Approximation algorithms for job scheduling with block-type conflict graphs

Hanna Furmańczyk; Tytus Pikies; Inka Sokołowska; Krzysztof Turowski

doi:10.1016/j.cor.2024.106606

Approximation algorithms for job scheduling with block-type conflict graphs

Abstrakt

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 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. . 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 , the result establishes the approximation status of . The PTAS might be of independent interest because the problem is tightly related to the NUMERICAL -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. The paper ends with extensive tests of the selected algorithms.

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Autorzy (4)

Hanna Furmańczyk
- Uniwersytet Gdański
Tytus Pikies dr inż.
Inka Sokołowska
- Uniwersytet Jagielloński
Krzysztof Turowski dr inż.
- Uniwersytet Jagielloński

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Kategoria:

Publikacja w czasopiśmie

Typ:

artykuły w czasopismach dostępnych w wersji elektronicznej [także online]

Opublikowano w:

COMPUTERS & OPERATIONS RESEARCH
ISSN: 0305-0548

Język:

angielski

Rok wydania:

2024

Opis bibliograficzny:

Furmańczyk H., Pikies T., Sokołowska I., Turowski K., Approximation algorithms for job scheduling with block-type conflict graphs, COMPUTERS & OPERATIONS RESEARCH, 2024,10.1016/j.cor.2024.106606

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