Łącki, Jakub, Oćwieja, Jakub, Pilipczuk, Marcin, Sankowski, Piotr and Zych, Anna (2015) The power of dynamic distance oracles : efficient dynamic algorithms for the Steiner tree. In: STOC '15 Forty-Seventh Annual ACM on Symposium on Theory of Computing, Portland, OR, 14-17 Jun 2015. Published in: STOC '15 Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing pp. 11-20. ISBN 9781450335362. doi:10.1145/2746539.2746615

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Abstract

In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an n-vertex graph G=(V,E,w) with positive real edge weights, and our goal is to maintain a tree which is a good approximation of the minimum Steiner tree spanning a terminal set S ⊆ V, which changes over time. The changes applied to the terminal set are either terminal additions (incremental scenario), terminal removals (decremental scenario), or both (fully dynamic scenario). Our task here is twofold. We want to support updates in sublinear o(n) time, and keep the approximation factor of the algorithm as small as possible.

We show that we can maintain a (6+ε)-approximate Steiner tree of a general graph in ~O(√n log D) time per terminal addition or removal. Here, strecz denotes the stretch of the metric induced by G. For planar graphs we achieve the same running time and the approximation ratio of (2+ε). Moreover, we show faster algorithms for incremental and decremental scenarios. Finally, we show that if we allow higher approximation ratio, even more efficient algorithms are possible. In particular we show a polylogarithmic time (4+ε)-approximate algorithm for planar graphs.

One of the main building blocks of our algorithms are dynamic distance oracles for vertex-labeled graphs, which are of independent interest. We also improve and use the online algorithms for the Steiner tree problem.

Item Type:	Conference Item (Paper)
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions:	Faculty of Science, Engineering and Medicine > Science > Computer Science
Library of Congress Subject Headings (LCSH):	Trees (Graph theory), Steiner systems, Graph algorithms
Journal or Publication Title:	STOC '15 Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing
Publisher:	ACM
ISBN:	9781450335362
Book Title:	Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing - STOC '15
Editor:	Servedio, Rocco A. and Rubinfeld, Ronitt
Official Date:	2015
Dates:	Date Event 2015 Published
Page Range:	pp. 11-20
DOI:	10.1145/2746539.2746615
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Google (Firm), European Research Council (ERC), Seventh Framework Programme (European Commission) (FP7)
Grant number:	259515 (ERC), 267959 (ERC)
Conference Paper Type:	Paper
Title of Event:	STOC '15 Forty-Seventh Annual ACM on Symposium on Theory of Computing
Type of Event:	Conference
Location of Event:	Portland, OR
Date(s) of Event:	14-17 Jun 2015

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