Global Inverse Consistency for Interactive Constraint Satisfaction

International audienceSome applications require the interactive resolution of a constraint problem by a human user. In such cases, it is highly desirable that the person who interactively solves the problem is not given the choice to select values that do not lead to solutions. We call this property global inverse consistency. Existing systems simulate this either by maintaining arc consistency after each assignment performed by the user or by compiling offline the problem as a multi-valued decision diagram. In this paper, we define several questions related to global inverse consistency and analyse their complexity. Despite their theoretical intractability, we propose several algorithms for enforcing global inverse consistency and we show that the best version is efficient enough to be used in an interactive setting on several configuration and design problems. We finally extend our contribution to the inverse consistency of tuples

Minimizing Maximum Dissatisfaction in the Allocation of Indivisible Items under a Common Preference Graph

We consider the task of allocating indivisible items to agents, when the agents' preferences over the items are identical. The preferences are captured by means of a directed acyclic graph, with vertices representing items and an edge $(a,b)$, meaning that each of the agents prefers item $a$ over item $b$. The dissatisfaction of an agent is measured by the number of items that the agent does not receive and for which it also does not receive any more preferred item. The aim is to allocate the items to the agents in a fair way, i.e., to minimize the maximum dissatisfaction among the agents. We study the status of computational complexity of that problem and establish the following dichotomy: the problem is NP-hard for the case of at least three agents, even on fairly restricted graphs, but polynomially solvable for two agents. We also provide several polynomial-time results with respect to different underlying graph structures, such as graphs of width at most two and tree-like structures such as stars and matchings. These findings are complemented with fixed parameter tractability results related to path modules and independent set modules. Techniques employed in the paper include bottleneck assignment problem, greedy algorithm, dynamic programming, maximum network flow, and integer linear programming.Comment: 26 pages, 2 figure

Variable and value elimination in binary constraint satisfaction via forbidden patterns

Variable or value elimination in a constraint satisfaction problem (CSP) can be used in preprocessing or during search to reduce search space size. A variable elimination rule (value elimination rule) allows the polynomial-time identification of certain variables (domain elements) whose elimination, without the introduction of extra compensatory constraints, does not affect the satisfiability of an instance. We show that there are essentially just four variable elimination rules and three value elimination rules defined by forbidding generic sub-instances, known as irreducible existential patterns, in arc-consistent CSP instances. One of the variable elimination rules is the already-known Broken Triangle Property, whereas the other three are novel. The three value elimination rules can all be seen as strict generalisations of neighbourhood substitution.Comment: A full version of an IJCAI'13 paper to appear in Journal of Computer and System Sciences (JCSS

STR2: Optimized Simple Tabular Reduction for Table Constraints

International audienceTable constraints play an important role within constraint programming. Recently, many schemes or algorithms have been proposed to propagate table constraints and/or to compress their representation. In this paper, we describe an optimization of simple tabular reduction (STR), a technique proposed by J. Ullmann to dynamically maintain the tables of supports when generalized arc consistency (GAC) is enforced/maintained. STR2, the new refined GAC algorithm we propose, allows us to limit the number of operations related to validity checking and search of supports. Interestingly enough, this optimization makes simple tabular reduction potentially r times faster where r is the arity of the constraint(s). The results of an extensive experimentation that we have conducted with respect to random and structured instances indicate that STR2 is usually around twice as fast as the original STR, two or three times faster than the approach based on the hidden variable encoding, and can be up to one order of magnitude faster than previously state-of-the art (generic) GAC algorithms on some series of instances. When comparing STR2 with the more recently developed algorithm based on multi-valued decision diagrams (MDDs), we show that both approaches are rather complementary

Heuristic Algorithms for Best Match Graph Editing

Best match graphs (BMGs) are a class of colored digraphs that naturally appear in mathematical phylogenetics and can be approximated with the help of similarity measures between gene sequences, albeit not without errors. The corresponding graph editing problem can be used as a means of error correction. Since the arc set modification problems for BMGs are NP-complete, efficient heuristics are needed if BMGs are to be used for the practical analysis of biological sequence data. Since BMGs have a characterization in terms of consistency of a certain set of rooted triples, we consider heuristics that operate on triple sets. As an alternative, we show that there is a close connection to a set partitioning problem that leads to a class of top-down recursive algorithms that are similar to Aho's supertree algorithm and give rise to BMG editing algorithms that are consistent in the sense that they leave BMGs invariant. Extensive benchmarking shows that community detection algorithms for the partitioning steps perform best for BMG editing

Sequence-Oriented Diagnosis of Discrete-Event Systems

Model-based diagnosis has always been conceived as set-oriented, meaning that a candidate is a set of faults, or faulty components, that explains a collection of observations. This perspective applies equally to both static and dynamical systems. Diagnosis of discrete-event systems (DESs) is no exception: a candidate is traditionally a set of faults, or faulty events, occurring in a trajectory of the DES that conforms with a given sequence of observations. As such, a candidate does not embed any temporal relationship among faults, nor does it account for multiple occurrences of the same fault. To improve diagnostic explanation and support decision making, a sequence-oriented perspective to diagnosis of DESs is presented, where a candidate is a sequence of faults occurring in a trajectory of the DES, called a fault sequence. Since a fault sequence is possibly unbounded, as the same fault may occur an unlimited number of times in the trajectory, the set of (output) candidates may be unbounded also, which contrasts with set-oriented diagnosis, where the set of candidates is bounded by the powerset of the domain of faults. Still, a possibly unbounded set of fault sequences is shown to be a regular language, which can be defined by a regular expression over the domain of faults, a property that makes sequence-oriented diagnosis feasible in practice. The task of monitoring-based diagnosis is considered, where a new candidate set is generated at the occurrence of each observation. The approach is based on three different techniques: (1) blind diagnosis, with no compiled knowledge, (2) greedy diagnosis, with total knowledge compilation, and (3) lazy diagnosis, with partial knowledge compilation. By knowledge we mean a data structure slightly similar to a classical DES diagnoser, which can be generated (compiled) either entirely offline (greedy diagnosis) or incrementally online (lazy diagnosis). Experimental evidence suggests that, among these techniques, only lazy diagnosis may be viable in non-trivial application domains