Computing the Maximum Detour and SpanningRatio of Planar Paths , Trees and Cy les ?
نویسندگان
چکیده
منابع مشابه
Computing the Maximum Detour and Spanning Ratio of Planar Paths, Trees, and Cycles
The maximum detour and spanning ratio of an embedded graph G are values that measure how well G approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe O(n logn) time algorithms for computing the maximum detour and spanning ratio of a planar polygonal path. These algorithms solve open problems posed in at least two previous works [5,10]. We also ge...
متن کاملComputing the Detour and Spanning Ratio of Paths, Trees, and Cycles in 2D and 3D
The detour and spanning ratio of a graph embedded in measure how well approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe time algorithms for computing the detour and spanning ratio of a planar polygonal path. By generalizing these algorithms, we obtain -time algorithms for computing the detour or spanning ratio of planar trees and cycles. Fina...
متن کاملA SIMPLE ALGORITHM FOR COMPUTING DETOUR INDEX OF NANOCLUSTERS
Let G be the chemical graph of a molecule. The matrix D = [dij ] is called the detour matrix of G, if dij is the length of longest path between atoms i and j. The sum of all entries above the main diagonal of D is called the detour index of G. In this paper, a new algorithm for computing the detour index of molecular graphs is presented. We apply our algorithm on copper and silver nanoclusters ...
متن کاملDetour Monophonic Graphoidal Covering Number of Corona Product Graph of Some Standard Graphs with the Wheel
A chord of a path $P$ is an edge joining two non-adjacent vertices of $P$. A path $P$ is called a monophonic path if it is a chordless path. A longest $x-y$ monophonic path is called an $x-y$ detour monophonic path. A detour monophonic graphoidal cover of a graph $G$ is a collection $psi_{dm}$ of detour monophonic paths in $G$ such that every vertex of $G$ is an internal vertex of at most on...
متن کاملComputing the Maximum Detour of a Plane Geometric Graph in Subquadratic Time
Let G be a plane graph where each edge is a line segment. We consider the problem of computing the maximum detour of G, defined as the maximum over all pairs of distinct points p and q of G of the ratio between the distance between p and q in G and the Euclidean distance ‖pq‖. The fastest known algorithm for this problem has Θ(n2) running time where n is the number of vertices. We show how to o...
متن کامل