We introduce a novel domination problem, which we call Dual Domination (DD). We assume that the nodes in a network are partitioned into two categories: Positive nodes (V+) and negative nodes (V−). We study the Maximum Bounded Dual Domination, where, given a bound k, the problem is to find a set D⊆V+, which maximizes the number of nodes dominated in V+, dominating at most k nodes in V−. We show that such problem is hard to approximate to a factor better than (1−1/e). We give a polynomial time algorithm with approximation guaranteed (1−e−1/Δ), where Δ represents the maximum number of neighbors in V+ of any node in V−, and an O(|V|k2) time algorithm to solve the problem on trees. We also study two related problems named Maximum Dual Domination and minimum Negative Dual Domination. For both problems, we show hardness results and provide O(|V|) time algorithms on trees.

Dual domination problems in graphs

Cordasco G.;Gargano L.;Rescigno A. A.
2022-01-01

Abstract

We introduce a novel domination problem, which we call Dual Domination (DD). We assume that the nodes in a network are partitioned into two categories: Positive nodes (V+) and negative nodes (V−). We study the Maximum Bounded Dual Domination, where, given a bound k, the problem is to find a set D⊆V+, which maximizes the number of nodes dominated in V+, dominating at most k nodes in V−. We show that such problem is hard to approximate to a factor better than (1−1/e). We give a polynomial time algorithm with approximation guaranteed (1−e−1/Δ), where Δ represents the maximum number of neighbors in V+ of any node in V−, and an O(|V|k2) time algorithm to solve the problem on trees. We also study two related problems named Maximum Dual Domination and minimum Negative Dual Domination. For both problems, we show hardness results and provide O(|V|) time algorithms on trees.
2022
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4783289
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact