Journal ArticleDOI
All-Pairs Small-Stretch Paths
Edith Cohen,Uri Zwick +1 more
Reads0
Chats0
TLDR
Three algorithms for finding small-stretch paths between all pairs of vertices in a weighted graph with n vertices and m edges are described.About:
This article is published in Journal of Algorithms.The article was published on 2001-02-01. It has received 79 citations till now. The article focuses on the topics: Path graph & Graph power.read more
Citations
More filters
Journal ArticleDOI
Approximate distance oracles
Mikkel Thorup,Uri Zwick +1 more
TL;DR: The most impressive feature of the data structure is its constant query time, hence the name "oracle", and it provides faster constructions of sparse spanners of weighted graphs, and improved tree covers and distance labelings of weighted or unweighted graphs.
Proceedings ArticleDOI
Approximate distance oracles
Mikkel Thorup,Uri Zwick +1 more
TL;DR: The most impressive feature of the data structure is its constant query time, hence the name ``oracle', which provides faster constructions of sparse spanners of weighted graphs, and improved tree covers and distance labelings of weighted or unweighted graphs.
Journal ArticleDOI
All pairs shortest paths using bridging sets and rectangular matrix multiplication
TL;DR: Two new algorithms for solving the All Pairs Shortest Paths (APSP) problem for weighted directed graphs using fast matrix multiplication algorithms are presented.
Proceedings ArticleDOI
Fast approximation algorithms for the diameter and radius of sparse graphs
TL;DR: This paper presents the first improvement over the diameter approximation algorithm of Aingworth et.
Book ChapterDOI
Deterministic constructions of approximate distance oracles and spanners
TL;DR: The first deterministic linear time algorithm for constructing optimal spanners of weighted graphs is obtained by derandomizing the O(km) expected time algorithm of Baswana and Sen for constructing (2k–1)-spanners of size O(kn) of weighted undirected graphs without incurring any asymptotic loss in the running time or in the size of the spanners produced.
References
More filters
Journal ArticleDOI
A note on two problems in connexion with graphs
TL;DR: A tree is a graph with one and only one path between every two nodes, where at least one path exists between any two nodes and the length of each branch is given.
Book
Introduction to Algorithms
TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
Book
The Probabilistic Method
TL;DR: A particular set of problems - all dealing with “good” colorings of an underlying set of points relative to a given family of sets - is explored.
Journal ArticleDOI
Fibonacci heaps and their uses in improved network optimization algorithms
TL;DR: Using F-heaps, a new data structure for implementing heaps that extends the binomial queues proposed by Vuillemin and studied further by Brown, the improved bound for minimum spanning trees is the most striking.
Journal ArticleDOI
Matrix multiplication via arithmetic progressions
Don Coppersmith,Shmuel Winograd +1 more
TL;DR: In this article, a new method for accelerating matrix multiplication asymptotically is presented, based on the ideas of Volker Strassen, by using a basic trilinear form which is not a matrix product.