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Journals and Conferences
Let G be a connected plane geometric graph with n vertices. In this paper, we study bounds on the number of edges required to be added to G to obtain 2-vertex or 2-edge connected plane geometric graphs. In particular, we show that for G to become 2-edge connected, 2n 3 additional edges are required in some cases and that 6n 7 additional edges are always… (More)
We consider combinatorial and computational issues that are related to the problem of moving coins from one configuration to another. Coins are defined as non-overlapping discs, and moves are defined as collision free translations, all in the Euclidean plane. We obtain combinatorial bounds on the number of moves that are necessary and/or sufficient to move… (More)
Two non-crossing geometric graphs on the same set of points are compatible if their union is also non-crossing. In this paper, we prove that every graph G that has an outerplanar embedding admits a non-crossing perfect matching compatible with G. Moreover, for non-crossing geometric trees and simple polygons, we study bounds on the minimum number of edges… (More)
Given a Laman graph G, i.e. a minimally rigid graph in R 2, we provide a Θ(n 2) algorithm to augment G to a redundantly rigid graph, by adding a minimum number of edges. Moreover, we prove that this problem of augmenting is NP-hard for an arbitrary rigid graph G in R 2.
a Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza, Pedro Cerbuna, 12, 50009 Zaragoza, Spain b Dept. Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034 Barcelona, Spain c Dept. Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Avinguda del Canal Olímpic 15, 08860… (More)
We provide an optimal algorithm for the problem of augmenting an outerplanar graph G by adding a minimum number of edges in such a way that the augmented graph G′ is outerplanar and 2-connected. We also solve optimally the same problem when instead we require G′ to be 2-edge-connected.
We present 0( N log N) algorithms for the two following problems: finding the minimum Hamiltonian curve from point pl to point p,,, for N points on a convex polygon, and solving the travelling salesman problem for N points on a convex polygon and a segment line inside the polygon. The complexity of the algorithms improves the complexity of the best known… (More)
1 Let P be a set of n points in the plane in general position. A 2 subset H of P consisting of k elements that are the vertices of a convex 3 polygon is called a k-hole of P , if there is no element of P in the interior 4 of its convex hull. A set B of points in the plane blocks the k-holes of 5 P if any k-hole of P contains at least one element of B in the… (More)