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| Presentation | 2020-10-23 17:05 Polynomial Delay Enumeration for Steiner Problems Yasuaki Kobayashi (Kyoto Univ.), Kazuhiro Kurita (NII), Kunihiro Wasa (Toyohashi Tech)  COMP2020-17 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | Let $G = (V, E)$ be a undirected graph and let $W subseteq V$ be a set of terminals. A emph{Steiner subgraph} of $(G, W)$ is a subgraph of $G$ that contains all vertices of $W$ and there is a path between every pair of vertices of $W$ in the subgraph. We say that a Steiner subgraph is minimal if it has no proper Steiner subgraph. It is easy to observe that every minimal Steiner subgraph forms a tree, which is called a minimal Steiner tree. We propose a linear delay and polynomial space algorithm for enumerating all minimal Steiner trees of $(G, W)$, which improves a previously known polynomial delay enumeration algorithm in [Kimelfeld and Sagiv, Inf. Syst., 2008]. Our enumeration algorithm can be extended to other Steiner problems: minimal Steiner forests, minimal terminal Steiner trees, minimal directed Steiner trees. As another variant of the minimal Steiner subgraph problem, we study the problem of enumerating minimal induced Steiner subgraphs. We propose a polynomial delay and exponential space enumeration algorithm of minimal induced Steiner subgraphs for claw-free graphs, whereas the problem on general graphs is shown to be at least as hard as the problem of enumerating minimal transversals in hypergraphs. Contrary to these tractable results, we show that the problem of enumerating minimal group Steiner trees is at least as hard as the minimal transversal enumeration problem on hypergraphs. | |
| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | Minimal Steiner tree / Minimal Steiner forests / Enumeration problem / Polynomial delay / Graph algorithm / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 120, no. 209, COMP2020-17, pp. 39-46, Oct. 2020. | |
| Paper # | COMP2020-17 | |
| Date of Issue | 2020-10-16 (COMP) | |
| ISSN | 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 | COMP2020-17 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2020-10-23 - 2020-10-23 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Osaka Univ. |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2020-10-COMP |
| Language | English |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Polynomial Delay Enumeration for Steiner Problems |
| Sub Title (in English) | |
| Keyword(1) | Minimal Steiner tree |
| Keyword(2) | Minimal Steiner forests |
| Keyword(3) | Enumeration problem |
| Keyword(4) | Polynomial delay |
| Keyword(5) | Graph algorithm |
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| Keyword(8) | |
| 1st Author's Name | Yasuaki Kobayashi |
| 1st Author's Affiliation | Kyoto University (Kyoto Univ.) |
| 2nd Author's Name | Kazuhiro Kurita |
| 2nd Author's Affiliation | National Institute Informatics (NII) |
| 3rd Author's Name | Kunihiro Wasa |
| 3rd Author's Affiliation | Toyohashi University of Technology (Toyohashi Tech) |
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| Speaker | Author-2 |
| Date Time | 2020-10-23 17:05:00 |
| Presentation Time | 35 minutes |
| Registration for | COMP |
| Paper # | COMP2020-17 |
| Volume (vol) | vol.120 |
| Number (no) | no.209 |
| Page | pp.39-46 |
| #Pages | 8 |
| Date of Issue | 2020-10-16 (COMP) |
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