Computing hypergraph width measures exactly

Hypergraph width measures are a class of hypergraph invariants important in studying the complexity of constraint satisfaction problems (CSPs). We present a general exact exponential algorithm for a large variety of these measures. A connection between these and tree decompositions is established. This enables us to almost seamlessly adapt the combinatorial and algorithmic results known for tree decompositions of graphs to the case of hypergraphs and obtain fast exact algorithms. As a consequence, we provide algorithms which, given a hypergraph H on n vertices and m hyperedges, compute the generalized hypertree-width of H in time O*(2^n) and compute the fractional hypertree-width of H in time O(m*1.734601^n).Comment: 12 pages, 1 figur

Tractable Optimization Problems through Hypergraph-Based Structural Restrictions

Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal solution is an NP-hard problem in general; yet, when restricted over classes of instances whose constraint interactions can be modelled via (nearly-)acyclic graphs, this problem is known to be solvable in polynomial time. In this paper, larger classes of tractable instances are singled out, by discussing solution approaches based on exploiting hypergraph acyclicity and, more generally, structural decomposition methods, such as (hyper)tree decompositions

Tractable Combinations of Global Constraints

We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used; indeed, they are one of the key reasons for the success of constraint programming in solving real-world problems. Previous work has focused on the development of efficient propagators for individual constraints. In this paper, we identify a new tractable class of constraint problems involving global constraints of unbounded arity. To do so, we combine structural restrictions with the observation that some important types of global constraint do not distinguish between large classes of equivalent solutions.Comment: To appear in proceedings of CP'13, LNCS 8124. arXiv admin note: text overlap with arXiv:1307.179

A Backtracking-Based Algorithm for Computing Hypertree-Decompositions

Hypertree decompositions of hypergraphs are a generalization of tree decompositions of graphs. The corresponding hypertree-width is a measure for the cyclicity and therefore tractability of the encoded computation problem. Many NP-hard decision and computation problems are known to be tractable on instances whose structure corresponds to hypergraphs of bounded hypertree-width. Intuitively, the smaller the hypertree-width, the faster the computation problem can be solved. In this paper, we present the new backtracking-based algorithm det-k-decomp for computing hypertree decompositions of small width. Our benchmark evaluations have shown that det-k-decomp significantly outperforms opt-k-decomp, the only exact hypertree decomposition algorithm so far. Even compared to the best heuristic algorithm, we obtained competitive results as long as the hypergraphs are not too large.Comment: 19 pages, 6 figures, 3 table

Hypertree-Width and Related Hypergraph Invariants

We study the notion of hypertree-width of hypergraphs. We prove that, up to a constant factor, hypertree-width is the same as a number of other hypergraph invariants that resemble graph invariants such as bramble-number, branch-width, linkedness, and the minimum number of cops required to win Seymour and Thomas's robber and cops game

Approximating acyclicity parameters of sparse hypergraphs

The notions of hypertree width and generalized hypertree width were introduced by Gottlob, Leone, and Scarcello in order to extend the concept of hypergraph acyclicity. These notions were further generalized by Grohe and Marx, who introduced the fractional hypertree width of a hypergraph. All these width parameters on hypergraphs are useful for extending tractability of many problems in database theory and artificial intelligence. In this paper, we study the approximability of (generalized, fractional) hyper treewidth of sparse hypergraphs where the criterion of sparsity reflects the sparsity of their incidence graphs. Our first step is to prove that the (generalized, fractional) hypertree width of a hypergraph H is constant-factor sandwiched by the treewidth of its incidence graph, when the incidence graph belongs to some apex-minor-free graph class. This determines the combinatorial borderline above which the notion of (generalized, fractional) hypertree width becomes essentially more general than treewidth, justifying that way its functionality as a hypergraph acyclicity measure. While for more general sparse families of hypergraphs treewidth of incidence graphs and all hypertree width parameters may differ arbitrarily, there are sparse families where a constant factor approximation algorithm is possible. In particular, we give a constant factor approximation polynomial time algorithm for (generalized, fractional) hypertree width on hypergraphs whose incidence graphs belong to some H-minor-free graph class

Evolving robot empathy towards humans with motor disabilities through artificial pain generation

© 2018 the Author(s). In contact assistive robots, a prolonged physical engagement between robots and humans with motor disabilities due to shoulder injuries, for instance, may at times lead humans to experience pain. In this situation, robots will require sophisticated capabilities, such as the ability to recognize human pain in advance and generate counter-responses as follow up emphatic action. Hence, it is important for robots to acquire an appropriate pain concept that allows them to develop these capabilities. This paper conceptualizes empathy generation through the realization of synthetic pain classes integrated into a robot's self-awareness framework, and the implementation of fault detection on the robot body serves as a primary source of pain activation. Projection of human shoulder motion into the robot arm motion acts as a fusion process, which is used as a medium to gather information for analyses then to generate corresponding synthetic pain and emphatic responses. An experiment is designed to mirror a human peer's shoulder motion into an observer robot. The results demonstrate that the fusion takes place accurately whenever unified internal states are achieved, allowing accurate classification of synthetic pain categories and generation of empathy responses in a timely fashion. Future works will consider a pain activation mechanism development