clique-width at most k.) It was already known that several graph problems, NPhard on general graphs, are solvable in polynomial time if the input graph comes equipped with a k-expression (for fixed k). As a consequence of our algorithm, the same conclusion follows under the weaker hypothesis that the input graph has clique-width at most k (thus, we no longer need to be provided with an explicit k-expression). Another application is to the area of matroid branch-width. For fixed k, we find an O(n 4)time algorithm that, with input an n-element matroid in terms of its rank oracle, either outputs a branch-decomposition of width at most 3k − 1 or a true statement that the matroid has branch-width at least k + 1. The previous algorithm by Hliněn´y [11] was only for representable matroids.

We present an algorithm that induces a class of models with thin junction trees---models that are characterized by an upper bound on the size of the maximal cliques of their triangulated graph. By ensuring that the junction tree is thin, inference in our models remains tractable throughout the learning process. This allows both an efficient implementation of an iterative scaling parameter estimation algorithm and also ensures that inference can be performed efficiently with the final model. We illustrate the approach with applications in handwritten digit recognition and DNA splice site detection.

We systematically investigate the connections between constraint satisfaction problems, structures of bounded treewidth, and definability in logics with a finite number of variables. We first show that constraint satisfaction problems on inputs of treewidth less than k are definable using Datalog programs with at most k variables; this provides a new explanation for the tractability of these classes of problems. After this, we investigate constraint satisfaction on inputs that are homomorphically equivalent to structures of bounded treewidth.

We demonstrate a new connection between fixed-parameter tractability and approximation algorithms for combinatorial optimization problems on planar graphs and their generalizations. Specifically, we extend the theory of so-called “bidimensional” problems to show that essentially all such problems have both subexponential fixed-parameter algorithms and PTASs. Bidimensional problems include e.g. feedback vertex set, vertex cover, minimum maximal matching, face cover, a series of vertex-removal problems, dominating set, edge dominating set, r-dominating set, diameter, connected dominating set, connected edge dominating set, and connected r-dominating set. We obtain PTASs for all of these problems in planar graphs and certain generalizations; of particular interest are our results for the two well-known problems of connected dominating set and general feedback vertex set for planar graphs and their generalizations, for which PTASs were not known to exist. Our techniques generalize and in some sense unify the two main previous approaches for designing PTASs in planar graphs, namely, the Lipton-Tarjan separator approach [FOCS’77] and the Baker layerwise decomposition approach [FOCS’83]. In particular, we replace the notion of separators with a more powerful tool from the bidimensionality theory, enabling the first approach to apply to a much broader class of minimization problems than previously possible; and through the use of a structural backbone and thickening of layers we demonstrate how the second approach can be applied to problems with a “nonlocal” structure.

We prove that every n-vertex graph G with pathwidth pw(G) has a three-dimensional straight-line grid drawing with O(pw(G) n) volume. Thus for