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| Presentation | 2007-06-29 09:50 Testing k-Edge-Connectivity of Digraphs Yuichi Yoshida, Hiro Ito (Kyoto Univ.)  COMP2007-20 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | In this paper, we show constant time algorithm for testing whether a given degree-bounded digraph is $k$-edge-connected or $\epsilon$-far from k$-edge-connected. A digraph of $n$ vertices with degree bound $d$ is $\epsilon$-far from $k$-edge-connected, if at least $\epsilon dn$ edges have to be added or deleted to make the graph $k$-edge-connected, preserving the degree bound. Our algorithm is a testing algorithm in the sense of ``Property Testing''. Property testing is defined as follows: If the input graph is $k$-edge-connected, it must output ``Accept'' with probability at least $2/3$, and if the input graph is $\epsilon$-far from $k$-edge-connected, it must output ``Reject'' with probability at least $2/3$. It can output any for a graph which is neither $k$-edge-connected nor $\epsilon$-far from $k$-edge-connected. Since testing can be regarded as reduction of decision, the complexity of testing algorithms is expected to be smaller than that of decision algorithms. This paper presents an $O\left(d\left(\frac{c}{\epsilon d}\right)^{k}\log\frac{1}{\epsilon d}\right)$$($$c>1$ is a constant$)$ time algorithm for ($k$-1)-edge connected graphs and an $O\left(d\left(\frac{ck}{\epsilon d}\right)^{k}\log\frac{k}{\epsilon d}\right)$$($$c>1$ is a constant$)$ time algorithm for general graphs. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | graph theory / property testring / digraph / $k$-edge-connectivity / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 107, no. 127, COMP2007-20, pp. 17-23, June 2007. | |
| Paper # | COMP2007-20 | |
| Date of Issue | 2007-06-22 (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) | |
| Download PDF | COMP2007-20 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2007-06-29 - 2007-06-29 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Hokkaido University |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2007-06-COMP |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Testing k-Edge-Connectivity of Digraphs |
| Sub Title (in English) | |
| Keyword(1) | graph theory |
| Keyword(2) | property testring |
| Keyword(3) | digraph |
| Keyword(4) | $k$-edge-connectivity |
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| 1st Author's Name | Yuichi Yoshida |
| 1st Author's Affiliation | Kyoto University (Kyoto Univ.) |
| 2nd Author's Name | Hiro Ito |
| 2nd Author's Affiliation | Kyoto University (Kyoto Univ.) |
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| Speaker | Author-1 |
| Date Time | 2007-06-29 09:50:00 |
| Presentation Time | 25 minutes |
| Registration for | COMP |
| Paper # | COMP2007-20 |
| Volume (vol) | vol.107 |
| Number (no) | no.127 |
| Page | pp.17-23 |
| #Pages | 7 |
| Date of Issue | 2007-06-22 (COMP) |
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