AN OPTIMAL MORPHING BETWEEN POLYLINES

2002 ◽  
Vol 12 (03) ◽  
pp. 217-228 ◽  
Author(s):  
SERGEI BESPAMYATNIKH
Keyword(s):  
Shortest Path ◽  
Minimum Width ◽  
Longest Path ◽  
Previous Algorithm

We address the problem of continuously transforming or morphing one simple polyline into another so that every point p of the initial polyline moves to a point q of the final polyline using the geodesic shortest path from p to q. We optimize the width of the morphing, that is, the longest path made by a point on the polyline. We present an algorithm for finding the minimum width morphing in O(n2) time using O(n) space, where n is the total number of vertices of polylines. This improves the previous algorithm7 by a factor of log 2 n.

AN APPROXIMATE MORPHING BETWEEN POLYLINES

2005 ◽  
Vol 15 (02) ◽  
pp. 193-208 ◽  
Author(s):  
SERGEY BEREG
Keyword(s):  
Shortest Path ◽  
Optimization Problem ◽  
Linear Time ◽  
Medial Axis ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Geodesic Path ◽  
Minimum Width ◽  
Approximation Factor ◽  
Previous Algorithm

We consider the problem of continuously transforming or morphing one simple polyline into another polyline so that every point p of the initial polyline moves to a point q of the final polyline using the geodesic shortest path from p to q. The width of a morphing is defined as the longest geodesic path between corresponding points of the polylines. The optimization problem is to compute a morphing that minimizes the width. We present a linear-time algorithm for finding a morphing with width guaranteed to be at most two times the minimum width of a morphing. This improves the previous algorithm10 by a factor of log n. We develop a linear-time algorithm for computing a medial axis separator. We also show that the approximation factor is less than two for κ-straight polylines.

scholarly journals DEPTH FIRST SEARCH (DFS) UNTUK MENENTUKAN DIAMETER GRAF HIRARKI

2019 ◽  
Vol 11 (2) ◽  
pp. 29
Author(s):  
Nugroho Arif Sudibyo ◽  
Ardymulya Iswardani
Keyword(s):  
Shortest Path ◽  
Shortest Paths ◽  
Depth First Search ◽  
Longest Path

Let G = (V, E) be a graph. The distance d (u, v) between two vertices u and v is the length of the shortest path between them. The diameter of the graph is the length of the longest path of the shortest paths between any two graph vertices (u ,v) of a graph, . In this paper we propose algorithms for finding diameter of a hierarchy graph using DFS. Diameter of the hierarchy graph using DFS algoritm is four.

scholarly journals Graphs and Matroids Weighted in a Bounded Incline Algebra

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Ling-Xia Lu ◽  
Bei Zhang
Keyword(s):  
Shortest Path ◽  
Independent Set ◽  
Shortest Path Problem ◽  
Maximum Independent Set ◽  
Independent Set Problem ◽  
Uniform Approach ◽  
Longest Path ◽  
Longest Path Problem ◽  
Maximum Independent Set Problem ◽  
Reliable Path

Firstly, for a graph weighted in a bounded incline algebra (or called a dioid), a longest path problem (LPP, for short) is presented, which can be considered the uniform approach to the famous shortest path problem, the widest path problem, and the most reliable path problem. The solutions for LPP and related algorithms are given. Secondly, for a matroid weighted in a linear matroid, the maximum independent set problem is studied.

The Map-Based Shortest Route Selection by Using Ant Colony Optimization Algorithm

2018 ◽  
Vol 1 (1) ◽  
pp. 15
Author(s):  
Achmad Fanany Onnilita Gaffar ◽  
Agusma Wajiansyah ◽  
Supriadi Supriadi
Keyword(s):  
Ant Colony Optimization ◽  
Shortest Path ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Google Earth ◽  
Ant Colony ◽  
Food Sources ◽  
Shortest Route ◽  
Study Results ◽  
Destination Point

The shortest path problem is one of the optimization problems where the optimization value is a distance. In general, solving the problem of the shortest route search can be done using two methods, namely conventional methods and heuristic methods. The Ant Colony Optimization (ACO) is the one of the optimization algorithm based on heuristic method. ACO is adopted from the behavior of ant colonies which naturally able to find the shortest route on the way from the nest to the food sources. In this study, ACO is used to determine the shortest route from Bumi Senyiur Hotel (origin point) to East Kalimantan Governor's Office (destination point). The selection of the origin and destination points is based on a large number of possible major roads connecting the two points. The data source used is the base map of Samarinda City which is cropped on certain coordinates by using Google Earth app which covers the origin and destination points selected. The data pre-processing is performed on the base map image of the acquisition results to obtain its numerical data. ACO is implemented on the data to obtain the shortest path from the origin and destination point that has been determined. From the study results obtained that the number of ants that have been used has an effect on the increase of possible solutions to optimal. The number of tours effect on the number of pheromones that are left on each edge passed ant. With the global pheromone update on each tour then there is a possibility that the path that has passed the ant will run out of pheromone at the end of the tour. This causes the possibility of inconsistent results when using the number of ants smaller than the number of tours.

The Restricted Arc-Width of a Graph

10.37236/1734 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
David Arthur
Keyword(s):  
Unit Circle ◽  
Single Point ◽  
Minimum Width ◽  
Graph Operations ◽  
Function Mapping

An arc-representation of a graph is a function mapping each vertex in the graph to an arc on the unit circle in such a way that adjacent vertices are mapped to intersecting arcs. The width of such a representation is the maximum number of arcs passing through a single point. The arc-width of a graph is defined to be the minimum width over all of its arc-representations. We extend the work of Barát and Hajnal on this subject and develop a generalization we call restricted arc-width. Our main results revolve around using this to bound arc-width from below and to examine the effect of several graph operations on arc-width. In particular, we completely describe the effect of disjoint unions and wedge sums while providing tight bounds on the effect of cones.

A Nettree for Simple Paths with Length Constraint and the Longest Path in Directed Acyclic Graphs

2012 ◽  
Vol 35 (10) ◽  
pp. 2194 ◽  
Author(s):  
Yan LI ◽  
Le SUN ◽  
Huai-Zhong ZHU ◽  
You-Xi WU
Keyword(s):  
Directed Acyclic Graphs ◽  
Length Constraint ◽  
Acyclic Graphs ◽  
Longest Path ◽  
Simple Paths
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