Matches in SemOpenAlex for { <https://semopenalex.org/work/W4288284163> ?p ?o ?g. }
Showing items 1 to 57 of
57
with 100 items per page.
- W4288284163 abstract "In the Maximum Independent Set problem we are asked to find a set of pairwise nonadjacent vertices in a given graph with the maximum possible cardinality. In general graphs, this classical problem is known to be NP-hard and hard to approximate within a factor of $n^{1-varepsilon}$ for any $varepsilon > 0$. Due to this, investigating the complexity of Maximum Independent Set in various graph classes in hope of finding better tractability results is an active research direction. In $H$-free graphs, that is, graphs not containing a fixed graph $H$ as an induced subgraph, the problem is known to remain NP-hard and APX-hard whenever $H$ contains a cycle, a vertex of degree at least four, or two vertices of degree at least three in one connected component. For the remaining cases, where every component of $H$ is a path or a subdivided claw, the complexity of Maximum Independent Set remains widely open, with only a handful of polynomial-time solvability results for small graphs $H$ such as $P_5$, $P_6$, the claw, or the fork. We show that for every graph $H$ for which Maximum Independent Set is not known to be APX-hard and SUBEXP-hard in $H$-free graphs, the problem admits a quasi-polynomial time approximation scheme and a subexponential-time exact algorithm in this graph class. Our algorithm works also in the more general weighted setting, where the input graph is supplied with a weight function on vertices and we are maximizing the total weight of an independent set." @default.
- W4288284163 created "2022-07-28" @default.
- W4288284163 creator A5000479623 @default.
- W4288284163 creator A5028345325 @default.
- W4288284163 creator A5033238040 @default.
- W4288284163 creator A5059330513 @default.
- W4288284163 date "2019-07-10" @default.
- W4288284163 modified "2023-10-18" @default.
- W4288284163 title "Quasi-polynomial time approximation schemes for the Maximum Weight Independent Set Problem in H-free graphs" @default.
- W4288284163 doi "https://doi.org/10.48550/arxiv.1907.04585" @default.
- W4288284163 hasPublicationYear "2019" @default.
- W4288284163 type Work @default.
- W4288284163 citedByCount "0" @default.
- W4288284163 crossrefType "posted-content" @default.
- W4288284163 hasAuthorship W4288284163A5000479623 @default.
- W4288284163 hasAuthorship W4288284163A5028345325 @default.
- W4288284163 hasAuthorship W4288284163A5033238040 @default.
- W4288284163 hasAuthorship W4288284163A5059330513 @default.
- W4288284163 hasBestOaLocation W42882841631 @default.
- W4288284163 hasConcept C102192266 @default.
- W4288284163 hasConcept C114614502 @default.
- W4288284163 hasConcept C118615104 @default.
- W4288284163 hasConcept C122818955 @default.
- W4288284163 hasConcept C132525143 @default.
- W4288284163 hasConcept C160446614 @default.
- W4288284163 hasConcept C18359143 @default.
- W4288284163 hasConcept C311688 @default.
- W4288284163 hasConcept C33923547 @default.
- W4288284163 hasConcept C80899671 @default.
- W4288284163 hasConcept C8554925 @default.
- W4288284163 hasConceptScore W4288284163C102192266 @default.
- W4288284163 hasConceptScore W4288284163C114614502 @default.
- W4288284163 hasConceptScore W4288284163C118615104 @default.
- W4288284163 hasConceptScore W4288284163C122818955 @default.
- W4288284163 hasConceptScore W4288284163C132525143 @default.
- W4288284163 hasConceptScore W4288284163C160446614 @default.
- W4288284163 hasConceptScore W4288284163C18359143 @default.
- W4288284163 hasConceptScore W4288284163C311688 @default.
- W4288284163 hasConceptScore W4288284163C33923547 @default.
- W4288284163 hasConceptScore W4288284163C80899671 @default.
- W4288284163 hasConceptScore W4288284163C8554925 @default.
- W4288284163 hasLocation W42882841631 @default.
- W4288284163 hasOpenAccess W4288284163 @default.
- W4288284163 hasPrimaryLocation W42882841631 @default.
- W4288284163 hasRelatedWork W1608132493 @default.
- W4288284163 hasRelatedWork W179301118 @default.
- W4288284163 hasRelatedWork W1977973532 @default.
- W4288284163 hasRelatedWork W1985956090 @default.
- W4288284163 hasRelatedWork W1994963913 @default.
- W4288284163 hasRelatedWork W2046755592 @default.
- W4288284163 hasRelatedWork W2139428469 @default.
- W4288284163 hasRelatedWork W2497554862 @default.
- W4288284163 hasRelatedWork W2952271241 @default.
- W4288284163 hasRelatedWork W4293002939 @default.
- W4288284163 isParatext "false" @default.
- W4288284163 isRetracted "false" @default.
- W4288284163 workType "article" @default.