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

Anders Dessmark, Carsten Dorgerloh, Andrzej Lingas, Jürgen Wirtgen
1998 Lecture Notes in Computer Science  
We present a rst 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.  ... 
doi:10.1007/3-540-64359-1_713 fatcat:cr7jiwspszb45i25irviorighy

Optimal parallel algorithms on planar graphs

Torben Hagerup
1990 Information and Computation  
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  ...  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  ... 
doi:10.1016/0890-5401(90)90034-f fatcat:w3zm46mljvh73cqhrctew5ukfi

The Euler tour technique and parallel rooted spanning tree

Guojin Cong, D.A. Bader
2004 International Conference on Parallel Processing, 2004. ICPP 2004.  
With a 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  ... 
doi:10.1109/icpp.2004.1327954 dblp:conf/icpp/CongB04 fatcat:5jgivpkdxncthcsb5wv2mog3re

An Adaptive Parallel Hierarchical Clustering Algorithm [chapter]

Zhaopeng Li, Kenli Li, Degui Xiao, Lei Yang
2007 Lecture Notes in Computer Science  
This paper proposed a parallel 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] .  ... 
doi:10.1007/978-3-540-75444-2_15 fatcat:lfnaehonznfhlhnnagwjo2ypxa

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

S. Rajasekaran
2005 IEEE Transactions on Parallel and Distributed Systems  
Clustering of data has numerous applications 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.  ... 
doi:10.1109/tpds.2005.72 fatcat:epykotvodfgohbmy6yyown64sa

Fast Connected Components Algorithms for the EREW PRAM

David R. Karger, Noam Nisan, Michal Parnas
1998 SIAM journal on computing (Print)  
We present fast 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.  ... 
doi:10.1137/s009753979325247x fatcat:uky3he743ba4racjxj56l32pfe

Fast connected components algorithms for the EREW PRAM

David R. Karger, Noam Nisan, Michal Parnas
1992 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures - SPAA '92  
We present fast 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.  ... 
doi:10.1145/140901.141920 dblp:conf/spaa/KargerNP92 fatcat:5cmyqdmswnhzleuzsyybmwnt4q

Simple and Work-Efficient Parallel Algorithms for the Minimum Spanning Tree Problem

Christos D. Zaroliagis
1997 Parallel Processing Letters  
Two simple 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.  ... 
doi:10.1142/s012962649700005x fatcat:avrs4fkrrndtfgydrpglshox4i

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)

David A. Bader, Guojing Cong
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  ... 
doi:10.1016/j.jpdc.2005.03.011 fatcat:uzsbaowjljehlmfgnbcc457jla

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

Seth Pettie, Vijaya Ramachandran
2002 SIAM journal on computing (Print)  
We present a 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.  ... 
doi:10.1137/s0097539700371065 fatcat:wxhdypksmjgblkjluiz4h5oc4u

A Randomized Time-Work Optimal Parallel Algorithm for Finding a Minimum Spanning Forest [chapter]

Seth Pettie, Vijaya Ramachandran
1999 Lecture Notes in Computer Science  
We present a 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.  ... 
doi:10.1007/978-3-540-48413-4_24 fatcat:jamt62p2rjdf5nbnad7fqr4xte

An Optimal Randomised Logarithmic Time Connectivity Algorithm for the EREW PRAM

Shay Halperin, Uri Zwick
1996 Journal of computer and system sciences (Print)  
Improving a long chain of works we obtain a randomised 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  ... 
doi:10.1006/jcss.1996.0078 fatcat:ksh55czujvabrhdxgqzjsqbrci
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