We show that some common and important global constraints like ALLDIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These decompositions can be easily added to new solvers. They also provide other constraints with access to the state of the propagator by sharing variables. Such sharing can be used to improve propagation between constraints. We report experiments with our decomposition in a pseudo-Boolean solver.

We show that tools from circuit complexity can be used to study decompositions of global constraints. In particular, we study decompositions of global constraints into conjunctive normal form with the property that unit propagation on the decomposition enforces the same level of consistency as a specialized propagation algorithm. We prove that a constraint propagator has a a polynomial size decomposition if and only if it can be computed by a polynomial size monotone Boolean circuit. Lower bounds on the size of monotone Boolean circuits thus translate to lower bounds on the size of decompositions of global constraints. For instance, we prove that there is no polynomial sized decomposition of the domain consistency propagator for the alldiff constraint.

Beside impressive progresses made by SAT solvers over the last ten years, only few works tried to understand why Conflict Directed Clause Learning algorithms (CDCL) are so strong and efficient on most industrial applications. We report in this work a key observation of CDCL solvers behavior on this family of benchmarks and explain it by an unsuspected side effect of their particular Clause Learning scheme. This new paradigm allows us to solve an important, still open, question: How to designing a fast, static, accurate, and predictive measure of new learnt clauses pertinence. Our paper is followed by empirical evidences that show how our new learning scheme improves state-of-the art results by an order of magnitude on both SAT and UNSAT industrial problems.

Many combinatorial optimization problems entail a number of hierarchically dependent optimization problems. An often used solution is to associate a suitably large cost with each individual optimization problem, such that the solution of the resulting aggregated optimization problem solves the original set of optimization problems. This paper starts by studying the package upgradeability problem in software distributions. Straightforward solutions based on Maximum Satisfiability (MaxSAT) and pseudo-Boolean (PB) optimization are shown to be ineffective, and unlikely to scale for large problem instances. Afterwards, the package upgradeability problem is related to multilevel optimization. The paper then develops new algorithms for Boolean Multilevel Optimization (BMO) and highlights a large number of potential applications. The experimental results indicate that the proposed algorithms for BMO allow solving optimization problems that existing MaxSAT and PB solvers would otherwise be unable to solve.

We focus on the random generation of SAT instances that have computational properties that are similar to real-world instances. It is known that industrial instances, even with a great number of variables, can be solved by a clever solver in a reasonable amount of time. This is not possible, in general, with classical randomly generated instances. We provide different generation models of SAT instances, extending the uniform and regular 3-CNF models. They are based on the use of non-uniform probability distributions to select variables. Our last model also uses a mechanism to produce clauses of different lengths as in industrial instances. We show the existence of the phase transition phenomena for our models and we study the hardness of the generated instances as a function of the parameters of the probability distributions. We prove that, with these parameters we can adjust the difficulty of the problems in the phase transition point. We measure hardness in terms of the performance of different solvers. We show how these models will allow us to generate random instances similar to industrial instances, of interest for testing purposes.

In this paper we address the problem of designing an interruptible system in a setting in which n problem instances, all equally important, must be solved. The system involves  scheduling executions of contract algorithms (which offer a trade-off between allowable computation time and quality of the solution) in m identical parallel processors. When an interruption occurs, the system must report a solution to each of the n problem instances. The quality of this output is then compared to the best-possible algorithm that has foreknowledge of the interruption time and must, likewise, produce solutions to all n problem instances. This extends the well-studied setting in which only one problem instance is queried at interruption time. We propose a schedule which we prove is optimal for the case of a single processor. For multiple processors, we show that the quality of the schedule is within a small factor from optimal.

In this paper, we study distributed algorithms for cooperative agents that  allow them to exchange their assigned tasks in order to reduce their team  cost. We define a new type of contract, called K-swaps, that describes multiple task exchanges among multiple agents at a time, which generalizes the concept of single task exchanges. We design a distributed algorithm that constructs all possible K-swaps that reduce the team cost of a given task allocation and show that each agent typically only needs to communicate a small part of its local computation results to the other agents. We then demonstrate empirically that K-swaps can reduce the team costs of several existing task-allocation algorithms significantly even if K is small.

This paper presents an axiomatic analysis of negotiation problems within task-oriented domains (TOD). We start by applying three classical bargaining solutions of Nash, Kalai-Smorodinsky and Egalitarian to the domains of problems with a pre-process of randomization on possible agreements. We find out that these three solutions coincide within any TOD and can be characterized by the same set of axioms, which specify a solution of task oriented negotiation as an outcome of dual-process of maximizing cost reduction and minimizing workload imbalance. This axiomatic characterization is then used to produce an approximate solution to the domain of problems without randomization on possible agreements.

Sequential voting rules and correspondences provide a way for agents to make group decisions when the set of available options has a multi-issue structure. One important question about sequential voting rules (correspondences) is whether they satisfy two crucial criteria, namely neutrality and efficiency. Recently, Benoit and Kornhauser established an important result about seat-by-seat voting rules (which are a special case of sequential voting rules): they proved that if the multi-issue domain satisfies some properties, then the only seat-by-seat rules being either efficient or neutral are dictatorships. However, there are still some cases not covered by their results, including a very important and interesting case—voting correspondences. In this paper, we extend the impossibility theorems by Benoit and Kornhauser to voting correspondences, and obtain a dichotomy theoremon the existence of efficient or neutral sequential (seat-by-seat) voting rules and correspondences. Therefore, the question of whether sequential (seat-by-seat) voting rules (correspondences) can be efficient or neutral is now completely answered.

Recently, online reputation mechanisms have been proposed that reward agents for honest feedback about products and services with fixed quality. Many real-world settings, however, are inherently dynamic. As an example, consider a web service that wishes to publish the expected download speed of a file mirrored on different server sites. In contrast to the models of Miller, Resnick and Zeckhauser and of Jurca and Faltings, the quality of the service (e. g., a server’s available bandwidth) changes over time and future agents are solely interested in the present quality levels. We show that hidden Markov models (HMM) provide natural generalizations of these static models and design a payment scheme that elicits honest reports from the agents after they have experienced the quality of the service.