Matches in SemOpenAlex for { <https://semopenalex.org/work/W4285483902> ?p ?o ?g. }
Showing items 1 to 69 of
69
with 100 items per page.
- W4285483902 abstract "The problem of scheduling jobs on parallel machines (identical, uniform, or unrelated), under incompatibility relation modeled as a block graph, under the makespan optimality criterion, is considered in this paper. No two jobs that are in the relation (equivalently in the same block) may be scheduled on the same machine in this model. The presented model stems from a well-established line of research combining scheduling theory with methods relevant to graph coloring. Recently, cluster graphs and their extensions like block graphs were given additional attention. We complement hardness results provided by other researchers for block graphs by providing approximation algorithms. In particular, we provide a $2$-approximation algorithm for $P|G = block graph|C_{max}$ and a PTAS for the case when the jobs are unit time in addition. In the case of uniform machines, we analyze two cases. The first one is when the number of blocks is bounded, i.e. $Q|G = k-block graph|C_{max}$. For this case, we provide a PTAS, improving upon results presented by D. Page and R. Solis-Oba. The improvement is two-fold: we allow richer graph structure, and we allow the number of machine speeds to be part of the input. Due to strong NP-hardness of $Q|G = 2-clique graph|C_{max}$, the result establishes the approximation status of $Q|G = k-block graph|C_{max}$. The PTAS might be of independent interest because the problem is tightly related to the NUMERICAL k-DIMENSIONAL MATCHING WITH TARGET SUMS problem. The second case that we analyze is when the number of blocks is arbitrary, but the number of cut-vertices is bounded and jobs are of unit time. In this case, we present an exact algorithm. In addition, we present an FPTAS for graphs with bounded treewidth and a bounded number of unrelated machines." @default.
- W4285483902 created "2022-07-15" @default.
- W4285483902 creator A5004340905 @default.
- W4285483902 creator A5008432845 @default.
- W4285483902 creator A5014284502 @default.
- W4285483902 creator A5048481911 @default.
- W4285483902 date "2022-07-12" @default.
- W4285483902 modified "2023-10-14" @default.
- W4285483902 title "Approximation algorithms for job scheduling with block-type conflict graphs" @default.
- W4285483902 doi "https://doi.org/10.48550/arxiv.2207.05868" @default.
- W4285483902 hasPublicationYear "2022" @default.
- W4285483902 type Work @default.
- W4285483902 citedByCount "0" @default.
- W4285483902 crossrefType "posted-content" @default.
- W4285483902 hasAuthorship W4285483902A5004340905 @default.
- W4285483902 hasAuthorship W4285483902A5008432845 @default.
- W4285483902 hasAuthorship W4285483902A5014284502 @default.
- W4285483902 hasAuthorship W4285483902A5048481911 @default.
- W4285483902 hasBestOaLocation W42854839021 @default.
- W4285483902 hasConcept C111919701 @default.
- W4285483902 hasConcept C11413529 @default.
- W4285483902 hasConcept C114614502 @default.
- W4285483902 hasConcept C118615104 @default.
- W4285483902 hasConcept C126255220 @default.
- W4285483902 hasConcept C132525143 @default.
- W4285483902 hasConcept C134306372 @default.
- W4285483902 hasConcept C148764684 @default.
- W4285483902 hasConcept C203776342 @default.
- W4285483902 hasConcept C206729178 @default.
- W4285483902 hasConcept C33923547 @default.
- W4285483902 hasConcept C34388435 @default.
- W4285483902 hasConcept C41008148 @default.
- W4285483902 hasConcept C43413943 @default.
- W4285483902 hasConcept C43517604 @default.
- W4285483902 hasConcept C55416958 @default.
- W4285483902 hasConcept C68387754 @default.
- W4285483902 hasConceptScore W4285483902C111919701 @default.
- W4285483902 hasConceptScore W4285483902C11413529 @default.
- W4285483902 hasConceptScore W4285483902C114614502 @default.
- W4285483902 hasConceptScore W4285483902C118615104 @default.
- W4285483902 hasConceptScore W4285483902C126255220 @default.
- W4285483902 hasConceptScore W4285483902C132525143 @default.
- W4285483902 hasConceptScore W4285483902C134306372 @default.
- W4285483902 hasConceptScore W4285483902C148764684 @default.
- W4285483902 hasConceptScore W4285483902C203776342 @default.
- W4285483902 hasConceptScore W4285483902C206729178 @default.
- W4285483902 hasConceptScore W4285483902C33923547 @default.
- W4285483902 hasConceptScore W4285483902C34388435 @default.
- W4285483902 hasConceptScore W4285483902C41008148 @default.
- W4285483902 hasConceptScore W4285483902C43413943 @default.
- W4285483902 hasConceptScore W4285483902C43517604 @default.
- W4285483902 hasConceptScore W4285483902C55416958 @default.
- W4285483902 hasConceptScore W4285483902C68387754 @default.
- W4285483902 hasLocation W42854839021 @default.
- W4285483902 hasOpenAccess W4285483902 @default.
- W4285483902 hasPrimaryLocation W42854839021 @default.
- W4285483902 hasRelatedWork W2005947718 @default.
- W4285483902 hasRelatedWork W2022054586 @default.
- W4285483902 hasRelatedWork W2046324913 @default.
- W4285483902 hasRelatedWork W2076099212 @default.
- W4285483902 hasRelatedWork W2079220110 @default.
- W4285483902 hasRelatedWork W2186006531 @default.
- W4285483902 hasRelatedWork W2507810539 @default.
- W4285483902 hasRelatedWork W2913253550 @default.
- W4285483902 hasRelatedWork W4249035196 @default.
- W4285483902 hasRelatedWork W4386557457 @default.
- W4285483902 isParatext "false" @default.
- W4285483902 isRetracted "false" @default.
- W4285483902 workType "article" @default.