NDLI: Parallel Tree Contraction Part 2: Further Applications

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Miller, Gary L. Reif, John H.
Copyright Year	1991
Abstract	This paper applies the parallel tree contraction techniques developed in Miller and Reifs paper [Randomness and Computation, Vol. 5, S. Micali, ed., JAI Press, 1989, pp. 4772] to a number of fundamental graph problems. The paper presents an $O(\log n)$ time and $n / \log n$ processor, a 0-sided randomized algorithm for testing the isomorphism of trees, and an $O(\log n)$ time, n algorithm for maximal subtree isomorphism and for common subexpression elimination. An O(log n) time, n-processor algorithm for computing the canonical forms of trees and subtrees is given. An Olog n time algorithm for computing the tree of 3-connected components of a graph, an $O(\log ^2 n)$ time algorithm for computing an explicit planar embedding of a planar graph, and an $O(\log ^3 n)$ time algorithm for computing a canonical form for a planar graph are also given. All these latter algorithms use only $n^{O(1)} $ processors on a Parallel Random Access Machine (PRAM) model with concurrent writes and concurrent reads.
Starting Page	1128
Ending Page	1147
Page Count	20
File Format	PDF
ISSN	00975397
DOI	10.1137/0220070
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	6
Volume Number	20
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-13
Access Restriction	Subscribed
Subject Keyword	Planar graphs; geometric and topological aspects of graph theory Trees parallel algorithms graph connectivity Analysis of algorithms and problem complexity tree contraction graph isomorphism Connectivity subexpression elimination
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Parallel tree contraction part 2: further applications*.

Optimal Parallel Algorithms for Straight-Line Grid Embeddings of Planar Graphs

Parallel Tree Contraction Part 2: Further Applications (1991)

Collective tree spanners of graphs

Navigating in a Graph by Aid of Its Spanning Tree Metric

An Efficient Parallel Algorithm for the General Planar Monotone Circuit Value Problem

Angles of Planar Triangular Graphs

Conditions for Unique Graph Realizations

A Nearly Optimal Parallel Algorithm for Constructing Depth First Spanning Trees in Planar Graphs

Parallel Tree Contraction Part 2: Further Applications

Similar Documents

Parallel tree contraction part 2: further applications*.

Optimal Parallel Algorithms for Straight-Line Grid Embeddings of Planar Graphs

Parallel Tree Contraction Part 2: Further Applications (1991)

Collective tree spanners of graphs

Navigating in a Graph by Aid of Its Spanning Tree Metric

An Efficient Parallel Algorithm for the General Planar Monotone Circuit Value Problem

Angles of Planar Triangular Graphs

Conditions for Unique Graph Realizations

A Nearly Optimal Parallel Algorithm for Constructing Depth First Spanning Trees in Planar Graphs

Parallel Tree Contraction Part 2: Further Applications