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We propose a novel incomplete cooperative algorithm for distributed constraint optimization problems (DCOPs) denoted as Cooperative Constraint Approximation (CoCoA). The key strategy of the algorithm is to use a semi-greedy approach in which knowledge is distributed amongst neighboring agents, and assigning a value only once instead of an iterative approach. Furthermore, CoCoA uses a unique-first approach to improve the solution quality. It is designed such that it can solve DCOPs as well as Asymmetric DCOPS, with only few messages being communicated between neighboring agents. Experimentally, through evaluating graph coloring problems, randomized (A)DCOPs, and a sensor network communication problem, we show that CoCoA is able to very quickly find solutions of high quality with a smaller communication overhead than state-of-the-art DCOP solvers such as DSA, MGM-2, ACLS, MCS-MGM and Max-Sum. In our asymmetric use case problem of a sensor network, we show that CoCoA not only finds the best solution, but also finds this solution faster than any other algorithm.
The study of broken-triangles is becoming increasingly ambitious, by both solving constraint satisfaction problems (CSPs) in polynomial time and reducing search space size through value merging or variable elimination. Considerable progress has been made in extending this important concept, such as dual broken-triangle and weakly broken-triangle, in order to maximize the number of captured tractable CSP instances and/or the number of merged values. Specifically, m-wBTP allows to merge more values than BTP. k-BTP, WBTP and m-BTP permit to capture more tractable instances than BTP. Here, we introduce a new weaker form of BTP, which will be called m-fBTP for flexible broken-triangle property. m-fBTP allows on the one hand to eliminate more variables than BTP while preserving satisfiability and on the other to define new bigger tractable class for which arc consistency is a decision procedure. Likewise, m-fBTP permits to merge more values than BTP but less than m-wBTP.
Table constraints are very useful for modeling combinatorial constrained problems, and thus play an important role in Constraint Programming (CP). During the last decade, many algorithms have been proposed for enforcing the property known as Generalized Arc Consistency (GAC) on such constraints. A state-of-the art GAC algorithm called Compact-Table (CT), which has been recently proposed, significantly outperforms all previously proposed algorithms. In this paper, we extend this algorithm in order to deal with both short supports and negative tables, i.e., tables that contain universal values and conflicts. Our experimental results show the interest of using this fast general algorithm.
We present a SAT-based approach for solving the modal logic S5-satisfiability problem. That problem being NP-complete, the translation into SAT is not a surprise. Our contribution is to greatly reduce the number of propositional variables and clauses required to encode the problem. We first present a syntactic property called diamond degree. We show that the size of an S5-model satisfying a formula phi can be bounded by its diamond degree. Such measure can thus be used as an upper bound for generating a SAT encoding for the S5-satisfiability of that formula. We also propose a lightweight caching system which allows us to further reduce the size of the propositional formula.We implemented a generic SAT-based approach within the modal logic S5 solver S52SAT. It allowed us to compare experimentally our new upper-bound against previously known one, i.e. the number of modalities of phi and to evaluate the effect of our caching technique. We also compared our solver againstexisting modal logic S5 solvers. The proposed approach outperforms previous ones on the benchmarks used. These promising results open interesting research directions for the practical resolution of others modal logics (e.g. K, KT, S4)
We study algorithms for fragments of first order logic ex- tended with counting quantifiers, which are known to be highly complex in general. We propose a fragment over unary predicates that is NP-complete and for which there is a nor- mal form where Counting Quantification sentences have a single Unary predicate, thus call it the CQU fragment. We provide an algebraic formulation of the CQU satisfiability problem in terms of Integer Linear Programming based on which two algorithms are proposed, a direct reduction to SAT instances and an Integer Linear Programming version extended with a column generation mechanism. The latter is shown to lead to a viable implementation and experiments shows this algorithm presents a phase transition behavior.
Recent developments of efficient propagators, operations and creation methods for MDDs allow us to directly build efficient MDD-based models, without the need for intermediate data structures. In this paper, we take another step in this direction by improving the propagators of cost MDDs. In addition, we introduce a soft MDD propagator in order to deal with unsatisfiable problems. This directly offers cost and soft versions for table constraints and any constraints which can be represented by an MDD (regular, slide, knapsack...).
For non-expert users, a textual query is the most popular and simple means for communicating with a retrieval or question answering system.However, there is a risk of receiving queries which do not match with the background knowledge.Query expansion and query rewriting are solutions for this problem but they are in danger of potentially yielding a large number of irrelevant words, which in turn negatively influences runtime as well as accuracy.In this paper, we propose a new method for automatic rewriting input queries on graph-structured RDF knowledge bases.We employ a Hidden Markov Model to determine the most suitable derived words from linguistic resources.We introduce the concept of triple-based co-occurrence for recognizing co-occurred words in RDF data.This model was bootstrapped with three statistical distributions.Our experimental study demonstrates the superiority of the proposed approach to the traditional n-gram model.
