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Ultrafast randomized parallel construction and approximation algorithms for spanning forests in dense graphs
[chapter]

1998
*
Lecture Notes in Computer Science
*

We present a rst

doi:10.1007/3-540-64359-1_713
fatcat:cr7jiwspszb45i25irviorighy
*randomized*Olog k n time*and*On+m w ork CRCW-*PRAM**algorithm**for*nding a*spanning**forest*of an undirected dense*graph*with n vertices. ... Furthermore we construct a*randomized*Olog log n time*and*On log n w ork CREW-*PRAM**algorithm**for*nding*spanning*trees in*random**graphs*. ... Introduction*Finding*a*spanning**forest*of an undirected*graph*G = V;E is one of the most*basic**algorithmic**graph**problems*. ...##
###
Optimal parallel algorithms on planar graphs

1990
*
Information and Computation
*

We describe

doi:10.1016/0890-5401(90)90034-f
fatcat:w3zm46mljvh73cqhrctew5ukfi
*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*... We also give (non-*optimal*)*randomized**EREW**PRAM**algorithms*using O(logn) time*and*n processors,*and*non-uniform deterministic*EREW**PRAM**algorithms*using O(log n) time*and*O(n') processors. ! ... Our CRCW*PRAM**and**EREW**PRAM**algorithms**for*the*connected*components*and*the closely related undirected*spanning*tree*problems*are presented in Sections 3*and*4, respectively, while Section 5 gives efficient ...##
###
The Euler tour technique and parallel rooted spanning tree

2004
*
International Conference on Parallel Processing, 2004. ICPP 2004.
*

With a

doi:10.1109/icpp.2004.1327954
dblp:conf/icpp/CongB04
fatcat:5jgivpkdxncthcsb5wv2mog3re
*randomized*work-time*optimal*unrooted*spanning*tree*algorithm**and*work-time*optimal*list ranking,*finding*rooted*spanning*trees can be done work-time*optimally*on*EREW**PRAM*w.h.p. ... Many parallel*algorithms**for**graph**problems*start with*finding*a*spanning*tree*and*rooting the tree to define some structural relationship on the vertices which can be used by following*problem*specific ...*For*example, pre-*and*post-order numbering, computing the vertex level, computing the number of descendants,*and**finding*a centroid, can be done work-time*optimally*on*EREW**PRAM*by applying the Euler tour ...##
###
An Adaptive Parallel Hierarchical Clustering Algorithm
[chapter]

2007
*
Lecture Notes in Computer Science
*

This paper proposed a parallel

doi:10.1007/978-3-540-75444-2_15
fatcat:lfnaehonznfhlhnnagwjo2ypxa
*EREW*deterministic*algorithm**for*hierarchical clustering. ... Based on*algorithms*of complete*graph**and*Euclidean minimum*spanning*tree, the proposed*algorithms*can cluster n objects with O(p) processors in O(n 2 /p) time where n n p log 1 ≤ ≤ . ... So the main wok*for*hierarchical clustering is to*finding*EMST*and*identifying the*connected*components of a*graph*[2, 3, 4] . ...##
###
Page 531 of Mathematical Reviews Vol. , Issue 2002A
[page]

2002
*
Mathematical Reviews
*

*Algorithms*39 (2001), no. 1, 1-46 Halperin

*and*Zwick present an

*optimal*

*randomized*

*algorithm*

*for*

*finding*

*spanning*

*forests*in the

*EREW*

*PRAM*model. ...

*Algorithms*2002a:68148 2002a:68145 68W10 68R10 Halperin, Shay (I1L-TLAV-C; Tel Aviv); Zwick, Uri (IL-TLAV-C; Tel Aviv

*Optimal*

*randomized*

*EREW*

*PRAM*

*algorithms*

*for*

*finding*

*spanning*

*forests*. ...

##
###
Efficient parallel hierarchical clustering algorithms

2005
*
IEEE Transactions on Parallel and Distributed Systems
*

Clustering of data has numerous applications

doi:10.1109/tpds.2005.72
fatcat:epykotvodfgohbmy6yyown64sa
*and*has been studied extensively. Though most of the*algorithms*in the literature are sequential, many parallel*algorithms*have also been designed. ... In this paper, we present parallel*algorithms*with better performance than known*algorithms*. ... ACKNOWLEDGMENTS This research has been supported in part by US National Science Foundation Grants CCR9912395*and*ITR0326155. ...##
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Fast Connected Components Algorithms for the EREW PRAM

1998
*
SIAM journal on computing (Print)
*

We present fast

doi:10.1137/s009753979325247x
fatcat:uky3he743ba4racjxj56l32pfe
*and*e cient parallel*algorithms**for*nding the*connected*components of an undirected*graph*. These*algorithms*run on the exclusive-read, exclusive-write (*EREW*)*PRAM*. ... On a*graph*with n vertices*and*m edges, our*randomized**algorithm*runs in O(log n) time using (m+n 1+ )= log n*EREW*processors (*for*any xed > 0). ... Thanks also to Rajeev Motwani*and*Serge Plotkin*for*helpful discussions. ...##
###
Fast connected components algorithms for the EREW PRAM

