3 Search Results for "Amit, Mika"

Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.19
Communication Complexity of Collision

Authors: Mika Göös and Siddhartha Jain

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
The Collision problem is to decide whether a given list of numbers (x_1,…,x_n) ∈ [n]ⁿ is 1-to-1 or 2-to-1 when promised one of them is the case. We show an n^Ω(1) randomised communication lower bound for the natural two-party version of Collision where Alice holds the first half of the bits of each x_i and Bob holds the second half. As an application, we also show a similar lower bound for a weak bit-pigeonhole search problem, which answers a question of Itsykson and Riazanov (CCC 2021).
Cite as

Mika Göös and Siddhartha Jain. Communication Complexity of Collision. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 19:1-19:9, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{goos_et_al:LIPIcs.APPROX/RANDOM.2022.19,
  author =	{G\"{o}\"{o}s, Mika and Jain, Siddhartha},
  title =	{{Communication Complexity of Collision}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{19:1--19:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.19},
  URN =		{urn:nbn:de:0030-drops-171415},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.19},
  annote =	{Keywords: Collision, Communication complexity, Lifting}
}
Document
DOI: 10.4230/LIPIcs.CCC.2018.23
A Tight Lower Bound for Entropy Flattening

Authors: Yi-Hsiu Chen, Mika Göös, Salil P. Vadhan, and Jiapeng Zhang

Published in: LIPIcs, Volume 102, 33rd Computational Complexity Conference (CCC 2018)

Abstract
We study entropy flattening: Given a circuit C_X implicitly describing an n-bit source X (namely, X is the output of C_X on a uniform random input), construct another circuit C_Y describing a source Y such that (1) source Y is nearly flat (uniform on its support), and (2) the Shannon entropy of Y is monotonically related to that of X. The standard solution is to have C_Y evaluate C_X altogether Theta(n^2) times on independent inputs and concatenate the results (correctness follows from the asymptotic equipartition property). In this paper, we show that this is optimal among black-box constructions: Any circuit C_Y for entropy flattening that repeatedly queries C_X as an oracle requires Omega(n^2) queries. Entropy flattening is a component used in the constructions of pseudorandom generators and other cryptographic primitives from one-way functions [Johan Håstad et al., 1999; John Rompel, 1990; Thomas Holenstein, 2006; Iftach Haitner et al., 2006; Iftach Haitner et al., 2009; Iftach Haitner et al., 2013; Iftach Haitner et al., 2010; Salil P. Vadhan and Colin Jia Zheng, 2012]. It is also used in reductions between problems complete for statistical zero-knowledge [Tatsuaki Okamoto, 2000; Amit Sahai and Salil P. Vadhan, 1997; Oded Goldreich et al., 1999; Vadhan, 1999]. The Theta(n^2) query complexity is often the main efficiency bottleneck. Our lower bound can be viewed as a step towards proving that the current best construction of pseudorandom generator from arbitrary one-way functions by Vadhan and Zheng (STOC 2012) has optimal efficiency.
Cite as

Yi-Hsiu Chen, Mika Göös, Salil P. Vadhan, and Jiapeng Zhang. A Tight Lower Bound for Entropy Flattening. In 33rd Computational Complexity Conference (CCC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 102, pp. 23:1-23:28, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chen_et_al:LIPIcs.CCC.2018.23,
  author =	{Chen, Yi-Hsiu and G\"{o}\"{o}s, Mika and Vadhan, Salil P. and Zhang, Jiapeng},
  title =	{{A Tight Lower Bound for Entropy Flattening}},
  booktitle =	{33rd Computational Complexity Conference (CCC 2018)},
  pages =	{23:1--23:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-069-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{102},
  editor =	{Servedio, Rocco A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2018.23},
  URN =		{urn:nbn:de:0030-drops-88669},
  doi =		{10.4230/LIPIcs.CCC.2018.23},
  annote =	{Keywords: Entropy, One-way function}
}
Document
DOI: 10.4230/LIPIcs.CPM.2016.20
Boxed Permutation Pattern Matching

Authors: Mika Amit, Philip Bille, Patrick Hagge Cording, Inge Li Gørtz, and Hjalte Wedel Vildhøj

Published in: LIPIcs, Volume 54, 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)

Abstract
Given permutations T and P of length n and m, respectively, the Permutation Pattern Matching problem asks to find all m-length subsequences of T that are order-isomorphic to P. This problem has a wide range of applications but is known to be NP-hard. In this paper, we study the special case, where the goal is to only find the boxed subsequences of T that are order-isomorphic to P. This problem was introduced by Bruner and Lackner who showed that it can be solved in O(n^3) time. Cho et al. [CPM 2015] gave an O(n^2m) time algorithm and improved it to O(n^2 log m). In this paper we present a solution that uses only O(n^2) time. In general, there are instances where the output size is Omega(n^2) and hence our bound is optimal. To achieve our results, we introduce several new ideas including a novel reduction to 2D offline dominance counting. Our algorithm is surprisingly simple and straightforward to implement.
Cite as

Mika Amit, Philip Bille, Patrick Hagge Cording, Inge Li Gørtz, and Hjalte Wedel Vildhøj. Boxed Permutation Pattern Matching. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 20:1-20:11, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)

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@InProceedings{amit_et_al:LIPIcs.CPM.2016.20,
  author =	{Amit, Mika and Bille, Philip and Hagge Cording, Patrick and Li G{\o}rtz, Inge and Wedel Vildh{\o}j, Hjalte},
  title =	{{Boxed Permutation Pattern Matching}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{20:1--20:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-012-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{54},
  editor =	{Grossi, Roberto and Lewenstein, Moshe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2016.20},
  URN =		{urn:nbn:de:0030-drops-60744},
  doi =		{10.4230/LIPIcs.CPM.2016.20},
  annote =	{Keywords: Permutation, Subsequence, Pattern Matching, Order Preserving, Boxed Mesh Pattern}
}
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