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Article overview
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Precedence-constrained scheduling problems parameterized by partial order width | | René van Bevern
; Robert Bredereck
; Laurent Bulteau
; Christian Komusiewicz
; Nimrod Talmon
; Gerhard J. Woeginger
; | | Date: |
3 May 2016 | | Abstract: | Negatively answering a question posed by Mnich and Wiese (Math. Program.
154(1-2):533-562), we show that P2|prec,$p_j{in}{1,2}$|$C_{max}$, the
problem of finding a non-preemptive minimum-makespan schedule for
precedence-constrained jobs of lengths 1 and 2 on two parallel identical
machines, is W[2]-hard parameterized by the width of the partial order giving
the precedence constraints. To this end, we show that Shuffle Product, the
problem of deciding whether a given word can be obtained by interleaving the
letters of $k$ other given words, is W[2]-hard parameterized by $k$, thus
additionally answering a question posed by Rizzi and Vialette (CSR 2013).
Finally, refining a geometric algorithm due to Servakh (Diskretn. Anal. Issled.
Oper. 7(1):75-82), we show that the more general Resource-Constrained Project
Scheduling problem is fixed-parameter tractable parameterized by the partial
order width combined with the maximum allowed difference between the earliest
possible and factual starting time of a job. | | Source: | arXiv, 1605.0901 | | Services: | Forum | Review | PDF | Favorites | |
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