We consider the class of logic programs under the restriction of bounded predicate arities. Previous results showed that the complexity answer set semantics for such class of logic programs is lower than unrestricted programs. In particular, evaluation under answer set semantics is possible within polynomial space. However, current ASP solvers and grounders do not seem to respect this complexit...

We prove that for any integers m; k, there is an integer n 0 such that if G is a graph of girth n 0 then any partial k-tree homomorphic to G is also homomorphic to C 2m+1. As a corollary, every non-bipartite graph does not have bounded treewidth duality.

We consider the problem of nding an independent dominating set of minimum cardinality in bounded degree and regular graphs. We rst give an approximation algorithm for at most cubic graphs, that achieves ratio 2, based on greedy and local search techniques. We then propose an heuristic based on an iterative application of the greedy technique on graphs of lower and lower degree. When the graph i...

This paper presents an O(n) algorithm for deciding isomorphism of graphs that have bounded feedback vertex set number. This number is defined as the minimum number of vertex deletions required to obtain a forest. Our result implies that Graph Isomorphism is fixedparameter tractable with respect to the feedback vertex set number. Central to the algorithm is a new technique consisting of an appli...

Let V be a normal affine R-variety, and let S be a semi-algebraic subset of V (R) which is Zariski dense in V . We study the subring BV (S) of R[V ] consisting of the polynomials that are bounded on S. We introduce the notion of S-compatible completions of V , and we prove the existence of such completions when dim(V ) ≤ 2 or S = V (R). An S-compatible completionX of V yields a ring isomorphism...

Since in general it is NP-hard to solve the minimum dominating set problem even approximatively, a lot of work has been dedicated to central and distributed approximation algorithms on restricted graph classes. In this paper, we compromise between generality and efficiency by considering the problem on graphs of small arboricity a. These family includes, but is not limited to, graphs excluding ...

An Optimal Bounding Ellipsoid (OBE) algorithm with asymptotic convergence properties and a selective update capability is developed in this paper. Interesting geometrical insights into the updating rule are found. This algorithm is shown to be robust with respect to certain model violations. Convergence of the algorithm can be established even when the assumption of bounding ellipsoids breaks d...

In this note we consider the set of metric spaces which are the limits with respect to Lipschitz distance dL of compact connected C°°-Riemannian manifolds of curvature uniformly bounded above and below. We call this set "bounded curvature closure" (BCC). It is well known that the limit spaces need not be C-Riemannian manifolds [P, Example 1.8]. Hence, the problem arising is to give a geometrica...

We study the fixed-parameter tractability, subexponential time computability, and approximability of the well-known NP-hard problems: INDEPENDENT SET, VERTEX COVER, and DOMINATING SET. We derive tight results and show that the computational complexity of these problems, with respect to the above complexity measures, is dependent on the genus of the underlying graph. For instance, we show that, ...

A bounded-degree-1 set S in an undirected graph G = (V,E) is a vertex subset such that the maximum degree of G[S] is at most one. Given a graph G, the Maximum Bounded-Degree1 Set problem is to find a bounded-degree-1 set S of maximum size in G. A notion related to bounded-degree sets is that of an s-plex used to define the cohesiveness of subgraphs in social networks. An s-plex S in a graph G =...