Ramón Béjar

Sensor networks and distributed CSP: communication, computation and complexity

We introduce SensorDCSP, a naturally distributed benchmark based on a real-world application that arises in the context of networked distributed systems. In order to study the performance of Distributed CSP (DisCSP) algorithms in a truly distributed setting, we use a discrete-event network simulator, which allows us to model the impact of different network traffic conditions on the performance of the algorithms. We consider two complete DisCSP algorithms: asynchronous backtracking (ABT) and asynchronous weak commitment search (AWC), and perform performance comparison for these algorithms on both satisfiable and unsatisfiable instances of SensorDCSP. We found that random delays (due to network traffic or in some cases actively introduced by the agents) combined with a dynamic decentralized restart strategy can improve the performance of DisCSP algorithms. In addition, we introduce GSensorDCSP, a plain-embedded version of SensorDCSP that is closely related to various real-life dynamic tracking systems. We perform both analytical and empirical study of this benchmark domain. In particular, this benchmark allows us to study the attractiveness of solution repairing for solving a sequence of DisCSPs that represent the dynamic tracking of a set of moving objects.

On the Complexity of Distributed Self-Configuration in Wireless Networks

We consider three distributed configuration tasks that arise in the setup and operation of multi-hop wireless networks: partition into coordinating cliques, Hamiltonian cycle formation and conflict-free channel allocation. We show that the probabilities of accomplishing these tasks undergo zero-one phase transitions with respect to the transmission range of individual nodes. We model these tasks as distributed constraint satisfaction problems (DCSPs) and show that, even though they are NP-hard in general, these problems can be solved efficiently on average when the network is operated sufficiently far from the transition region. Phase transition analysis is shown to be a useful mechanism for quantifying the critical range of energy and bandwidth resources needed for the scalable performance of self-configuring wireless networks.

Capturing Structure with Satisfiability

We present Regular-SAT, an extension of Boolean Satisfiability basedon a class of many-valuedCNF formulas. Regular-SAT shares many properties with Boolean SAT, which allows us to generalize some of the best known SAT results and apply them to Regular-SAT. In addition, Regular-SAT has a number of advantages over Boolean SAT. Most importantly, it produces more compact encodings that capture problem structure more naturally. Furthermore, its simplicity allows us to develop Regular-SAT solvers that are competitive with SAT and CSP procedures. We present a detailed performance analysis of Regular-SAT on several benchmark domains. These results show a clear computational advantage of using a Regular-SAT approach over a pure Boolean SAT or CSP approach, at least on the domains under consideration. We therefore believe that an approach basedon Regular-SAT provides a compelling intermediate approach between SAT and CSPs, bringing together some of the best features of each paradigm.

Phase Transitions in the Regular Random 3-SAT Problem

In this paper we investigate phase transitions in the random 3-SAT problem but we move from the usual setting of classical logic to the more general setting of multiple-valued logics. We deal with regular CNF formulas and use a generalized Davis-Putnam (DP) procedure for testing their satisfiability. We establish the location of the threshold for different cardinalities of the truth value set and show experimentally that the location of the threshold increases logarithmically in the cardinality of the truth value set. We also provide a theoretical explanation of this fact. The DP procedure and the classical random 3-SAT problem appear to be a particular case of our approach.

Solving Combinatorial Problems with Regular Local Search Algorithms

In this paper we describe new local secirch algorithms for regular CNP formulcis and investigate their suitability for solving problems from the dom2uns of graph coloring and sports scheduling. First, we define suitable encodings for such problems in the logic of regular CNF formulas. Second, we describe Regular-GSAT and Regular-WSAT, as well as some varisuits, which are a natured generalization of two prominent local search algorithms - GSAT and WSAT - used to solve the prepositional satisfiability (SAT) problem in classical logic. Third, we report on experimented results that demonstrate that encoding graph coloring and sports scheduling problems as instances of the SAT problem in regular CNF formulas and then solving these instances with local search algorithms can outperform or compete with state-of-the-art approciches to solving hard combinatorial problems.

