scispace - formally typeset


About: Distance is a(n) research topic. Over the lifetime, 1933 publication(s) have been published within this topic receiving 68872 citation(s). The topic is also known as: Euclidian distance & Euclidean distance. more


Open accessJournal ArticleDOI: 10.1007/BF01386390
Abstract: We consider n points (nodes), some or all pairs of which are connected by a branch; the length of each branch is given. We restrict ourselves to the case where at least one path exists between any two nodes. We now consider two problems. Problem 1. Constrnct the tree of minimum total length between the n nodes. (A tree is a graph with one and only one path between every two nodes.) In the course of the construction that we present here, the branches are subdivided into three sets: I. the branches definitely assignec~ to the tree under construction (they will form a subtree) ; II. the branches from which the next branch to be added to set I, will be selected ; III. the remaining branches (rejected or not yet considered). The nodes are subdivided into two sets: A. the nodes connected by the branches of set I, B. the remaining nodes (one and only one branch of set II will lead to each of these nodes), We start the construction by choosing an arbitrary node as the only member of set A, and by placing all branches that end in this node in set II. To start with, set I is empty. From then onwards we perform the following two steps repeatedly. Step 1. The shortest branch of set II is removed from this set and added to more

Topics: Ternary tree (60%), Tree (data structure) (54%), Longest path problem (52%) more

21,172 Citations

Journal ArticleDOI: 10.1017/S0305004100034095
01 Oct 1959-
Abstract: We prove that the length of the shortest closed path through n points in a bounded plane region of area v is ‘almost always’ asymptotically proportional to √(nv) for large n; and we extend this result to bounded Lebesgue sets in k–dimensional Euclidean space. The constants of proportionality depend only upon the dimensionality of the space, and are independent of the shape of the region. We give numerical bounds for these constants for various values of k; and we estimate the constant in the particular case k = 2. The results are relevant to the travelling-salesman problem, Steiner's street network problem, and the Loberman—Weinberger wiring problem. They have possible generalizations in the direction of Plateau's problem and Douglas' problem. more

Topics: Euclidean shortest path (65%), Shortest path problem (60%), Widest path problem (58%) more

861 Citations

Open accessProceedings ArticleDOI: 10.5555/1070432.1070455
Andrew V. Goldberg1, Chris Harrelson2Institutions (2)
23 Jan 2005-
Abstract: We propose shortest path algorithms that use A* search in combination with a new graph-theoretic lower-bounding technique based on landmarks and the triangle inequality. Our algorithms compute optimal shortest paths and work on any directed graph. We give experimental results showing that the most efficient of our new algorithms outperforms previous algorithms, in particular A* search with Euclidean bounds, by a wide margin on road networks and on some synthetic problem families. more

Topics: K shortest path routing (69%), Euclidean shortest path (68%), Widest path problem (68%) more

821 Citations

Proceedings ArticleDOI: 10.1109/SFCS.1994.365697
David Eppstein1Institutions (1)
20 Nov 1994-
Abstract: We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m+n log n+k). We can also find the k shortest paths from a given source s to each vertex in the graph, in total time O(m+n log n+kn). We describe applications to dynamic programming problems including the knapsack problem, sequence alignment, and maximum inscribed polygons. > more

Topics: Distance (61%), Floyd–Warshall algorithm (59%), Vertex (geometry) (56%) more

708 Citations

Journal ArticleDOI: 10.1007/BF01840360
Leonidas J. Guibas1, John Hershberger1, Daniel Leven2, Micha Sharir2  +3 moreInstitutions (5)
01 Nov 1987-Algorithmica
Abstract: Given a triangulation of a simple polygonP, we present linear-time algorithms for solving a collection of problems concerning shortest paths and visibility withinP. These problems include calculation of the collection of all shortest paths insideP from a given source vertexS to all the other vertices ofP, calculation of the subpolygon ofP consisting of points that are visible from a given segment withinP, preprocessingP for fast "ray shooting" queries, and several related problems. more

Topics: Euclidean shortest path (62%), K shortest path routing (62%), Distance (59%) more

523 Citations

No. of papers in the topic in previous years

Top Attributes

Show by:

Topic's top 5 most impactful authors

Christos D. Zaroliagis

10 papers, 377 citations

Dieter Mitsche

8 papers, 111 citations

Mikkel Thorup

5 papers, 671 citations

Danny Z. Chen

5 papers, 174 citations

Tadao Takaoka

5 papers, 19 citations

Network Information
Related Topics (5)
Modular decomposition

3.8K papers, 124.5K citations

90% related

8.3K papers, 252.2K citations

89% related
Planar graph

10K papers, 204.5K citations

88% related
Complement graph

6.4K papers, 166.5K citations

88% related
Time complexity

36K papers, 879.5K citations

88% related