3 Search Results for "Gavoille, Cyril"

Document
DOI: 10.4230/LIPIcs.DISC.2022.37
Space-Stretch Tradeoff in Routing Revisited

Authors: Anatoliy Zinovyev

Published in: LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)

Abstract
We present several new proofs of lower bounds for the space-stretch tradeoff in labeled network routing. First, we give a new proof of an important result of Cyril Gavoille and Marc Gengler that any routing scheme with stretch < 3 must use Ω(n) bits of space at some node on some network with n vertices, even if port numbers can be changed. Compared to the original proof, our proof is significantly shorter and, we believe, conceptually and technically simpler. A small extension of the proof can show that, in fact, any constant fraction of the n nodes must use Ω(n) bits of space on some graph. Our main contribution is a new result that if port numbers are chosen adversarially, then stretch < 2k+1 implies some node must use Ω(n^(1/k) log n) bits of space on some graph, assuming a girth conjecture by Erdős. We conclude by showing that all known methods of proving a space lower bound in the labeled setting, in fact, require the girth conjecture.
Cite as

Anatoliy Zinovyev. Space-Stretch Tradeoff in Routing Revisited. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 37:1-37:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{zinovyev:LIPIcs.DISC.2022.37,
  author =	{Zinovyev, Anatoliy},
  title =	{{Space-Stretch Tradeoff in Routing Revisited}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{37:1--37:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.37},
  URN =		{urn:nbn:de:0030-drops-172281},
  doi =		{10.4230/LIPIcs.DISC.2022.37},
  annote =	{Keywords: Compact routing, labeled network routing, lower bounds}
}
Document
Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management
DOI: 10.4230/LIPIcs.ICALP.2019.134
Temporal Cliques Admit Sparse Spanners

Authors: Arnaud Casteigts, Joseph G. Peters, and Jason Schoeters

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
Let G=(V,E) be an undirected graph on n vertices and lambda:E -> 2^{N} a mapping that assigns to every edge a non-empty set of positive integer labels. These labels can be seen as discrete times when the edge is present. Such a labeled graph {G}=(G,lambda) is said to be temporally connected if a path exists with non-decreasing times from every vertex to every other vertex. In a seminal paper, Kempe, Kleinberg, and Kumar (STOC 2000) asked whether, given such a temporal graph, a sparse subset of edges can always be found whose labels suffice to preserve temporal connectivity - a temporal spanner. Axiotis and Fotakis (ICALP 2016) answered negatively by exhibiting a family of Theta(n^2)-dense temporal graphs which admit no temporal spanner of density o(n^2). The natural question is then whether sparse temporal spanners always exist in some classes of dense graphs. In this paper, we answer this question affirmatively, by showing that if the underlying graph G is a complete graph, then one can always find temporal spanners of density O(n log n). The best known result for complete graphs so far was that spanners of density binom{n}{2}- floor[n/4] = O(n^2) always exist. Our result is the first positive answer as to the existence of o(n^2) sparse spanners in adversarial instances of temporal graphs since the original question by Kempe et al., focusing here on complete graphs. The proofs are constructive and directly adaptable as an algorithm.
Cite as

Arnaud Casteigts, Joseph G. Peters, and Jason Schoeters. Temporal Cliques Admit Sparse Spanners. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 134:1-134:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{casteigts_et_al:LIPIcs.ICALP.2019.134,
  author =	{Casteigts, Arnaud and Peters, Joseph G. and Schoeters, Jason},
  title =	{{Temporal Cliques Admit Sparse Spanners}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{134:1--134:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.134},
  URN =		{urn:nbn:de:0030-drops-107108},
  doi =		{10.4230/LIPIcs.ICALP.2019.134},
  annote =	{Keywords: Dynamic networks, Temporal graphs, Temporal connectivity, Sparse spanners}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2016.19
Towards Plane Spanners of Degree 3

Authors: Ahmad Biniaz, Prosenjit Bose, Jean-Lou De Carufel, Cyril Gavoille, Anil Maheshwari, and Michiel Smid

Published in: LIPIcs, Volume 64, 27th International Symposium on Algorithms and Computation (ISAAC 2016)

Abstract
Let S be a finite set of points in the plane that are in convex position. We present an algorithm that constructs a plane frac{3+4 pi}{3}-spanner of S whose vertex degree is at most 3. Let Lambda be the vertex set of a finite non-uniform rectangular lattice in the plane. We present an algorithm that constructs a plane 3 sqrt{2}-spanner for Lambda whose vertex degree is at most 3. For points that are in the plane and in general position, we show how to compute plane degree-3 spanners with a linear number of Steiner points.
Cite as

Ahmad Biniaz, Prosenjit Bose, Jean-Lou De Carufel, Cyril Gavoille, Anil Maheshwari, and Michiel Smid. Towards Plane Spanners of Degree 3. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{biniaz_et_al:LIPIcs.ISAAC.2016.19,
  author =	{Biniaz, Ahmad and Bose, Prosenjit and De Carufel, Jean-Lou and Gavoille, Cyril and Maheshwari, Anil and Smid, Michiel},
  title =	{{Towards Plane Spanners of Degree 3}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Hong, Seok-Hee},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.19},
  URN =		{urn:nbn:de:0030-drops-67887},
  doi =		{10.4230/LIPIcs.ISAAC.2016.19},
  annote =	{Keywords: plane spanners, degree-3 spanners, convex position, non-uniform lattice}
}
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