2 Search Results for "Sankararaman, Karthik Abinav"

Document
DOI: 10.4230/LIPIcs.ISAAC.2022.7
Approximating the Minimum Logarithmic Arrangement Problem

Authors: Julián Mestre and Sergey Pupyrev

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
We study a graph reordering problem motivated by compressing massive graphs such as social networks and inverted indexes. Given a graph, G = (V, E), the Minimum Logarithmic Arrangement problem is to find a permutation, π, of the vertices that minimizes ∑_{(u, v) ∈ E} (1 + ⌊ lg |π(u) - π(v)| ⌋). This objective has been shown to be a good measure of how many bits are needed to encode the graph if the adjacency list of each vertex is encoded using relative positions of two consecutive neighbors under the π order in the list rather than using absolute indices or node identifiers, which requires at least lg n bits per edge. We show the first non-trivial approximation factor for this problem by giving a polynomial time 𝒪(log k)-approximation algorithm for graphs with treewidth k.
Cite as

Julián Mestre and Sergey Pupyrev. Approximating the Minimum Logarithmic Arrangement Problem. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{mestre_et_al:LIPIcs.ISAAC.2022.7,
  author =	{Mestre, Juli\'{a}n and Pupyrev, Sergey},
  title =	{{Approximating the Minimum Logarithmic Arrangement Problem}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.7},
  URN =		{urn:nbn:de:0030-drops-172924},
  doi =		{10.4230/LIPIcs.ISAAC.2022.7},
  annote =	{Keywords: approximation algorithms, graph compression}
}
Document
DOI: 10.4230/LIPIcs.ESA.2016.24
New Algorithms, Better Bounds, and a Novel Model for Online Stochastic Matching

Authors: Brian Brubach, Karthik Abinav Sankararaman, Aravind Srinivasan, and Pan Xu

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract
Online matching has received significant attention over the last 15 years due to its close connection to Internet advertising. As the seminal work of Karp, Vazirani, and Vazirani has an optimal (1 - 1/epsilon) competitive ratio in the standard adversarial online model, much effort has gone into developing useful online models that incorporate some stochasticity in the arrival process. One such popular model is the "known I.I.D. model" where different customer-types arrive online from a known distribution. We develop algorithms with improved competitive ratios for some basic variants of this model with integral arrival rates, including: (a) the case of general weighted edges, where we improve the best-known ratio of 0.667 due to [Haeupler, Mirrokni and Zadimoghaddam WINE 2011] to 0.705; and (b) the vertex-weighted case, where we improve the 0.7250 ratio of [Jaillet and Lu Math. Oper. Res 2013] to 0.7299. We also consider two extensions, one is "known I.I.D." with non-integral arrival rate and stochastic rewards; the other is "known I.I.D." b-matching with non-integral arrival rate and stochastic rewards. We present a simple non-adaptive algorithm which works well simultaneously on the two extensions. One of the key ingredients of our improvement is the following (offline) approach to bipartite-matching polytopes with additional constraints. We first add several valid constraints in order to get a good fractional solution f; however, these give us less control over the structure of f. We next remove all these additional constraints and randomly move from f to a feasible point on the matching polytope with all coordinates being from the set {0, 1/k, 2/k,..., 1} for a chosen integer k. The structure of this solution is inspired by [Jaillet and Lu Math. Oper. Res 2013] and is a tractable structure for algorithm design and analysis. The appropriate random move preserves many of the removed constraints (approximately [exactly] with high probability [in expectation]). This underlies some of our improvements, and, we hope, could be of independent interest.
Cite as

Brian Brubach, Karthik Abinav Sankararaman, Aravind Srinivasan, and Pan Xu. New Algorithms, Better Bounds, and a Novel Model for Online Stochastic Matching. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 24:1-24:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{brubach_et_al:LIPIcs.ESA.2016.24,
  author =	{Brubach, Brian and Sankararaman, Karthik Abinav and Srinivasan, Aravind and Xu, Pan},
  title =	{{New Algorithms, Better Bounds, and a Novel Model for Online Stochastic Matching}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{24:1--24:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.24},
  URN =		{urn:nbn:de:0030-drops-63753},
  doi =		{10.4230/LIPIcs.ESA.2016.24},
  annote =	{Keywords: Ad-Allocation, Online Matching, Randomized Algorithms}
}
  • Refine by Author
  • 1 Brubach, Brian
  • 1 Mestre, Julián
  • 1 Pupyrev, Sergey
  • 1 Sankararaman, Karthik Abinav
  • 1 Srinivasan, Aravind
  • Show More...

  • Refine by Classification
  • 1 Theory of computation → Approximation algorithms analysis

  • Refine by Keyword
  • 1 Ad-Allocation
  • 1 Online Matching
  • 1 Randomized Algorithms
  • 1 approximation algorithms
  • 1 graph compression

  • Refine by Type
  • 2 document

  • Refine by Publication Year
  • 1 2016
  • 1 2022

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact