Nearly ETH-tight algorithms for planar Steiner Tree with terminals on few faces

Sándor Kisfaludi-Bak, Jesper Nederlof, Erik Jan van Leeuwen

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

3 Citations (Scopus)

Abstract

The Steiner Tree problem is one of the most fundamental NP-complete problems as it models many network design problems. Recall that an instance of this problem consists of a graph with edge weights, and a subset of vertices (often called terminals); the goal is to find a subtree of the graph of minimum total weight that connects all terminals. A seminal paper by Erickson et al. [Math. Oper. Res., 1987] considers instances where the underlying graph is planar and all terminals can be covered by the boundary of k faces. Erickson et al. show that the problem can be solved by an algorithm using nO(k) time and nO(k) space, where n denotes the number of vertices of the input graph. In the past 30 years there has been no significant improvement of this algorithm, despite several efforts. In this work, we give an algorithm for Planar Steiner Tree with running time 2O(k)nO(k) using only polynomial space. Furthermore, we show the running time of our algo-rithm is almost tight: we prove that there is no f(k)no(k) algorithm for Planar Steiner Tree for any computable function f, unless the Exponential Time Hypothesis fails.

Original languageEnglish
Title of host publicationProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms
EditorsTimothy M. Chan
Place of PublicationNew York
PublisherAssociation for Computing Machinery, Inc
Pages1015-1034
Number of pages20
ISBN (Electronic)978-1-61197-548-2
DOIs
Publication statusPublished - 2019
Event30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 - San Diego, United States
Duration: 6 Jan 20199 Jan 2019

Conference

Conference30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019
CountryUnited States
CitySan Diego
Period6/01/199/01/19

Fingerprint Dive into the research topics of 'Nearly ETH-tight algorithms for planar Steiner Tree with terminals on few faces'. Together they form a unique fingerprint.

Cite this