TY - GEN

T1 - Algorithm and Hardness Results on Liar’s Dominating Set and k-tuple Dominating Set

AU - Banerjee, Sandip

AU - Bhore, Sujoy

N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Given a graph G=(V,E), the dominating set problem asks for a minimum subset of vertices D⊆V such that every vertex u ∈ V \ D is adjacent to at least one vertex v ∈ D. That is, the set D satisfies the condition that |N[v] ∩ D| ≥ 1 for each v ∈ V, where N[v] is the closed neighborhood of v. In this paper, we study two variants of the classical dominating set problem: k-tuple dominating set (k-DS) problem and Liar’s dominating set (LDS) problem, and obtain several algorithmic and hardness results. On the algorithmic side, we present a constant factor (11/2)-approximation algorithm for the Liar’s dominating set problem on unit disk graphs. Then, we design a polynomial time approximation scheme (PTAS) for the k-tuple dominating set problem on unit disk graphs. On the hardness side, we show a Ω(n2) bits lower bound for the space complexity of any (randomized) streaming algorithm for Liar’s dominating set problem as well as for the k-tuple dominating set problem. Furthermore, we prove that the Liar’s dominating set problem on bipartite graphs is W[2]-hard.

AB - Given a graph G=(V,E), the dominating set problem asks for a minimum subset of vertices D⊆V such that every vertex u ∈ V \ D is adjacent to at least one vertex v ∈ D. That is, the set D satisfies the condition that |N[v] ∩ D| ≥ 1 for each v ∈ V, where N[v] is the closed neighborhood of v. In this paper, we study two variants of the classical dominating set problem: k-tuple dominating set (k-DS) problem and Liar’s dominating set (LDS) problem, and obtain several algorithmic and hardness results. On the algorithmic side, we present a constant factor (11/2)-approximation algorithm for the Liar’s dominating set problem on unit disk graphs. Then, we design a polynomial time approximation scheme (PTAS) for the k-tuple dominating set problem on unit disk graphs. On the hardness side, we show a Ω(n2) bits lower bound for the space complexity of any (randomized) streaming algorithm for Liar’s dominating set problem as well as for the k-tuple dominating set problem. Furthermore, we prove that the Liar’s dominating set problem on bipartite graphs is W[2]-hard.

UR - http://www.scopus.com/inward/record.url?scp=85069700991&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-25005-8_5

DO - 10.1007/978-3-030-25005-8_5

M3 - Conference contribution

AN - SCOPUS:85069700991

SN - 9783030250041

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 48

EP - 60

BT - Combinatorial Algorithms - 30th International Workshop, IWOCA 2019, Proceedings

A2 - Colbourn, Charles J.

A2 - Grossi, Roberto

A2 - Pisanti, Nadia

PB - Springer Verlag

T2 - 30th International Workshop on Combinatorial Algorithms, IWOCA 2019

Y2 - 23 July 2019 through 25 July 2019

ER -