TY - JOUR

T1 - A linear-time algorithm for minimum k-hop dominating set of a cactus graph

AU - Abu-Affash, A. Karim

AU - Carmi, Paz

AU - Krasin, Adi

N1 - Funding Information:
This work was partially supported by Grant 2016116 from the United States–Israel Binational Science Foundation .
Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2022/10/30

Y1 - 2022/10/30

N2 - Given a graph G=(V,E) and an integer k≥1, a k-hop dominating set D of G is a subset of V, such that, for every vertex v∈V, there exists a node u∈D whose distance from v is at most k. A k-hop dominating set of minimum cardinality is called a minimum k-hop dominating set. In this paper, we present a linear-time algorithm that finds a minimum k-hop dominating set in cactus graphs, which improves the O(n3)-time algorithm of Borradaile and Le (2017). To achieve this, we show that the k-hop dominating set problem for unicyclic graphs reduces to the piercing circular arcs problem, and show a linear-time algorithm for piercing sorted circular arcs, which improves the best known O(nlogn)-time algorithm.

AB - Given a graph G=(V,E) and an integer k≥1, a k-hop dominating set D of G is a subset of V, such that, for every vertex v∈V, there exists a node u∈D whose distance from v is at most k. A k-hop dominating set of minimum cardinality is called a minimum k-hop dominating set. In this paper, we present a linear-time algorithm that finds a minimum k-hop dominating set in cactus graphs, which improves the O(n3)-time algorithm of Borradaile and Le (2017). To achieve this, we show that the k-hop dominating set problem for unicyclic graphs reduces to the piercing circular arcs problem, and show a linear-time algorithm for piercing sorted circular arcs, which improves the best known O(nlogn)-time algorithm.

KW - Cactus graph

KW - Dominating set

KW - Piercing circular arcs

KW - Unicyclic graph

UR - http://www.scopus.com/inward/record.url?scp=85132849922&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2022.06.006

DO - 10.1016/j.dam.2022.06.006

M3 - Article

VL - 320

SP - 488

EP - 499

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -