Matches in SemOpenAlex for { <https://semopenalex.org/work/W1913458311> ?p ?o ?g. }
Showing items 1 to 83 of
83
with 100 items per page.
- W1913458311 abstract "A $k$-dimensional box is the Cartesian product $R_1 times R_2 times ... times R_k$ where each $R_i$ is a closed interval on the real line. The {it boxicity} of a graph $G$, denoted as $boxi(G)$, is the minimum integer $k$ such that $G$ can be represented as the intersection graph of a collection of $k$-dimensional boxes. A unit cube in $k$-dimensional space or a $k$-cube is defined as the Cartesian product $R_1 times R_2 times ... times R_k$ where each $R_i$ is a closed interval on the real line of the form $[a_i,a_i + 1]$. The {it cubicity} of $G$, denoted as $cub(G)$, is the minimum integer $k$ such that $G$ can be represented as the intersection graph of a collection of $k$-cubes. The {it threshold dimension} of a graph $G(V,E)$ is the smallest integer $k$ such that $E$ can be covered by $k$ threshold spanning subgraphs of $G$. In this paper we will show that there exists no polynomial-time algorithm to approximate the threshold dimension of a graph on $n$ vertices with a factor of $O(n^{0.5-epsilon})$ for any $epsilon >0$, unless $NP=ZPP$. From this result we will show that there exists no polynomial-time algorithm to approximate the boxicity and the cubicity of a graph on $n$ vertices with factor $O(n^{0.5-epsilon})$ for any $ epsilon >0$, unless $NP=ZPP$. In fact all these hardness results hold even for a highly structured class of graphs namely the split graphs. We will also show that it is NP-complete to determine if a given split graph has boxicity at most 3." @default.
- W1913458311 created "2016-06-24" @default.
- W1913458311 creator A5019703184 @default.
- W1913458311 creator A5024359075 @default.
- W1913458311 creator A5056606992 @default.
- W1913458311 date "2009-03-05" @default.
- W1913458311 modified "2023-09-27" @default.
- W1913458311 title "The Hardness of Approximating the Threshold Dimension, Boxicity and Cubicity of a Graph" @default.
- W1913458311 cites W1603384057 @default.
- W1913458311 cites W161777220 @default.
- W1913458311 cites W1974534721 @default.
- W1913458311 cites W2003154502 @default.
- W1913458311 cites W2013288868 @default.
- W1913458311 cites W2047899424 @default.
- W1913458311 cites W2085486788 @default.
- W1913458311 cites W2143474538 @default.
- W1913458311 cites W2314893179 @default.
- W1913458311 cites W2325654786 @default.
- W1913458311 hasPublicationYear "2009" @default.
- W1913458311 type Work @default.
- W1913458311 sameAs 1913458311 @default.
- W1913458311 citedByCount "0" @default.
- W1913458311 crossrefType "posted-content" @default.
- W1913458311 hasAuthorship W1913458311A5019703184 @default.
- W1913458311 hasAuthorship W1913458311A5024359075 @default.
- W1913458311 hasAuthorship W1913458311A5056606992 @default.
- W1913458311 hasConcept C114614502 @default.
- W1913458311 hasConcept C118615104 @default.
- W1913458311 hasConcept C127413603 @default.
- W1913458311 hasConcept C132525143 @default.
- W1913458311 hasConcept C146978453 @default.
- W1913458311 hasConcept C199360897 @default.
- W1913458311 hasConcept C203776342 @default.
- W1913458311 hasConcept C33676613 @default.
- W1913458311 hasConcept C33923547 @default.
- W1913458311 hasConcept C41008148 @default.
- W1913458311 hasConcept C54540088 @default.
- W1913458311 hasConcept C60432849 @default.
- W1913458311 hasConcept C64543145 @default.
- W1913458311 hasConcept C65236422 @default.
- W1913458311 hasConcept C97137487 @default.
- W1913458311 hasConceptScore W1913458311C114614502 @default.
- W1913458311 hasConceptScore W1913458311C118615104 @default.
- W1913458311 hasConceptScore W1913458311C127413603 @default.
- W1913458311 hasConceptScore W1913458311C132525143 @default.
- W1913458311 hasConceptScore W1913458311C146978453 @default.
- W1913458311 hasConceptScore W1913458311C199360897 @default.
- W1913458311 hasConceptScore W1913458311C203776342 @default.
- W1913458311 hasConceptScore W1913458311C33676613 @default.
- W1913458311 hasConceptScore W1913458311C33923547 @default.
- W1913458311 hasConceptScore W1913458311C41008148 @default.
- W1913458311 hasConceptScore W1913458311C54540088 @default.
- W1913458311 hasConceptScore W1913458311C60432849 @default.
- W1913458311 hasConceptScore W1913458311C64543145 @default.
- W1913458311 hasConceptScore W1913458311C65236422 @default.
- W1913458311 hasConceptScore W1913458311C97137487 @default.
- W1913458311 hasLocation W19134583111 @default.
- W1913458311 hasOpenAccess W1913458311 @default.
- W1913458311 hasPrimaryLocation W19134583111 @default.
- W1913458311 hasRelatedWork W1480836847 @default.
- W1913458311 hasRelatedWork W1534643528 @default.
- W1913458311 hasRelatedWork W1535607409 @default.
- W1913458311 hasRelatedWork W1582586167 @default.
- W1913458311 hasRelatedWork W1604333196 @default.
- W1913458311 hasRelatedWork W1613559019 @default.
- W1913458311 hasRelatedWork W1869392848 @default.
- W1913458311 hasRelatedWork W1907955461 @default.
- W1913458311 hasRelatedWork W1974876810 @default.
- W1913458311 hasRelatedWork W1996988774 @default.
- W1913458311 hasRelatedWork W2063428625 @default.
- W1913458311 hasRelatedWork W2078903417 @default.
- W1913458311 hasRelatedWork W2086041504 @default.
- W1913458311 hasRelatedWork W2133883172 @default.
- W1913458311 hasRelatedWork W2170810426 @default.
- W1913458311 hasRelatedWork W2191376159 @default.
- W1913458311 hasRelatedWork W2949126241 @default.
- W1913458311 hasRelatedWork W2952750031 @default.
- W1913458311 hasRelatedWork W3083711241 @default.
- W1913458311 hasRelatedWork W31199682 @default.
- W1913458311 isParatext "false" @default.
- W1913458311 isRetracted "false" @default.
- W1913458311 magId "1913458311" @default.
- W1913458311 workType "article" @default.