TY - GEN

T1 - Parameterized study of steiner tree on unit disk graphs

AU - Bhore, Sujoy

AU - Carmi, Paz

AU - Kolay, Sudeshna

AU - Zehavi, Meirav

N1 - Funding Information:
Funding Sujoy Bhore: Research of Sujoy Bhore was supported by the Austrian Science Fund (FWF), grant P 31119. Paz Carmi: Research of Paz Carmi was partially supported by the Lynn and William Frankel Center for Computer Science and by Grant 2016116 from the United States-Israel Binational Science Foundation. Meirav Zehavi: Research of Meirav Zehavi was supported by the Israel Science Foundation (ISF) grant no. 1176/18 and United States - Israel Binational Science Foundation (BSF) grant no. 2018302.
Publisher Copyright:
© Sujoy Bhore, Paz Carmi, Sudeshna Kolay, and Meirav Zehavi; licensed under Creative Commons License CC-BY

PY - 2020/6/1

Y1 - 2020/6/1

N2 - We study the Steiner Tree problem on unit disk graphs. Given a n vertex unit disk graph G, a subset R ⊆ V(G) of t vertices and a positive integer k, the objective is to decide if there exists a tree T in G that spans over all vertices of R and uses at most k vertices from V \R. The vertices of R are referred to as terminals and the vertices of V(G) \R as Steiner vertices. First, we show that the problem is NP-hard. Next, we prove that the Steiner Tree problem on unit disk graphs can be solved in nO(√t+k) time. We also show that the Steiner Tree problem on unit disk graphs parameterized by k has an FPT algorithm with running time 2O(k)nO(1). In fact, the algorithms are designed for a more general class of graphs, called clique-grid graphs [16]. We mention that the algorithmic results can be made to work for Steiner Tree on disk graphs with bounded aspect ratio. Finally, we prove that Steiner Tree on disk graphs parameterized by k is W[1]-hard.

AB - We study the Steiner Tree problem on unit disk graphs. Given a n vertex unit disk graph G, a subset R ⊆ V(G) of t vertices and a positive integer k, the objective is to decide if there exists a tree T in G that spans over all vertices of R and uses at most k vertices from V \R. The vertices of R are referred to as terminals and the vertices of V(G) \R as Steiner vertices. First, we show that the problem is NP-hard. Next, we prove that the Steiner Tree problem on unit disk graphs can be solved in nO(√t+k) time. We also show that the Steiner Tree problem on unit disk graphs parameterized by k has an FPT algorithm with running time 2O(k)nO(1). In fact, the algorithms are designed for a more general class of graphs, called clique-grid graphs [16]. We mention that the algorithmic results can be made to work for Steiner Tree on disk graphs with bounded aspect ratio. Finally, we prove that Steiner Tree on disk graphs parameterized by k is W[1]-hard.

KW - FPT

KW - NP-Hardness

KW - Subexponential exact algorithms

KW - Unit Disk Graphs

KW - W-Hardness

UR - http://www.scopus.com/inward/record.url?scp=85090391601&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.SWAT.2020.13

DO - 10.4230/LIPIcs.SWAT.2020.13

M3 - Conference contribution

AN - SCOPUS:85090391601

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 17th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2020

A2 - Albers, Susanne

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 17th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2020

Y2 - 22 June 2020 through 24 June 2020

ER -