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| Presentation | 2007-09-20 13:15 Approximating the Distribution Function of Minimum Spanning Tree Cost with Normally Disributed Stochastic Edge Weights Ei Ando, Hirotaka Ono, Kunihiko Sadakane, Masafumi Yamashita (Kyushu Univ.)  COMP2007-35 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | Given a graph $G$ of $n$ vertices whose edge weights are random variables and obey mutually independent normal distributions, we consider a stochastic minimum spanning tree problem. The weight of the minimum spanning tree is also a random variable, but its distribution function $F_{\rm MST}(x)$ cannot be represented by a simple distribution function in general. We show an algorithm, whose output is a approximation function $\tilde F(x)$ of the distribution function of stochastic minimum spanning tree weight. Its running time is $O({\rm MST}(G) + m + n\log n)$, where $m$ is the number of edges in $G$ and ${\rm MST}(G)$ is the time complexity of the (deterministic) minimum spanning tree weights. Let $\cal{T}$ be the family of all spanning trees in $G$. $\tilde F(x)$ gives an upper bound on $F_{\rm MST}(x)$ for $x$ such that $\tilde F(x)\le 1-2^{-|\cal{T}|}$, and $\tilde F(x)$ satisfies that $|F_{\rm MST}^{-1}(a)-\tilde F^{-1}(a)|=o(n\sigma\sqrt{\log n})$ for $0< a \le 1-2^{-|\cal{T}|}$ where $\sigma^2$ is the maximum variance of edge weights. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | Minimum spanning tree / Stochastic edge weight / Normal distribution / / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 107, no. 219, COMP2007-35, pp. 21-27, Sept. 2007. | |
| Paper # | COMP2007-35 | |
| Date of Issue | 2007-09-13 (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 | COMP2007-35 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2007-09-20 - 2007-09-20 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2007-09-COMP |
| Language | English |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Approximating the Distribution Function of Minimum Spanning Tree Cost with Normally Disributed Stochastic Edge Weights |
| Sub Title (in English) | |
| Keyword(1) | Minimum spanning tree |
| Keyword(2) | Stochastic edge weight |
| Keyword(3) | Normal distribution |
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| 1st Author's Name | Ei Ando |
| 1st Author's Affiliation | Kyushu University (Kyushu Univ.) |
| 2nd Author's Name | Hirotaka Ono |
| 2nd Author's Affiliation | Kyushu University (Kyushu Univ.) |
| 3rd Author's Name | Kunihiko Sadakane |
| 3rd Author's Affiliation | Kyushu University (Kyushu Univ.) |
| 4th Author's Name | Masafumi Yamashita |
| 4th Author's Affiliation | Kyushu University (Kyushu Univ.) |
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| Speaker | Author-1 |
| Date Time | 2007-09-20 13:15:00 |
| Presentation Time | 35 minutes |
| Registration for | COMP |
| Paper # | COMP2007-35 |
| Volume (vol) | vol.107 |
| Number (no) | no.219 |
| Page | pp.21-27 |
| #Pages | 7 |
| Date of Issue | 2007-09-13 (COMP) |
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