Paper Abstract and Keywords |
Presentation |
2016-10-21 10:30
Further Algebraic Algorithms in the Congested Clique Model and Applications to Graph-Theoretic Problems Francois Le Gall (Kyoto Univ.) COMP2016-24 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
Censor-Hillel et al.~[PODC'15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in the past few years. This paper develops further algebraic techniques for designing algorithms in this model. We present deterministic and randomized algorithms, in the congested clique model, for efficiently computing multiple independent instances of matrix products, computing the determinant, the rank and the inverse of a matrix, and solving systems of linear equations. As applications of these techniques, we obtain more efficient algorithms for the computation, again in the congested clique model, of the all-pairs shortest paths and the diameter in directed and undirected graphs with small weights, improving over Censor-Hillel et al.'s work. We also obtain algorithms for several other graph-theoretic problems such as computing the number of edges in a maximum matching and the Gallai-Edmonds decomposition of a simple graph, and computing a minimum vertex cover of a bipartite graph. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
distributed computing / matrix multiplication / congested clique model / / / / / |
Reference Info. |
IEICE Tech. Rep., vol. 116, no. 262, COMP2016-24, pp. 9-15, Oct. 2016. |
Paper # |
COMP2016-24 |
Date of Issue |
2016-10-14 (COMP) |
ISSN |
Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 |
Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) |
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COMP2016-24 |
Conference Information |
Committee |
COMP |
Conference Date |
2016-10-21 - 2016-10-21 |
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(See Japanese page) |
Place (in English) |
Tohoku University |
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Paper Information |
Registration To |
COMP |
Conference Code |
2016-10-COMP |
Language |
English |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
Further Algebraic Algorithms in the Congested Clique Model and Applications to Graph-Theoretic Problems |
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distributed computing |
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matrix multiplication |
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congested clique model |
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Francois Le Gall |
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Kyoto University (Kyoto Univ.) |
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Speaker |
Author-1 |
Date Time |
2016-10-21 10:30:00 |
Presentation Time |
30 minutes |
Registration for |
COMP |
Paper # |
COMP2016-24 |
Volume (vol) |
vol.116 |
Number (no) |
no.262 |
Page |
pp.9-15 |
#Pages |
7 |
Date of Issue |
2016-10-14 (COMP) |
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