Scheduling of unit-length jobs with bipartite incompatibility graphs on four uniform machines
In the paper we consider the problem of scheduling n identical jobs on 4 uniform machines with speeds s ≥ s ≥ s ≥ s , respectively. Our aim is to find a schedule with a minimum possible length. We assume that jobs are subject to some kind of mutual exclusion constraints modeled by a bipartite incomp...
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| Published in: | Bulletin of the Polish Academy of Sciences. Technical sciences Vol. 65; no. 1; pp. 29 - 34 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Warsaw
De Gruyter Open
01.02.2017
Polish Academy of Sciences |
| Subjects: | |
| ISSN: | 2300-1917, 0239-7528, 2300-1917 |
| Online Access: | Get full text |
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| Summary: | In the paper we consider the problem of scheduling n identical jobs on 4 uniform machines with speeds s
≥ s
≥ s
≥ s
, respectively. Our aim is to find a schedule with a minimum possible length. We assume that jobs are subject to some kind of mutual exclusion constraints modeled by a bipartite incompatibility graph of degree Δ, where two incompatible jobs cannot be processed on the same machine. We show that the general problem is NP-hard even if s
= s
= s
. If, however, Δ ≤ 4 and s
≥ 12s
, s
= s
= s
, then the problem can be solved to optimality in time O(n
). The same algorithm returns a solution of value at most 2 times optimal provided that s
≥ 2s
. Finally, we study the case s
≥ s
≥ s
= s
and give a 32/15-approximation algorithm running also in O(n
) time. |
|---|---|
| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 2300-1917 0239-7528 2300-1917 |
| DOI: | 10.1515/bpasts-2017-0004 |