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Paper Abstract and Keywords
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
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 Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380
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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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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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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
Date Time 2020-10-23 17:05:00 
Presentation Time 35 
Registration for COMP 
Paper # IEICE-COMP2020-17 
Volume (vol) IEICE-120 
Number (no) no.209 
Page pp.39-46 
#Pages IEICE-8 
Date of Issue IEICE-COMP-2020-10-16 


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