2 Search Results for "Jäger, Sven"


Document
Gray Codes and Symmetric Chains

Authors: Petr Gregor, Sven Jäger, Torsten Mütze, Joe Sawada, and Kaja Wille

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)


Abstract
We consider the problem of constructing a cyclic listing of all bitstrings of length 2n+1 with Hamming weights in the interval [n+1-l,n+l], where 1 <= l <= n+1, by flipping a single bit in each step. This is a far-ranging generalization of the well-known middle two levels problem (l=1). We provide a solution for the case l=2 and solve a relaxed version of the problem for general values of l, by constructing cycle factors for those instances. Our proof uses symmetric chain decompositions of the hypercube, a concept known from the theory of posets, and we present several new constructions of such decompositions. In particular, we construct four pairwise edge-disjoint symmetric chain decompositions of the n-dimensional hypercube for any n >= 12.

Cite as

Petr Gregor, Sven Jäger, Torsten Mütze, Joe Sawada, and Kaja Wille. Gray Codes and Symmetric Chains. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 66:1-66:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{gregor_et_al:LIPIcs.ICALP.2018.66,
  author =	{Gregor, Petr and J\"{a}ger, Sven and M\"{u}tze, Torsten and Sawada, Joe and Wille, Kaja},
  title =	{{Gray Codes and Symmetric Chains}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{66:1--66:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.66},
  URN =		{urn:nbn:de:0030-drops-90703},
  doi =		{10.4230/LIPIcs.ICALP.2018.66},
  annote =	{Keywords: Gray code, Hamilton cycle, hypercube, poset, symmetric chain}
}
Document
Generalizing the Kawaguchi-Kyan Bound to Stochastic Parallel Machine Scheduling

Authors: Sven Jäger and Martin Skutella

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)


Abstract
Minimizing the sum of weighted completion times on m identical parallel machines is one of the most important and classical scheduling problems. For the stochastic variant where processing times of jobs are random variables, Möhring, Schulz, and Uetz (1999) presented the first and still best known approximation result, achieving, for arbitrarily many machines, performance ratio 1+1/2(1+Delta), where Delta is an upper bound on the squared coefficient of variation of the processing times. We prove performance ratio 1+1/2(sqrt(2)-1)(1+Delta) for the same underlying algorithm---the Weighted Shortest Expected Processing Time (WSEPT) rule. For the special case of deterministic scheduling (i.e., Delta=0), our bound matches the tight performance ratio 1/2(1+sqrt(2)) of this algorithm (WSPT rule), derived by Kawaguchi and Kyan in a 1986 landmark paper. We present several further improvements for WSEPT's performance ratio, one of them relying on a carefully refined analysis of WSPT yielding, for every fixed number of machines m, WSPT's exact performance ratio of order 1/2(1+sqrt(2))-O(1/m^2).

Cite as

Sven Jäger and Martin Skutella. Generalizing the Kawaguchi-Kyan Bound to Stochastic Parallel Machine Scheduling. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 43:1-43:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{jager_et_al:LIPIcs.STACS.2018.43,
  author =	{J\"{a}ger, Sven and Skutella, Martin},
  title =	{{Generalizing the Kawaguchi-Kyan Bound to Stochastic Parallel Machine Scheduling}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{43:1--43:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.43},
  URN =		{urn:nbn:de:0030-drops-85034},
  doi =		{10.4230/LIPIcs.STACS.2018.43},
  annote =	{Keywords: Stochastic Scheduling, Parallel Machines, Approximation Algorithm, List Scheduling, Weighted Shortest (Expected) Processing Time Rule}
}
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