License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ESA.2016.74
URN: urn:nbn:de:0030-drops-64157
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Schulz, Andreas S. ; Verschae, José

Min-Sum Scheduling Under Precedence Constraints

LIPIcs-ESA-2016-74.pdf (0.5 MB)


In many scheduling situations, it is important to consider non-linear functions of job completions times in the objective. This was already recognized by Smith (1956). Recently, the theory community has begun a thorough study of the resulting problems, mostly on single-machine instances for which all permutations of jobs are feasible. However, a typical feature of many scheduling problems is that some jobs can only be processed after others. In this paper, we give the first approximation algorithms for min-sum scheduling with (nonnegative, non-decreasing) non-linear functions and general precedence constraints. In particular, for 1|prec|sum w_j f(C_j), we propose a polynomial-time universal algorithm that performs well for all functions f simultaneously. Its approximation guarantee is 2 for all concave functions, at worst. We also provide a (non-universal) polynomial-time algorithm for the more general case 1|prec|sum f_j(C_j). The performance guarantee is no worse than 2+epsilon for all concave functions. Our results match the best bounds known for the case of linear functions, a widely studied problem, and considerably extend the results for minimizing sum w_jf(C_j) without precedence constraints.

BibTeX - Entry

  author =	{Andreas S. Schulz and Jos{\'e} Verschae},
  title =	{{Min-Sum Scheduling Under Precedence Constraints}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{74:1--74:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Piotr Sankowski and Christos Zaroliagis},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-64157},
  doi =		{10.4230/LIPIcs.ESA.2016.74},
  annote =	{Keywords: scheduling, approximation algorithms, linear programming relaxations, precedence constraints}

Keywords: scheduling, approximation algorithms, linear programming relaxations, precedence constraints
Collection: 24th Annual European Symposium on Algorithms (ESA 2016)
Issue Date: 2016
Date of publication: 18.08.2016

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