1992
*
Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures - SPAA '92
*

We present fast

doi:10.1145/140901.141920
dblp:conf/spaa/KargerNP92
fatcat:5cmyqdmswnhzleuzsyybmwnt4q
*and*e cient parallel*algorithms**for*nding the*connected*components of an undirected*graph*. These*algorithms*run on the exclusive-read, exclusive-write (*EREW*)*PRAM*. ... On a*graph*with n vertices*and*m edges, our*randomized**algorithm*runs in O(log n) time using (m+n 1+ )= log n*EREW*processors (*for*any xed > 0). ... Thanks also to Rajeev Motwani*and*Serge Plotkin*for*helpful discussions. ...##
###
Simple and Work-Efficient Parallel Algorithms for the Minimum Spanning Tree Problem

1997
*
Parallel Processing Letters
*

Two simple

doi:10.1142/s012962649700005x
fatcat:avrs4fkrrndtfgydrpglshox4i
*and*work-e cient parallel*algorithms**for*the minimum*spanning*tree*problem*are presented. Both*algorithms*perform O(m log n) w ork. ... The rst*algorithm*runs in O(log 2 n) time on an*EREW**PRAM*, while the second*algorithm*runs in O(log n) time on a Common CRCW*PRAM*. ... I w ould also like to thank Jesper Tr a*for*many helpful discussions*and*comments on an earlier version of this paper. ...##
###
Page 486 of Mathematical Reviews Vol. , Issue 98A
[page]

1998
*
Mathematical Reviews
*

*EREW*

*PRAM*

*algorithm*

*for*minimum

*spanning*tree verification. ... Summary: “We present a deterministic parallel

*algorithm*on the

*EREW*

*PRAM*model to verify a minimum

*spanning*tree of a

*graph*. ...

##
###
Page 7893 of Mathematical Reviews Vol. , Issue 99k
[page]

1999
*
Mathematical Reviews
*

The

*problem*of constructing a*spanning**forest*is to*find*a*spanning*tree*for*each*connected*component of G.*For*a simple*graph*, F. Y. Chin, J. Lam*and*I. N. Chen [Comm. ... In this paper, we propose an O(logn) time parallel*algorithm*with O(n/logn) processors on the*EREW**PRAM**for*constructing a*spanning**forest*on interval*graphs*.” 99k:68073 68Q22 68-01 68M05 68Q05 Xavier, ...##
###
A fast, parallel spanning tree algorithm for symmetric multiprocessors (SMPs)

2005
*
Journal of Parallel and Distributed Computing
*

*Spanning*tree is an important

*problem*in the sense that it is the building block

*for*many

*other*parallel

*graph*

*algorithms*

*and*also because * ... Many

*PRAM*

*algorithms*can be adapted to SMPs with few modifications. Yet there are few studies that deal with the implementation

*and*performance issues of running

*PRAM*

*algorithms*on SMPs. ... We plan to apply the techniques discussed in this paper to

*other*related

*graph*

*problems*,

*for*instance, minimum

*spanning*tree (

*forest*),

*connected*components,

*and*planarity testing

*algorithms*,

*for*symmetric ...

##
###
A Randomized Time-Work Optimal Parallel Algorithm for Finding a Minimum Spanning Forest

2002
*
SIAM journal on computing (Print)
*

We present a

doi:10.1137/s0097539700371065
fatcat:wxhdypksmjgblkjluiz4h5oc4u
*randomized**algorithm*to*find*a minimum*spanning**forest*(MSF) in an undirected*graph*. ... We present a*randomized*parallel*algorithm*to*find*a minimum*spanning**forest*(MSF) in an edge-weighted, undirected*graph*. ... Our*algorithm*improves on the*EREW**connectivity**and**spanning*tree*algorithms*in [HZ96, HZ01] since we compute a minimum*spanning*tree within the same time*and*work bounds. ...##
###
A Randomized Time-Work Optimal Parallel Algorithm for Finding a Minimum Spanning Forest
[chapter]

1999
*
Lecture Notes in Computer Science
*

We present a

doi:10.1007/978-3-540-48413-4_24
fatcat:jamt62p2rjdf5nbnad7fqr4xte
*randomized**algorithm*to*find*a minimum*spanning**forest*(MSF) in an undirected*graph*. ... We present a*randomized*parallel*algorithm*to*find*a minimum*spanning**forest*(MSF) in an edge-weighted, undirected*graph*. ... Our*algorithm*improves on the*EREW**connectivity**and**spanning*tree*algorithms*in [HZ96, HZ01] since we compute a minimum*spanning*tree within the same time*and*work bounds. ...##
###
An Optimal Randomised Logarithmic Time Connectivity Algorithm for the EREW PRAM

1996
*
Journal of computer and system sciences (Print)
*

Improving a long chain of works we obtain a randomised

doi:10.1006/jcss.1996.0078
fatcat:ksh55czujvabrhdxgqzjsqbrci
*EREW**PRAM**algorithm**for*nding the*connected*components of a*graph*G = (V; E) with n vertices*and*m edges in O(logn) time using an*optimal*number of ... Johnson*and*Metaxas have later shown JM92] that their*algorithm*can also be implemented in the*EREW**PRAM*model. ... Acknowlegement The authors would like to thank two anonymous referees*for*their careful reading of the paper*and**for*their extensive list of comments that helped us to improve the presentation*and*the ...
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