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International Conference on Integer Programming and Combinatorial Optimization

IPCO 2007: Integer Programming and Combinatorial Optimization pp 130–144Cite as

Scheduling with Precedence Constraints of Low Fractional Dimension

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4513))

Abstract

We consider the single machine scheduling problem to minimize the average weighted completion time under precedence constrains. Improving on the various 2-approximation algorithms is considered one of the ten most prominent open problems in scheduling theory. Recently, research has focused on special cases of the problem, mostly by restricting the set of precedence constraints to special classes such as convex bipartite, two-dimensional, and interval orders.

In this paper we extend our previous results by presenting a framework for obtaining (2 − 2/d)-approximation algorithms provided that the set of precedence constraints has fractional dimension d. Our generalized approach yields the best known approximation ratios for all previously considered classes of precedence constraints, and it provides the first results for bounded degree and interval dimension 2 orders.

As a negative result we show that the addressed problem remains NP-hard even when restricted to the special case of interval orders.

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Authors and Affiliations

  1. University of Liverpool, Great Britain

    Christoph Ambühl

  2. IDSIA, Switzerland

    Monaldo Mastrolilli, Nikolaus Mutsanas & Ola Svensson

Authors
  1. Christoph Ambühl
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  2. Monaldo Mastrolilli
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  3. Nikolaus Mutsanas
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  4. Ola Svensson
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Matteo Fischetti David P. Williamson

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Ambühl, C., Mastrolilli, M., Mutsanas, N., Svensson, O. (2007). Scheduling with Precedence Constraints of Low Fractional Dimension. In: Fischetti, M., Williamson, D.P. (eds) Integer Programming and Combinatorial Optimization. IPCO 2007. Lecture Notes in Computer Science, vol 4513. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72792-7_11

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  • DOI: https://doi.org/10.1007/978-3-540-72792-7_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72791-0

  • Online ISBN: 978-3-540-72792-7

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