Let G be a set of disjoint bi-chromatic straight line segments and H be a set of red and blue points in the plane, no three points are collinear. We give tight upper bounds on the maximum degree of a node in the color conforming minimum weight spanning tree (MST) formed by G and H. We also consider bounds on the total length of the edges of 1) the planar MST and the unrestricted MST, 2) the gre...

We present our system used in the CoNLL 2007 shared task on multilingual parsing. The system is composed of three components: a k-best maximum spanning tree (MST) parser, a tree labeler, and a reranker that orders the k-best labeled trees. We present two techniques for training the MST parser: tree-normalized and graphnormalized conditional training. The treebased reranking model allows us to e...

Abstract. In this paper, we introduce the Tree of Hubs Location Problem with Upgrading, a mixture of the Tree of Hubs Location Problem, presented in [15], and the Minimum Cost Spanning Tree Problem with Upgraded nodes, studied for the first time in [19]. In addition to locate the hubs, to determine the tree that connects the hubs and to allocate non-hub nodes to hubs, a decision has to be made ...

Given a set of nodes N (i 1, 2, ..., n) which may represent cities and a set of requirements ria which may represent the number of telephone calls between N and N j, the problem is to build a spanning tree connecting these n nodes such that the total cost of communication of the spanning tree is a minimum among all spanning trees. The cost of communication for a pair of nodes is r;a multiplied ...

This paper improves the complexity of a newly introduced MST (Majority Spanning Tree) algorithm for ranking players of a round-robin tournament previously published.

We show that for every n-point metric space M and positive integer k, there exists a spanning tree T with unweighted diameter O(k) and weight w(T ) = O(k · n) · w(MST (M)), and a spanning tree T ′ with weight w(T ′) = O(k) · w(MST (M)) and unweighted diameter O(k · n). These trees also achieve an optimal maximum degree. Furthermore, we demonstrate that these trees can be constructed efficiently...

We de…ne the canonical form of a cost spanning tree problem. The canonical form has the property that reducing the cost of any arc, the minimal cost of connecting agents to the source is also reduced. We argue that the canonical form is a relevant concept in this kind of problems and study a rule using it. This rule satis…es much more interesting properties than other rules in the literature. F...

The reconstruction of a surface model from a point cloud is an important task in the reverse engineering of industrial parts. We aim at constructing a curve network on the point cloud that will define the border of the various surface patches. In this paper, we present an algorithm to extract closed sharp feature lines, which is necessary to create such a closed curve network. We use a first or...

We are interested here in the design of a very efficient Time-Map Manager, able to deal with a large knowledge-base of several thou­ sand time-tokens in demanding applications such as reactive planning and execution con­ trol. A system, called IxTeT, aiming at that goal is described. It uses an original represen­ tation of a lattice of time-points that relies for efficiency on a maximum spannin...

We consider constrained versions of the prize-collecting traveling salesman and the minimum spanning tree problems. The goal is to maximize the number of vertices in the returned tour/tree subject to a bound on the tour/tree cost. We present a 2-approximation algorithm for these problems based on a primal-dual approach. The algorithm relies on finding a threshold value for the dual variable cor...