@inproceedings{98873d378c21424eb058f4a8362e576b,

title = "Parameterized study of steiner tree on unit disk graphs",

abstract = "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.",

keywords = "FPT, NP-Hardness, Subexponential exact algorithms, Unit Disk Graphs, W-Hardness",

author = "Sujoy Bhore and Paz Carmi and Sudeshna Kolay and Meirav Zehavi",

note = "Publisher Copyright: {\textcopyright} Sujoy Bhore, Paz Carmi, Sudeshna Kolay, and Meirav Zehavi; licensed under Creative Commons License CC-BY; 17th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2020 ; Conference date: 22-06-2020 Through 24-06-2020",

year = "2020",

month = jun,

day = "1",

doi = "10.4230/LIPIcs.SWAT.2020.13",

language = "English",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

editor = "Susanne Albers",

booktitle = "17th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2020",

address = "Germany",

}