2 Search Results for "Korteweg, Peter"

Document
DOI: 10.4230/LIPIcs.CCC.2021.32
Polynomial Time Algorithms in Invariant Theory for Torus Actions

Authors: Peter Bürgisser, M. Levent Doğan, Visu Makam, Michael Walter, and Avi Wigderson

Published in: LIPIcs, Volume 200, 36th Computational Complexity Conference (CCC 2021)

Abstract
An action of a group on a vector space partitions the latter into a set of orbits. We consider three natural and useful algorithmic "isomorphism" or "classification" problems, namely, orbit equality, orbit closure intersection, and orbit closure containment. These capture and relate to a variety of problems within mathematics, physics and computer science, optimization and statistics. These orbit problems extend the more basic null cone problem, whose algorithmic complexity has seen significant progress in recent years. In this paper, we initiate a study of these problems by focusing on the actions of commutative groups (namely, tori). We explain how this setting is motivated from questions in algebraic complexity, and is still rich enough to capture interesting combinatorial algorithmic problems. While the structural theory of commutative actions is well understood, no general efficient algorithms were known for the aforementioned problems. Our main results are polynomial time algorithms for all three problems. We also show how to efficiently find separating invariants for orbits, and how to compute systems of generating rational invariants for these actions (in contrast, for polynomial invariants the latter is known to be hard). Our techniques are based on a combination of fundamental results in invariant theory, linear programming, and algorithmic lattice theory.
Cite as

Peter Bürgisser, M. Levent Doğan, Visu Makam, Michael Walter, and Avi Wigderson. Polynomial Time Algorithms in Invariant Theory for Torus Actions. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 32:1-32:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{burgisser_et_al:LIPIcs.CCC.2021.32,
  author =	{B\"{u}rgisser, Peter and Do\u{g}an, M. Levent and Makam, Visu and Walter, Michael and Wigderson, Avi},
  title =	{{Polynomial Time Algorithms in Invariant Theory for Torus Actions}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{32:1--32:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.32},
  URN =		{urn:nbn:de:0030-drops-143062},
  doi =		{10.4230/LIPIcs.CCC.2021.32},
  annote =	{Keywords: computational invariant theory, geometric complexity theory, orbit closure intersection problem}
}
Document
DOI: 10.4230/LIPIcs.STACS.2008.1338
Minimizing Flow Time in the Wireless Gathering Problem

Authors: Vincenzo Bonifaci, Peter Korteweg, Alberto Marchetti-Spaccamela, and Leen Stougie

Published in: LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008)

Abstract
We address the problem of efficient data gathering in a wireless network through multi-hop communication. We focus on the objective of minimizing the maximum flow time of a data packet. We prove that no polynomial time algorithm for this problem can have approximation ratio less than $Omega(m^{1/3)$ when $m$ packets have to be transmitted, unless $P = NP$. We then use resource augmentation to assess the performance of a FIFO-like strategy. We prove that this strategy is 5-speed optimal, i.e., its cost remains within the optimal cost if we allow the algorithm to transmit data at a speed 5 times higher than that of the optimal solution we compare to.
Cite as

Vincenzo Bonifaci, Peter Korteweg, Alberto Marchetti-Spaccamela, and Leen Stougie. Minimizing Flow Time in the Wireless Gathering Problem. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 109-120, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{bonifaci_et_al:LIPIcs.STACS.2008.1338,
  author =	{Bonifaci, Vincenzo and Korteweg, Peter and Marchetti-Spaccamela, Alberto and Stougie, Leen},
  title =	{{Minimizing Flow Time in the Wireless Gathering Problem}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{109--120},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Albers, Susanne and Weil, Pascal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1338},
  URN =		{urn:nbn:de:0030-drops-13381},
  doi =		{10.4230/LIPIcs.STACS.2008.1338},
  annote =	{Keywords: Wireless networks, data gathering, approximation algorithms, distributed algorithms}
}
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