Search results for "MathematicsofComputing_DISCRETEMATHEMATICS"
showing 10 items of 123 documents
Almost disjoint spanning trees: relaxing the conditions for completely independent spanning trees
2017
International audience; The search of spanning trees with interesting disjunction properties has led to the introduction of edge-disjoint spanning trees, independent spanning trees and more recently completely independent spanning trees. We group together these notions by dening (i, j)-disjoint spanning trees, where i (j, respectively) is the number of vertices (edges, respectively) that are shared by more than one tree. We illustrate how (i, j)-disjoint spanning trees provide some nuances between the existence of disjoint connected dominating sets and completely independent spanning trees. We prove that determining if there exist two (i, j)-disjoint spanning trees in a graph G is NP-comple…
An efficient algorithm for stopping on a sink in a directed graph
2013
Abstract Vertices of an unknown directed graph of order n are revealed one by one in some random permutation. At each point, we know the subgraph induced by the revealed vertices. Our goal is to stop on a sink, a vertex with no out-neighbors. We show that if a sink exists this can be achieved with probability Θ ( 1 / n ) , which is best possible.
Theoretical and Experimental Studies on the Influence of Process Parameters on Strains and Forces of Single Point Incremental Forming
2014
These paper aims to determine the influence of the most important geometrical parameters (vertical step and punch diameter) on the main strains, thickness reduction and the forces along two directions during the single point incremental forming process (SPIF). The paper comprises a comparative numericalexperimental study, for a simple geometry part obtained by incremental forming. In fact, in the first stage, the punch has a vertical motion with the value of one vertical step. In the second stage, the punch follows a linear trajectory along one side of the die. After each linear trajectory the punch has successive vertical motions, taking one vertical step at a time until the entire geometr…
Strong chromatic index of products of graphs
2007
Graphs and Algorithms
Gray code for permutations with a fixed number of cycles
2007
AbstractWe give the first Gray code for the set of n-length permutations with a given number of cycles. In this code, each permutation is transformed into its successor by a product with a cycle of length three, which is optimal. If we represent each permutation by its transposition array then the obtained list still remains a Gray code and this allows us to construct a constant amortized time (CAT) algorithm for generating these codes. Also, Gray code and generating algorithm for n-length permutations with fixed number of left-to-right minima are discussed.
Curved Edge Routing
2001
We consider the problem of drawing a graph where edges are represented by smooth curves between the associated nodes. Previously curved edges were drawn as splines defined by carefully calculated control points. We present a completely different approach where finding an edge is reduced to solving a differential equation. This approach allows to represent the graph drawing aesthetics directly, even the most complex ones denoting the dependencies among the paths.
A walk on sunset boulevard
2016
A walk on sunset boulevard can teach us about transcendental functions associated to Feynman diagrams. On this guided tour we will see multiple polylogarithms, differential equations and elliptic curves. A highlight of the tour will be the generalisation of the polylogarithms to the elliptic setting and the all-order solution for the sunset integral in the equal mass case.
Hypergraph imaging: an overview
2002
Hypergraph theory as originally developed by Berge (Hypergraphe, Dunod, Paris, 1987) is a theory of finite combinatorial sets, modeling lot of problems of operational research and combinatorial optimization. This framework turns out to be very interesting for many other applications, in particular for computer vision. In this paper, we are going to survey the relationship between combinatorial sets and image processing. More precisely, we propose an overview of different applications from image hypergraph models to image analysis. It mainly focuses on the combinatorial representation of an image and shows the effectiveness of this approach to low level image processing; in particular to seg…
"Table 1" of "Search for long-lived, heavy particles in final states with a muon and multi-track displaced vertex in proton-proton collisions at sqrt…
2012
Efficiency-vs-radial-vertex-position without re-tracking The efficiency for reconstructing a displaced vertex passing all cuts, as a function of radial distance from the z-axis to the vertex positon. The retrack and noretrack suffixes refer to whether or not the procedure known as re-tracking, where the tracking algorithm is re-run with looser cuts, on the leftover hits from standard tracking, was used to select the tracks that were input to the vertexing algorithm.
"Table 2" of "Search for long-lived, heavy particles in final states with a muon and multi-track displaced vertex in proton-proton collisions at sqrt…
2012
Efficiency-vs-radial-vertex-position with re-tracking The efficiency for reconstructing a displaced vertex passing all cuts, as a function of radial distance from the z-axis to the vertex positon. The retrack and noretrack suffixes refer to whether or not the procedure known as re-tracking, where the tracking algorithm is re-run with looser cuts, on the leftover hits from standard tracking, was used to select the tracks that were input to the vertexing algorithm.