About: Hydras: Complexity on general graphs and a subclass of trees

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://www.cs.uic.edu/pub/Isaim2014/WebPreferences/ISAIM2014_Boolean_Kucera.pdf
Description	Hydra formulas were introduced in (Sloan, Stasi, and Turan 2012). A hydra formula is a Horn formula consisting of definite Horn clauses of size 3 specified by a set of bodies of size 2, and containing clauses formed by these bodies and all possible heads. A hydra formula can be specified by the undirected graph formed by the bodies occurring in the formula. The minimal formula size for hydras is then called the hydra number of the underlying graph. In this paper we aim to answer some open questions regarding complexity of determining the hydra number of a graph which were left open in (Sloan, Stasi, and Turan 2012). In particular we show that the problem of checking, whether a graph G = (V, E) is single-headed, i.e. whether the hydra number of G is equal to the number of edges, is NP-complete. We also consider hydra number of trees and we describe a family of trees for which the hydra number can be determined in polynomial time. Hydra formulas were introduced in (Sloan, Stasi, and Turan 2012). A hydra formula is a Horn formula consisting of definite Horn clauses of size 3 specified by a set of bodies of size 2, and containing clauses formed by these bodies and all possible heads. A hydra formula can be specified by the undirected graph formed by the bodies occurring in the formula. The minimal formula size for hydras is then called the hydra number of the underlying graph. In this paper we aim to answer some open questions regarding complexity of determining the hydra number of a graph which were left open in (Sloan, Stasi, and Turan 2012). In particular we show that the problem of checking, whether a graph G = (V, E) is single-headed, i.e. whether the hydra number of G is equal to the number of edges, is NP-complete. We also consider hydra number of trees and we describe a family of trees for which the hydra number can be determined in polynomial time. (en)
Title	Hydras: Complexity on general graphs and a subclass of trees Hydras: Complexity on general graphs and a subclass of trees (en)
skos:prefLabel	Hydras: Complexity on general graphs and a subclass of trees Hydras: Complexity on general graphs and a subclass of trees (en)
skos:notation	RIV/00216208:11320/14:10287895!RIV15-GA0-11320___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GAP202/10/1188)
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Kučera, Petr
http://linked.open.../riv/druhVysledku	O - Ostatní výsledky nezařaditelné do žádného z výše uvedených druhů výsledku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	20057
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/14:10287895
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Horn minimization; Horn formula; Hydra number (en)
http://linked.open.../riv/klicoveSlovo	Horn minimization Horn formula Hydra number
http://linked.open...ontrolniKodProRIV	[5C6B4CB7DACF]
http://linked.open...in/vavai/riv/obor	IN
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	KnowSched: Knowledge Techniques in Scheduling
http://linked.open...UplatneniVysledku	2014
http://linked.open...iv/tvurceVysledku	Kučera, Petr
http://localhost/t...ganizacniJednotka	11320

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