The problem of computing X-minimal models, that is, models minimal with respect to a subset X of all the atoms in a theory, is very relevant for computing circumscriptions and diagnosis. Unfortunately, the problem is NP-hard. In this paper we present two novel algorithms for computing X-minimal models. The advantage of these new algorithms is that, unlike existing ones, they are capable of gene...

We study the complexity of turning a given graph, by edge editing, into a target graph whose critical-clique graph is any fixed graph. The problem came up in practice, in an effort of mining huge word similarity graphs for well structured word clusters. It also adds to the rich field of graph modification problems. We show in a generic way that several variants of this problem are in SUBEPT. As...

Let .F be a family of subsets of S and let G be a graph with vertex set V= {XA IA E .Y) such that: (.K~,xB) is an edge iffAnB#O. The family .F is called a set representation of the graph G. It is proved that the problem of finding minimum k such that G can be represented by a family of sets of cardinality at most k is NP-complete. Moreover, it is NP-complete to decide whether a graph can be rep...

Given an embedding f: G -+ 2 of a graph G in the two-dimensional lattice, let Iff be the maximum L1 distance between points f(x) and f(y) where xy is an edge of G. Let B2 ( G) be the minimum Ifl over all embeddings f. It is shown that the determination of B2 ( G ) for arbitrary G is NP-complete. Essentially the same proof can be used in showing the NP-completeness of minimizing If I over all em...

It is shown that the knapsack problem, which was introduced by Myasnikov et al. for arbitrary finitely generated groups, can be solved in NP for graph groups. This result even holds if the group elements are represented in a compressed form by SLPs, which generalizes the classical NP-completeness result of the integer knapsack problem. We also prove general transfer results: NP-membership of th...

Consider the following problem: given an upper triangular matrix A, with rational entries and distinct diagonal elements, and a tolerance 1, decide whether there exists a nonsingu-lar matrix G, with condition number bounded by , such that G ?1 AG is 22 block diagonal. This problem, which we shall refer to as DICHOTOMY, is an important one in the theory of invariant subspaces. It has recently be...

The main aim of NP-completeness theory is the analysis of intractabil-ity. Many optimization problems were rst proved to be NP-hard. Since the complete solution of these problems requires exponential time, polynomial time algorithms to nd \near-optimal" solutions, i.e., approximation algorithms, appear to be viable. In this paper we show the basic principles of Approximation Theory for NP-compl...

We show that the Min Cut Linear Arrangement Problem (Min Cut) is NP-complete for trees with polynomial size edge weights and derive from this the NP-completeness of Min Cut for planar graphs with maximum vertex degree 3. This is used to show the NP-completeness of Search Number, Vertex Separation, Progressive Black/ White Pebble Demand, and Topological Bandwidth for planar graphs with maximum v...

We propose coalitional normative system (cns), which can selectively restrict the joint behavior of a coalition, in this paper. We extend the semantics of atl and propose Coordinated atl (co-atl) to support the formalizing of cns. We soundly and completely characterize the limitation of the normative power of a coalition by identifying two fragments of co-atl language corresponding to two types...

The pagenumber problem for ordered sets is known to be NP-complete, even if the order of the elements on the spine is fixed. In this paper, we investigate this problem for some classes of ordered sets. We provide an efficient algorithm for drawing bipartite interval orders in the minimum number of pages needed. We also give an upper bound for the pagenumber of general bipartite ordered sets and...