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by Giovanni Manzini
Discrete Mathematics & Theoretical Computer Science
http://dmtcs.loria.fr/volumes/abstracts/pdfpapers/dm020103.pdf
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Abstract:
In this paper we consider the problem of computing on a local memory machine the product y = Ax, whereA is a random n n sparse matrix with (n) nonzero elements. To study the average case communication cost of this problem, we introduce four different probability measures on the set of sparse matrices. We prove that on most local memory machines with p processors, this computation requires ((n=p) log p) time on the average. We prove that the same lower bound also holds, in the worst case, for matrices with only 2n or 3n nonzero elements.
Citations
|
1230
|
Introduction to Parallel Algorithms and Architectures: Arrays
– Leighton
- 1991
|
|
1192
|
Random Graphs
– Bollobás
- 1985
|
|
403
|
Introduction to parallel computing: design and analysis of algorithms, (Benjamin-Cummings Addison-Wesley Publishing Company,Inc
– Kumar, Grama, et al.
- 1994
|
|
128
|
Generalized nested dissection
– Lipton, Rose, et al.
- 1979
|
|
41
|
Data Distributions for Sparse Matrix Vector Multiplication
– Romero, Zapata
- 1995
|
|
33
|
Load Balancing, Selection and Sorting on the Hypercube
– Plaxton
- 1989
|
|
21
|
Cutting down on fill using nested dissection: Provably good elimination orderings
– AGRAWAL, KLEIN, et al.
- 1993
|
|
15
|
Parallel solution of sparse linear and path systems
– Pan
- 1993
|
|
6
|
A new storage scheme for an efficient implementation of the sparse matrix-vector product
– Fernandes, Girdinio
- 1989
|
|
4
|
Decomposing irregularly sparse matrices for parallel matrix-vector multiplications
– atalyurek, Aykanat
- 1996
|
|
3
|
Sparse matrix vector multiplication on distributed architectures: Lower bound and average complexity results
– Manzini
- 1994
|
|
3
|
Run-time optimization of sparse matrix-vector multiplication on simd machines
– Ziantz, Ozturan, et al.
- 1994
|
|
2
|
On the ordering of sparse linear systems
– Manzini
- 1996
|
|
1
|
Structured sparse matrix-vector multiplication on massively parallel SIMD architectures. Parallel Computing 21:1867–1894
– Dehn, Eiermann, et al.
- 1995
|
|
1
|
Sparse matrix computations on the hypercube and related networks
– Manzini
- 1994
|
