This paper introduces a novel parameter, called iterated type partition, that can be computed in polynomial time and nicely places between modular-width and neighborhood diversity. We prove that the Equitable Coloring problem is W[1]-hard when parametrized by the iterated type partition. This result extends to modular-width, answering an open question on the complexity of Equitable Coloring when parametrized by modular-width. On the contrary, we show that the Equitable Coloring problem is FPT when parameterized by neighborhood diversity. Furthermore, we present a scheme for devising FPT algorithms parameterized by iterated type partition, which enables us to find optimal solutions for several graph problems. While the considered problems are already known to be FPT with respect to modular-width, the novel algorithms are both simpler and more efficient. As an example, in this paper, we give an algorithm for the Dominating Set problem that outputs an optimal set in time O(2t + poly(n)), where n and t are the size and the iterated type partition of the input graph, respectively.

Iterated Type Partitions

Cordasco G.;Gargano L.;Rescigno A. A.
2020-01-01

Abstract

This paper introduces a novel parameter, called iterated type partition, that can be computed in polynomial time and nicely places between modular-width and neighborhood diversity. We prove that the Equitable Coloring problem is W[1]-hard when parametrized by the iterated type partition. This result extends to modular-width, answering an open question on the complexity of Equitable Coloring when parametrized by modular-width. On the contrary, we show that the Equitable Coloring problem is FPT when parameterized by neighborhood diversity. Furthermore, we present a scheme for devising FPT algorithms parameterized by iterated type partition, which enables us to find optimal solutions for several graph problems. While the considered problems are already known to be FPT with respect to modular-width, the novel algorithms are both simpler and more efficient. As an example, in this paper, we give an algorithm for the Dominating Set problem that outputs an optimal set in time O(2t + poly(n)), where n and t are the size and the iterated type partition of the input graph, respectively.
2020
978-3-030-48965-6
978-3-030-48966-3
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/11386/4773603
 Attenzione

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

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 5
social impact