A (δ ≥ k1, δ ≥ k2)-partition of a graph G is a vertex-partition (V1, V2) of G satisfying that δ(G[Vi]) ≥ ki for i = 1, 2. We determine, for all positive integers k1, k2, the complexity of deciding whether a given graph has a (δ ≥ k1, δ ≥ k2)-partition. We also address the problem of finding a function g(k1, k2) such that the (δ ≥ k1, δ ≥ k2)-partition problem is NP-complete for the class of gra...

Let P be a polygonal curve in R of length n, and S be a point set of size k. We consider the problem of finding a polygonal curve Q on S such that all points in S are visited and the Fréchet distance between Q and P is at most a given ε. We show that this problem is NP-complete, regardless of whether or not the points of S are allowed to be visited more than once.

In this paper we define a restricted version of Monotone NAE-3SAT and show that it remains NP-Complete even under that restriction. We expect this result would be useful in proving NP-Completeness results for problems on k-colourable graphs (k ≥ 5). We also prove the NPCompleteness of the Triangle-Free Cut problem.

Given a metric d on a permutation group G, the corresponding weight problem is to decide whether there exists an element g ∈ G such that d(g, e) = k for some k ∈ N. In this paper we show that this problem is NP-complete for many well known metrics.

We use a syntactic interpretation of MALL in BCI with ∧, defined in [5], to prove the undecidability of the consequence relations for BCI with ∧ and BCI with ∨, and the NP-completeness of BCI. Similar results are obtained for a variant of the Lambek calculus.

A classical problem in the theory of minimal submanifolds of Euclidean spaces is to study the existence of a minimal submanifold with a prescribed behavior at infinity, or to determine from the asymptotes the geometry of the whole submanifold. Beyond the intrinsic interest of these questions, they are also of crucial importance when studying the possible singularities of minimal submanifolds in...

We consider the complexity of problems related to the combinatorial game Free-Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number of flooding operations. Our main result is that computing the length of an optimal sequence is fixed parameter tractable (with the number of colours as a parameter) when restricted to rectangular 2× n boards. We also...

We prove NP-completeness of deciding the existence of an economic equilibrium in so-called house allocation markets. House allocation markets are markets with indivisible goods in which every agent holds exactly one copy of some good.  2003 Elsevier B.V. All rights reserved.

Developing an efficient heuristic algorithm to solve a supply chain operations planning model is the main purpose of this paper. The model considers multi period supply chain planning with capacitated resources. The concept of multi period capacity consumption has been developed recently at the context of supply chain management that realizes resource planning at a supply chain. Because of cons...