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Documents authored by Saks, Michael

Found 2 Possible Name Variants:

Saks, Michael E.

Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.596
The Power of Super-logarithmic Number of Players

Authors: Arkadev Chattopadhyay and Michael E. Saks

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

Abstract
In the `Number-on-Forehead' (NOF) model of multiparty communication, the input is a k times m boolean matrix A (where k is the number of players) and Player i sees all bits except those in the i-th row, and the players communicate by broadcast in order to evaluate a specified function f at A. We discover new computational power when k exceeds log m. We give a protocol with communication cost poly-logarithmic in m, for block composed functions with limited block width. These are functions of the form f o g where f is a symmetric b-variate function, and g is a (kr)-variate function and (f o g)(A) is defined, for a k times (br) matrix to be f(g(A-1),...,g(A-b)) where A-i is the i-th (k times r) block of A. Our protocol works provided that k > 1+ ln b + (2 to the power of r). Ada et al. (ICALP'2012) previously obtained simultaneous and deterministic efficient protocols for composed functions of block-width one. The new protocol is the first to work for block composed functions with block-width greather than one. Moreover, it is simultaneous, with vanishingly small error probability, if public coin randomness is allowed. The deterministic and zero-error version barely uses interaction.
Cite as

Arkadev Chattopadhyay and Michael E. Saks. The Power of Super-logarithmic Number of Players. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 596-603, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{chattopadhyay_et_al:LIPIcs.APPROX-RANDOM.2014.596,
  author =	{Chattopadhyay, Arkadev and Saks, Michael E.},
  title =	{{The Power of Super-logarithmic Number of Players}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{596--603},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.596},
  URN =		{urn:nbn:de:0030-drops-47243},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.596},
  annote =	{Keywords: Communication complexity, Number-On-Forehead model, composed functions}
}

Saks, Michael

Document
DOI: 10.4230/LIPIcs.CCC.2022.29
On Randomized Reductions to the Random Strings

Authors: Michael Saks and Rahul Santhanam

Published in: LIPIcs, Volume 234, 37th Computational Complexity Conference (CCC 2022)

Abstract
We study the power of randomized polynomial-time non-adaptive reductions to the problem of approximating Kolmogorov complexity and its polynomial-time bounded variants. As our first main result, we give a sharp dichotomy for randomized non-adaptive reducibility to approximating Kolmogorov complexity. We show that any computable language L that has a randomized polynomial-time non-adaptive reduction (satisfying a natural honesty condition) to ω(log(n))-approximating the Kolmogorov complexity is in AM ∩ coAM. On the other hand, using results of Hirahara [Shuichi Hirahara, 2020], it follows that every language in NEXP has a randomized polynomial-time non-adaptive reduction (satisfying the same honesty condition as before) to O(log(n))-approximating the Kolmogorov complexity. As our second main result, we give the first negative evidence against the NP-hardness of polynomial-time bounded Kolmogorov complexity with respect to randomized reductions. We show that for every polynomial t', there is a polynomial t such that if there is a randomized time t' non-adaptive reduction (satisfying a natural honesty condition) from SAT to ω(log(n))-approximating K^t complexity, then either NE = coNE or 𝖤 has sub-exponential size non-deterministic circuits infinitely often.
Cite as

Michael Saks and Rahul Santhanam. On Randomized Reductions to the Random Strings. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 29:1-29:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{saks_et_al:LIPIcs.CCC.2022.29,
  author =	{Saks, Michael and Santhanam, Rahul},
  title =	{{On Randomized Reductions to the Random Strings}},
  booktitle =	{37th Computational Complexity Conference (CCC 2022)},
  pages =	{29:1--29:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-241-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{234},
  editor =	{Lovett, Shachar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2022.29},
  URN =		{urn:nbn:de:0030-drops-165912},
  doi =		{10.4230/LIPIcs.CCC.2022.29},
  annote =	{Keywords: Kolmogorov complexity, randomized reductions}
}
Document
DOI: 10.4230/LIPIcs.CCC.2020.26
Circuit Lower Bounds from NP-Hardness of MCSP Under Turing Reductions

Authors: Michael Saks and Rahul Santhanam

Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)

