A linear-time algorithm for minimum k-hop dominating set of a cactus graph
Given a graph G=(V,E) and an integer k≥1, a k-hop dominating setD 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 minimumk-hop dominating set. In this paper, we present a lin...
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| Published in: | Discrete Applied Mathematics Vol. 320; pp. 488 - 499 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
30.10.2022
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| ISSN: | 0166-218X, 1872-6771 |
| Online Access: | Get full text |
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| Summary: | Given a graph G=(V,E) and an integer k≥1, a k-hop dominating setD 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 minimumk-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. |
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| ISSN: | 0166-218X 1872-6771 |
| DOI: | 10.1016/j.dam.2022.06.006 |