Abstract. In this paper, we present deterministic parallel algorithms for the coarse grained multicomputer (CGM) and bulk-synchronous parallel computer (BSP) models which solvethe following well known graph problems: (1) list ranking, (2) Euler tour construction, (3) computing the connected components and spanning forest, (4) lowest common ancestor preprocessing, (5) tree contraction and expression tree evaluation, (6) computing an ear decomposition or open ear decomposition, (7) 2-edge connectivity and biconnectivity (testing and component computation), and (8) cordal graph recognition ( nding a perfect elimination ordering). The algorithms for Problems 1-7 require O(log p) communication rounds and linear sequential work per round. Our results for Problems 1 and 2,i.e.they are fully scalable, andfor Problems hold for arbitrary ratios n p 3-8 it is assumed that n p,>0, which is true for all commercially
|
970
|
A bridging model for parallel computation
– Valiant
- 1997
|
|
557
|
An Introduction to Parallel Algorithms
– JaJa
- 1992
|
|
295
|
Parallel Merge Sort
– Cole
- 1988
|
|
274
|
Computational Geometry. An introduction through randomized algorithms
– Mulmuley
- 1994
|
|
245
|
Algorithmic Aspects of Vertex Elimination on Graphs
– Rose, Tarjan, et al.
- 1976
|
|
185
|
Direct Bulk-Synchronous Parallel Algorithms
– Gerbessiotis, Valiant
- 1992
|
|
174
|
A comparison of sorting algorithms for the connection machine CM-2
– Blelloch, Leiserson, et al.
- 1991
|
|
113
|
Parallel tree contraction and its applications
– Miller, Reif
- 1985
|
|
103
|
An O(log n) parallel connectivity algorithm
– Shiloach, Vishkin
- 1982
|
|
92
|
On rigid circuit graphs
– Dirac
- 1961
|
|
89
|
Scalable parallel geometric algorithms for coarse grained multicomputers
– Dehne, Fabri, et al.
- 1993
|
|
65
|
Type Architecture, Shared Memory and the Corollary of Moest Potential
– Snyder
- 1986
|
|
62
|
A randomized parallel 3D convex hull algorithm for coarse grained multicomputers
– Dehne, Deng, et al.
- 1995
|
|
60
|
Approximate Parallel Scheduling. Part I: The Basic Technique with Applications to Optimal Parallel List Ranking in Logarithmic Time
– Cole, Vishkin
- 1988
|
|
48
|
Non-separable and planar graphs
– Whitney
- 1932
|
|
42
|
Parallel ear decomposition search (eds) and st-numbering in graphs
– Maon, Vishkin
- 1986
|
|
38
|
Scalable and Architecture Independent Parallel Geometric Algorithms with High Probability Optimal Time
– Dehne, Fabri, et al.
- 1994
|
|
36
|
Parallel sorting by overpartitioning
– Li, Sevick
- 1994
|
|
35
|
A Comparison of Shared and Nonshared Memory Models of Computation
– Anderson, Snyder
- 1991
|
|
34
|
List Ranking and List Scan on the Cray C-90
– Reid-Miller
- 1994
|
|
30
|
Parallel open ear decomposition with applications to graph biconnectivity and triconnectivity. to appear, Synthesis of Parallel Algorithms
– Ramachandran
- 1992
|
|
27
|
Practical parallel algorithms for personalized communication and integer sorting
– Bader, Helman, et al.
- 1996
|
|
25
|
The E-BSP Model: Incorporating general locality and unbalanced communication into the BSP Model
– Juurlink, Wijshoff
- 1996
|
|
24
|
Efficient parallel ear decomposition with applications
– Miller, Ramachandran
- 1986
|
|
23
|
E cient routing and message bounds for optimal parallel algorithms
– Deng, Dymond
- 1995
|
|
22
|
Good programming style on multiprocessors
– Deng, Gu
- 1994
|
|
22
|
Efficient parallel algorithms for chordal graphs
– Klein
- 1996
|
|
20
|
A convex hull algorithm for coarse grained multiprocessors
– Deng
- 1994
|
|
20
|
Scalable 2d convex hull and triangulation algorithms for coarse grained multicomputers
– Ferreira, Rau-Chaplin, et al.
- 1995
|
|
15
|
Randomized Parallel List Ranking for Distributed Memory Multiprocessors
– Dehne, Song
- 1996
|
|
15
|
Practical Parallel List Ranking
– Sibeyn, Guillaume, et al.
- 1999
|
|
13
|
Parallel algorithms for image processing: Practical algorithms with experiments
– Baumker, Dittrich
- 1996
|
|
10
|
An e cient parallel biconnectivity algorithm
– Tarjan, Vishkin
- 1985
|
|
7
|
Parallel Computation
– Akl
- 1997
|
|
7
|
The queue-read queue-write asynchronous PRAM model
– Gibbons, Matias, et al.
- 1996
|
|
6
|
Communication-e cient parallel sorting
– Goodrich
- 1996
|
|
6
|
Reif (editor), Synthesis Of Parallel Algorithms
– H
- 1993
|
|
3
|
et al. General purpose parallel architectures
– Valiant
- 1990
|
|
1
|
cient Routing andMessage Bounds for Optimal Parallel Algorithms
– Dymond
- 1995
|
|
1
|
Algorithmica Special Issue on "Coarse grained parallel algorithms
– Dehne
- 1999
|