The satisfiability problem in regular CNF-formulas

Abstract In this paper we deal with the propositional satisfiability (SAT) problem for a kind of multiple-valued clausal forms known as regular CNF-formulas and extend some known results from classical logic to this kind of formulas. We present a Davis–Putnam-style satisfiability checking procedure for regular CNF-formulas equipped with suitable data structures and prove its completeness. Then, we describe a series of experiments for regular random 3-SAT instances. We observe that, for the regular 3-SAT problem with this procedure, there exists a threshold of the ratio of clauses to variables such that (i) the most computationally difficult instances tend to be found near the threshold, (ii) there is a sharp transition from satisfiable to unsatisfiable instances at the threshold and (iii) the value of the threshold increases as the number of truth values considered increases. Instances in the hard part provide benchmarks for the evaluation of regular satisfiability solvers.

A Comparison of Systematic and Local Search Algorithms for Regular CNF Formulas

This paper reports on a series of experiments performed with the aim of comparing the performance of Regular-DP and Regular-GSAT. Regular-DP is a Davis-Putnam-style procedure for solving the propositional satisfiability problem in regular CNF formulas (regular SAT). Regular-GSAT is a GSAT-style procedure for finding satisfying interpretations in regular CNF formulas. Our experimental results provide experimental evidence that Regular-GSAT outperforms Regular-DP on computationally difficult regular random 3-SAT instances, and suggest that local search methods can extend the range and size of satisfiability problems that can be efficiently solved in many-valued logics.

Edge Matching Puzzles as Hard SAT/CSP Benchmarks

Recently, edge matching puzzles, an NP-complete problem, have received, thanks to money-prized contests, considerable attention from wide audiences. This paper studies edge matching puzzles focusing on providing generation models of problem instances of variable hardness and on its resolution through the application of SAT and CSP techniques. From the generation side, we also identify the phase transition phenomena for each model. As solving methods, we employ both; SAT solvers through the translation to a SAT formula, and two ad-hoc CSP solvers we have developed, with different levels of consistency, employing generic and specialized heuristics. Finally, we conducted an extensive experimental investigation to identify the hardest generation models and the best performing solving techniques.

Optimizing Energy Consumption in Automated Vacuum Waste Collection Systems

Automated vacuum waste collection (AVWC) uses air suction on a closed network of underground pipes to transport waste from the drop off points scattered throughout the city to a central collection point, reducing greenhouse gas emissions and the inconveniences of conventional methods (odors, noise). Since a significant part of the cost of operating AVWC systems is energy consumption, we have started a project, together with a company that builds and installs such systems, with the aim of applying constraint programming technology to schedule the daily emptying sequences of the drop off points in such a way that energy consumption is minimized. In this paper we describe how the problem of deciding the drop off points that should be emptied at a given time can be modeled as a constraint integer programming (CIP) problem. Moreover, we report on experiments using real data from AVWC systems installed in different cities that provide empirical evidence that CIP offers a suitable technology for reducing energy consumption in AVWC.

Using Answer Set Programming for an Scalable Implementation of Defeasible Argumentation

In previous works, a recursive warrant semantics for Defeasible Logic Programming extended with levels of possibilistic uncertainty for defeasible rules was introduced. The resulting argumentation framework, called RP-DeLP, is based on a general notion of collective (non-binary) conflict among arguments allowing to ensure direct and indirect consistency properties with respect to the strict knowledge. In this paper we propose an efficient and scalable implementation of an interpreter for RP-DeLP using Answer Set Programming (ASP) encodings for the two main queries of the system: looking for valid arguments and finding collective conflicts among arguments. We perform an experimental evaluation of our ASP approach and we compare the results with a previously proposed SAT based approach. The results show that with ASP we are able to scale up to bigger problem instances.