2 Search Results for "Poirion, Pierre-Louis"

Document
DOI: 10.4230/LIPIcs.ESA.2025.48
The Support of Bin Packing Is Exponential

Authors: Klaus Jansen, Lis Pirotton, and Malte Tutas

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Consider the classical Bin Packing problem with d different item sizes s_i and amounts of items a_i. The support of a Bin Packing solution is the number of differently filled bins. In this work, we show that the lower bound on the support of this problem is 2^Ω(d). Our lower bound matches the upper bound of 2^d given by Eisenbrand and Shmonin [Oper.Research Letters '06] up to a constant factor. This result has direct implications for the time complexity of several Bin Packing algorithms, such as Goemans and Rothvoss [SODA '14], Jansen and Klein [SODA '17] and Jansen and Solis-Oba [IPCO '10]. To achieve our main result, we develop a technique to aggregate equality constrained ILPs with many constraints into an equivalent ILP with one constraint. Our technique contrasts existing aggregation techniques as we manage to integrate upper bounds on variables into the resulting constraint. We believe this technique can be useful for solving general ILPs or the d-dimensional knapsack problem.
Cite as

Klaus Jansen, Lis Pirotton, and Malte Tutas. The Support of Bin Packing Is Exponential. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 48:1-48:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jansen_et_al:LIPIcs.ESA.2025.48,
  author =	{Jansen, Klaus and Pirotton, Lis and Tutas, Malte},
  title =	{{The Support of Bin Packing Is Exponential}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{48:1--48:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.48},
  URN =		{urn:nbn:de:0030-drops-245167},
  doi =		{10.4230/LIPIcs.ESA.2025.48},
  annote =	{Keywords: Bin Packing, Integer Programming, Support}
}
Document
DOI: 10.4230/LIPIcs.SEA.2022.21
Practical Performance of Random Projections in Linear Programming

Authors: Leo Liberti, Benedetto Manca, and Pierre-Louis Poirion

Published in: LIPIcs, Volume 233, 20th International Symposium on Experimental Algorithms (SEA 2022)

Abstract
The use of random projections in mathematical programming allows standard solution algorithms to solve instances of much larger sizes, at least approximately. Approximation results have been derived in the relevant literature for many specific problems, as well as for several mathematical programming subclasses. Despite the theoretical developments, it is not always clear that random projections are actually useful in solving mathematical programs in practice. In this paper we provide a computational assessment of the application of random projections to linear programming.
Cite as

Leo Liberti, Benedetto Manca, and Pierre-Louis Poirion. Practical Performance of Random Projections in Linear Programming. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{liberti_et_al:LIPIcs.SEA.2022.21,
  author =	{Liberti, Leo and Manca, Benedetto and Poirion, Pierre-Louis},
  title =	{{Practical Performance of Random Projections in Linear Programming}},
  booktitle =	{20th International Symposium on Experimental Algorithms (SEA 2022)},
  pages =	{21:1--21:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-251-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{233},
  editor =	{Schulz, Christian and U\c{c}ar, Bora},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2022.21},
  URN =		{urn:nbn:de:0030-drops-165550},
  doi =		{10.4230/LIPIcs.SEA.2022.21},
  annote =	{Keywords: Linear Programming, Johnson-Lindenstrauss Lemma, Computational testing}
}
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