Topic
Strong orientation
About: Strong orientation is a research topic. Over the lifetime, 52 publications have been published within this topic receiving 840 citations.
Papers published on a yearly basis
Papers
TL;DR: A data structure is presented such that each entry in the adjacency matrix of a planar graph can be looked up in constant time, and can be constructed in linear time.
156 citations
TL;DR: This paper focuses on how similar questions can be asked about hypergraphs, and it is shown that often the answers are also similar many known graph orientation theorems can be extended to hyper graphs, using the familiar uncrossing techniques.
98 citations
TL;DR: It is proved that, if a mixed multigraph of radius r has any strongly connected orientation, it must have an orientation of radius at most 42 + Ar, and the proof gives a polynomial-time algorithm for constructing such an orientation.
Abstract: We study the problem of orienting all the undirected edges of a mixed multigraph so as to preserve reachability. Extending work by Robbins and by Boesch and Tindell, we develop a linear-time algorithm to test whether there is an orientation that preserves strong connectivity and to construct such an orientation whenever possible. This algorithm makes no attempt to minimize distances in the resulting directed graph, and indeed the maximum distance, for example, can blow up by a factor proportional to the number of vertices in the graph. Extending work by Chvatal and Thomassen, we then prove that, if a mixed multigraph of radius r has any strongly connected orientation, it must have an orientation of radius at most 42 + Ar. The proof gives a polynomial-time algorithm for constructing such an orientation.
67 citations
TL;DR: This work presents the first randomized O(logn) time and O(m+n) work EREW PRAM algorithm for finding a spanning forest of an undirected graph G=(V,E) with n vertices and m edges.
42 citations
TL;DR: This work describes optimal PRAM algorithms for the connected components, spanning tree, biconnected components, and strong orientation problems that work on classes of undirected graphs including planar graphs and graphs of bounded genus.
Abstract: Few existing parallel graph algorithms achieve optimality when applied to very sparse graphs such as planar graphs. We describe optimal PRAM algorithms for the connected components, spanning tree, biconnected components, and strong orientation problems that work on classes of undirected graphs including planar graphs and graphs of bounded genus. The running times achieved for n -vertex input graphs are O (log n ) on the CRCW PRAM and O( log n log ∗ n) on the EREW PRAM. We also give (non-optimal) randomized EREW PRAM algorithms using O (log n ) time and n processors, and non-uniform deterministic EREW PRAM algorithms using O (log n ) time and O ( n 2 ) processors.
41 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2020 | 2 |
| 2018 | 1 |
| 2017 | 2 |
| 2016 | 1 |
| 2015 | 3 |