Single-elimination tournaments (or knockout tournaments) are a popular format in sports competitions that is also widely used for decision making and elections. In this paper we study the algorithmic problem of manipulating the outcome of a tournament. More specifically, we study the problem of finding a seeding of the players such that a certain player wins the resulting tournament. The problem is known to be NP-hard in general. In this paper we present an algorithm for this problem that exploits structural restrictions on the tournament. More specifically, we establish that the problem is fixed-parameter tractable when parameterized by the size of a smallest feedback arc set of the tournament (interpreting the tournament as an oriented complete graph). This is a natural parameter because most problems on tournaments (including this one) are either trivial or easily solvable on acyclic tournaments, leading to the question — what about nearly acyclic tournaments or tournaments with a small feedback arc set? Our result significantly improves upon a recent algorithm by Aziz et al. (2014) whose running time is bounded by an exponential function where the size of a smallest feedback arc set appears in the exponent and the base is the number of players.
Recently, a number of non-uniform random satisfiability models have been proposed that are closer to practical satisfiability problems in some characteristics. In contrast to uniform random Boolean formulas, scale-free formulas have a variable occurrence distribution that follows a power law. It has been conjectured that such a distribution is a more accurate model for some industrial instances than the uniform random model. Though it seems that there is already an awareness of a threshold phenomenon in such models, there is still a complete picture lacking. In contrast to the uniform model, the critical density threshold does not lie at a single point, but instead exhibits a functional dependency on the power-law exponent. For scale-free formulas with clauses of length k=2, we give a lower bound on the phase transition threshold as a function of the scaling parameter. We also perform computational studies that suggest our bound is tight and investigate the critical density for formulas with higher clause lengths. Similar to the uniform model, on formulas with k>=3, we find that the phase transition regime corresponds to a set of formulas that are difficult to solve by backtracking search.
A backbone of a boolean formula F is a collection S of its variables for which there is a unique partial assignment aSsuch that F[aS] is satisfiable (Monasson et al. 1999; Williams, Gomes, and Selman 2003). This paper studies the nontransparency of backbones. We show that, under the widely believed assumption that integer factoring is hard, there exist sets of boolean formulas that have obvious, nontrivial backbones yet finding the values, aS, of those backbones is intractable. We also show that, under the same assumption, there exist sets of boolean formulas that obviously have large backbones yet producing such a backbone S is intractable. Further, we show that if integer factoring is not merely worst-case hard but is frequently hard, as is widely believed, then the frequency of hardness in our two results is not too much less than that frequency.
We analyze to what extent the random SAT and Max-SAT problems differ in their properties. Our findings suggest that for random k-CNF with ratio in a certain range, Max-SAT can be solved by any SAT algorithm with subexponential slowdown, while for formulae with ratios greater than some constant, algorithms under the random walk framework require substantially different heuristics. In light of these results, we propose a novel probabilistic approach for random Max-SAT called ProMS. Experimental results illustrate that ProMS outperforms many state-of-the-art local search solvers on random Max-SAT benchmarks.
Random constraint satisfaction problems (CSPs) have been widely studied both in AI and complexity theory. Empirically and theoretically, many random CSPs have been shown to exhibit a phase transition. As the ratio of constraints to variables passes certain thresholds, they transition from being almost certainly satisfiable to unsatisfiable. The exact location of this threshold has been thoroughly investigated, but only for certain common classes of constraints. In this paper, we present new bounds for the location of these thresholds in boolean CSPs. Our main contribution is that our bounds are fully general, and apply to any fixed constraint function that could be used to generate an ensemble of random CSPs. These bounds rely on a novel Fourier analysis and can be easily computed from the Fourier spectrum of a constraint function. Our bounds are within a constant factor of the exact threshold location for many well-studied random CSPs. We demonstrate that our bounds can be easily instantiated to obtain thresholds for many constraint functions that had not been previously studied, and evaluate them experimentally.
When a small pattern graph does not occur inside a larger target graph, we can ask how to find "as much of the pattern as possible" inside the target graph. In general, this is known as the maximum common subgraph problem, which is much more computationally challenging in practice than subgraph isomorphism. We introduce a restricted alternative, where we ask if all but k vertices from the pattern can be found in the target graph. This allows for the development of slightly weakened forms of certain invariants from subgraph isomorphism which are based upon degree and number of paths. We show that when k is small, weakening the invariants still retains much of their effectiveness. We are then able to solve this problem on the standard problem instances used to benchmark subgraph isomorphism algorithms, despite these instances being too large for current maximum common subgraph algorithms to handle. Finally, by iteratively increasing k, we obtain an algorithm which is also competitive for the maximum common subgraph
We introduce the problem Max#SAT, an extension of model counting (#SAT). Given a formula over sets of variables X, Y, and Z, the Max#SAT problem is to maximize over the variables X the number of assignments to Y that can be extended to a solution with some assignment to Z. We demonstrate that Max#SAT has applications in many areas, showing how it can be used to solve problems in probabilistic inference (marginal MAP), planning, program synthesis, and quantitative information flow analysis. We also give an algorithm which by making only polynomially many calls to an NP oracle can approximate the maximum count to within any desired multiplicative error. The NP queries needed are relatively simple, arising from recent practical approximate model counting and sampling algorithms, which allows our technique to be effectively implemented with a SAT solver. Through several experiments we show that our approach can be successfully applied to interesting problems.