Temporal reasoning problems arise in many areas of AI, including planning, natural language understanding, and reasoning about physical systems. The computational complexity of continuous-time temporal constraint reasoning is fairly well understood. There are, however, many different cases where discrete time must be considered; various scheduling problems and reasoning about sampled physical systems are two examples. Here, the complexity of temporal reasoning is not as well-studied nor as well-understood. In order to get a better understanding, we consider the powerful Horn DLR formalism adapted for discrete time and study its computational complexity. We show that the full formalism is NP-hard and identify several maximal tractable subclasses. We also ‘lift’ the maximality results to obtain hardness results for other families of constraints. Finally, we discuss how the results and techniques presented in this paper can be used for studying even more expressive classes of temporal constraints.

This paper considers matrix models, a class of CSPs which generally exhibit significant symmetries. It proposed the idea of LexLeader feasibility checkers that verify, during search, whether the current partial assignment can be extended into a canonical solution. The feasibility checkers are based on a novel result by [Katsirelos et al., 2010] on how to check efficiently whether a solution is canonical. The paper generalizes this result to partial assignments, various variable orderings, and value symmetries. Empirical results on 5 standard benchmarks shows that feasibility checkers may bring significant performance gains, when jointly used with DoubleLex or SnakeLex.

This paper considers a constraint-based scheduling approach to the flexible jobshop, a generalization of the traditional jobshop scheduling where activities have a choice of machines. It studies both large neighborhood (LNS) and adaptive randomized decomposition (ARD) schemes, using random, temporal, and machine decompositions. Empirical results on standard benchmarks show that, within 5 minutes, both LNS and ARD produce many new best solutions and are about 0.5% in average from the best-known solutions. Moreover, over longer runtimes, they improve 60% of the best-known solutions and match the remaining ones. The empirical results also show the importance of hybrid decompositions in LNS and ARD.

This paper introduces the Seqbin meta-constraint with a polytime algorithm achieving generalized arc-consistency. Seqbin can be used for encoding counting constraints such as Change, Smooth, or InncreasingNValue. For all of them the time and space complexity is linear in the sum of domain sizes, which improves or equals the best known results of the literature.

An elegant approach to learning temporal orderings from texts is to formulate this problem as a constraint optimization problem, which can be then given an exact solution using Integer Linear Programming. This works well for cases where the number of possible relations between temporal entities is restricted to the mere precedence relation [Bramsen et al., 2006; Chambers and Jurafsky, 2008], but becomes impractical when considering all possible interval relations. This paper proposes two innovations, inspired from work on temporal reasoning, that control this combinatorial blow-up, therefore rendering an exact ILP inference viable in the general case. First, we translate our network of constraints from temporal intervals to their endpoints, to handle a drastically smaller set of constraints, while preserving the same temporal information. Second, we show that additional efficiency is gained by enforcing coherence on particular subsets of the entire temporal graphs. We evaluate these innovations through various experiments on TimeBank 1.2, and compare our ILP formulations with various baselines and oracle systems.

Log-linear description logics are a family of probabilistic logics integrating various concepts and methods from the areas of knowledge representation and reasoning and statistical relational AI. We define the syntax and semantics of log-linear description logics, describe a convenient representation as sets of first-order formulas, and discuss computational and algorithmic aspects of probabilistic queries in the language. The paper concludes with an experimental evaluation of an implementation of a log-linear DL reasoner.

We introduce the MULTI-INTER-DISTANCE constraint that ensures no more than m variables are assigned to values lying in a window of p consecutive values. This constraint is useful for modeling scheduling problems where tasks of processing time p compete for m identical resources. We present a propagator that achieves bounds consistency in cubic time. Experiments show that this new constraint offers a much stronger filtering than an edge-finder and that it allows to solve larger instances of the runway scheduling problem.

We consider scenarios where several agents must aggregate their preferences over a large set of candidates with a combinatorial structure. That is, each candidate is an element of the Cartesian product of the domains of some variables. We assume agents compactly express their preferences over the candidates via soft constraints. We consider a sequential procedure that chooses one candidate by asking the agents to vote on one variable at a time. While some properties of this procedure have been already studied, here we focus on independence of irrelevant alternatives, non-dictatorship, and strategy-proofness. Also, we perform an experimental study that shows that the proposed sequential procedure yields a considerable saving in time with respect to a non-sequential approach, while the winners satisfy the agents just as well, independently of the variable ordering and of the presence of coalitions of agents.

We discuss a novel approach for dealing with single-stage stochastic constraint satisfaction problems (SCSPs) that include random variables over a continuous or large discrete support. Our approach is based on two novel tools: sampled SCSPs and (α,ϑ)-solutions. Instead of explicitly enumerating a very large or infinite set of future scenarios, we employ statistical estimation to determine if a given assignment is consistent for a SCSP. As in statistical estimation, the quality of our estimate is determined via confidence interval analysis. In contrast to existing approaches based on sampling, we provide likelihood guarantees for the quality of the solutions found. Our approach can be used in concert with existing strategies for solving SCSPs.

The paper investigates a novel approach, based on Constraint Logic Programming (CLP), to predict potential 3D conformations of a protein via fragments assembly. The fragments are extracted and clustered by a preprocessor from a database of known protein structures. Assembling fragments into a complete conformation is modeled as a constraint satisfaction problem solved using CLP. The approach makes use of a simplified CA-side chain centroid protein model, that offers efficiency and a good approximation for space filling. The approach adapts existing energy models for protein representation and applies a large neighboring search (LNS) strategy. The results show the feasibility and efficiency of the method, and the declarative nature of the approach simplifies the introduction of additional knowledge and variations of the model.