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DOI: 10.4230/LIPIcs.SWAT.2016.24
Estimating The Makespan of The Two-Valued Restricted Assignment Problem

Authors: Klaus Jansen, Kati Land, and Marten Maack

Published in: LIPIcs, Volume 53, 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)

Abstract
We consider a special case of the scheduling problem on unrelated machines, namely the Restricted Assignment Problem with two different processing times. We show that the configuration LP has an integrality gap of at most 5/3 ~ 1.667 for this problem. This allows us to estimate the optimal makespan within a factor of 5/3, improving upon the previously best known estimation algorithm with ratio 11/6 ~ 1.833 due to Chakrabarty, Khanna, and Li.
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Klaus Jansen, Kati Land, and Marten Maack. Estimating The Makespan of The Two-Valued Restricted Assignment Problem. In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 53, pp. 24:1-24:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{jansen_et_al:LIPIcs.SWAT.2016.24,
  author =	{Jansen, Klaus and Land, Kati and Maack, Marten},
  title =	{{Estimating The Makespan of The Two-Valued Restricted Assignment Problem}},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{24:1--24:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Pagh, Rasmus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2016.24},
  URN =		{urn:nbn:de:0030-drops-60467},
  doi =		{10.4230/LIPIcs.SWAT.2016.24},
  annote =	{Keywords: unrelated scheduling, restricted assignment, configuration LP, integrality gap, estimation algorithm}
}
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