Abstract
The fundamental Minimum Circuit Size Problem is a well-known example of a problem that is neither known to be in 𝖯 nor known to be NP-hard. Kabanets and Cai [Kabanets and Cai, 2000] showed that if MCSP is NP-hard under "natural" m-reductions, superpolynomial circuit lower bounds for exponential time would follow. This has triggered a long line of work on understanding the power of reductions to MCSP. Nothing was known so far about consequences of NP-hardness of MCSP under general Turing reductions. In this work, we consider two structured kinds of Turing reductions: parametric honest reductions and natural reductions. The latter generalize the natural reductions of Kabanets and Cai to the case of Turing-reductions. We show that NP-hardness of MCSP under these kinds of Turing-reductions imply superpolynomial circuit lower bounds for exponential time.
Cite as

Michael Saks and Rahul Santhanam. Circuit Lower Bounds from NP-Hardness of MCSP Under Turing Reductions. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 26:1-26:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{saks_et_al:LIPIcs.CCC.2020.26,
  author =	{Saks, Michael and Santhanam, Rahul},
  title =	{{Circuit Lower Bounds from NP-Hardness of MCSP Under Turing Reductions}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{26:1--26:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-156-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{169},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.26},
  URN =		{urn:nbn:de:0030-drops-125786},
  doi =		{10.4230/LIPIcs.CCC.2020.26},
  annote =	{Keywords: Minimum Circuit Size Problem, Turing reductions, circuit lower bounds}
}
Document
DOI: 10.4230/LIPIcs.STACS.2018.23
Lower Bounds for Combinatorial Algorithms for Boolean Matrix Multiplication

Authors: Debarati Das, Michal Koucký, and Michael Saks

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
In this paper we propose models of combinatorial algorithms for the Boolean Matrix Multiplication (BMM), and prove lower bounds on computing BMM in these models. First, we give a relatively relaxed combinatorial model which is an extension of the model by Angluin (1976), and we prove that the time required by any algorithm for the BMM is at least Omega(n^3 / 2^{O( sqrt{ log n })}). Subsequently, we propose a more general model capable of simulating the "Four Russian Algorithm". We prove a lower bound of Omega(n^{7/3} / 2^{O(sqrt{ log n })}) for the BMM under this model. We use a special class of graphs, called (r,t)-graphs, originally discovered by Rusza and Szemeredi (1978), along with randomization, to construct matrices that are hard instances for our combinatorial models.
Cite as

Debarati Das, Michal Koucký, and Michael Saks. Lower Bounds for Combinatorial Algorithms for Boolean Matrix Multiplication. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 23:1-23:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{das_et_al:LIPIcs.STACS.2018.23,
  author =	{Das, Debarati and Kouck\'{y}, Michal and Saks, Michael},
  title =	{{Lower Bounds for Combinatorial Algorithms for Boolean Matrix Multiplication}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{23:1--23:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.23},
  URN =		{urn:nbn:de:0030-drops-85050},
  doi =		{10.4230/LIPIcs.STACS.2018.23},
  annote =	{Keywords: Lower bounds, Combinatorial algorithm, Boolean matrix multiplication}
}
Document
DOI: 10.4230/LIPIcs.STACS.2013.526
On the practically interesting instances of MAXCUT

Authors: Yonatan Bilu, Amit Daniely, Nati Linial, and Michael Saks

Published in: LIPIcs, Volume 20, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)

Abstract
For many optimization problems, the instances of practical interest often occupy just a tiny part of the algorithm's space of instances. Following (Y. Bilu and N. Linial, 2010), we apply this perspective to MAXCUT, viewed as a clustering problem. Using a variety of techniques, we investigate practically interesting instances of this problem. Specifically, we show how to solve in polynomial time distinguished, metric, expanding and dense instances of MAXCUT under mild stability assumptions. In particular, (1 + epsilon)-stability (which is optimal) suffices for metric and dense MAXCUT. We also show how to solve in polynomial time Omega(sqrt(n))-stable instances of MAXCUT, substantially improving the best previously known result.
Cite as

Yonatan Bilu, Amit Daniely, Nati Linial, and Michael Saks. On the practically interesting instances of MAXCUT. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 526-537, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{bilu_et_al:LIPIcs.STACS.2013.526,
  author =	{Bilu, Yonatan and Daniely, Amit and Linial, Nati and Saks, Michael},
  title =	{{On the practically interesting instances of MAXCUT}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{526--537},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Portier, Natacha and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.526},
  URN =		{urn:nbn:de:0030-drops-39625},
  doi =		{10.4230/LIPIcs.STACS.2013.526},
  annote =	{Keywords: MAXCUT, Clustering, Hardness in practice, Stability, Non worst-case analysis}
}
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