9 Search Results for "Vinodchandran, N. V."

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.26
Improved Streaming Algorithm for the Klee’s Measure Problem and Generalizations

Authors: Mridul Nandi, N. V. Vinodchandran, Arijit Ghosh, Kuldeep S. Meel, Soumit Pal, and Sourav Chakraborty

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
Estimating the size of the union of a stream of sets S₁, S₂, …, S_M where each set is a subset of a known universe Ω is a fundamental problem in data streaming. This problem naturally generalizes the well-studied 𝖥₀ estimation problem in the streaming literature, where each set contains a single element from the universe. We consider the general case when the sets S_i can be succinctly represented and allow efficient membership, cardinality, and sampling queries (called a Delphic family of sets). A notable example in this framework is the Klee’s Measure Problem (KMP), where every set S_i is an axis-parallel rectangle in d-dimensional spaces (Ω = [Δ]^d where [Δ] := {1, … ,Δ} and Δ ∈ ℕ). Recently, Meel, Chakraborty, and Vinodchandran (PODS-21, PODS-22) designed a streaming algorithm for (ε,δ)-estimation of the size of the union of set streams over Delphic family with space and update time complexity O((log³|Ω|)/ε² ⋅ log 1/δ) and Õ((log⁴|Ω|)/ε² ⋅ log 1/(δ)), respectively. This work presents a new, sampling-based algorithm for estimating the size of the union of Delphic sets that has space and update time complexity Õ((log²|Ω|)/ε² ⋅ log 1/(δ)). This improves the space complexity bound by a log|Ω| factor and update time complexity bound by a log² |Ω| factor. A critical question is whether quadratic dependence of log|Ω| on space and update time complexities is necessary. Specifically, can we design a streaming algorithm for estimating the size of the union of sets over Delphic family with space and complexity linear in log|Ω| and update time poly(log|Ω|)? While this appears technically challenging, we show that establishing a lower bound of ω(log|Ω|) with poly(log|Ω|) update time is beyond the reach of current techniques. Specifically, we show that under certain hard-to-prove computational complexity hypothesis, there is a streaming algorithm for the problem with optimal space complexity O(log|Ω|) and update time poly(log(|Ω|)). Thus, establishing a space lower bound of ω(log|Ω|) will lead to break-through complexity class separation results.
Cite as

Mridul Nandi, N. V. Vinodchandran, Arijit Ghosh, Kuldeep S. Meel, Soumit Pal, and Sourav Chakraborty. Improved Streaming Algorithm for the Klee’s Measure Problem and Generalizations. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 26:1-26:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{nandi_et_al:LIPIcs.APPROX/RANDOM.2024.26,
  author =	{Nandi, Mridul and Vinodchandran, N. V. and Ghosh, Arijit and Meel, Kuldeep S. and Pal, Soumit and Chakraborty, Sourav},
  title =	{{Improved Streaming Algorithm for the Klee’s Measure Problem and Generalizations}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{26:1--26:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.26},
  URN =		{urn:nbn:de:0030-drops-210191},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.26},
  annote =	{Keywords: Sampling, Streaming, Klee’s Measure Problem}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2023.37
Brief Announcement: Relations Between Space-Bounded and Adaptive Massively Parallel Computations

Authors: Michael Chen, A. Pavan, and N. V. Vinodchandran

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)

Abstract
In this work, we study the class of problems solvable by (deterministic) Adaptive Massively Parallel Computations in constant rounds from a computational complexity theory perspective. A language L is in the class AMPC⁰ if, for every ε > 0, there is a deterministic AMPC algorithm running in constant rounds with a polynomial number of processors, where the local memory of each machine s = O(N^ε). We prove that the space-bounded complexity class ReachUL is a proper subclass of AMPC⁰. The complexity class ReachUL lies between the well-known space-bounded complexity classes Deterministic Logspace (DLOG) and Nondeterministic Logspace (NLOG). In contrast, we establish that it is unlikely that PSPACE admits AMPC algorithms, even with polynomially many rounds. We also establish that showing PSPACE is a subclass of nonuniform-AMPC with polynomially many rounds leads to a significant separation result in complexity theory, namely PSPACE is a proper subclass of EXP^{Σ₂^{𝖯}}.
Cite as

Michael Chen, A. Pavan, and N. V. Vinodchandran. Brief Announcement: Relations Between Space-Bounded and Adaptive Massively Parallel Computations. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 37:1-37:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chen_et_al:LIPIcs.DISC.2023.37,
  author =	{Chen, Michael and Pavan, A. and Vinodchandran, N. V.},
  title =	{{Brief Announcement: Relations Between Space-Bounded and Adaptive Massively Parallel Computations}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{37:1--37:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.37},
  URN =		{urn:nbn:de:0030-drops-191634},
  doi =		{10.4230/LIPIcs.DISC.2023.37},
  annote =	{Keywords: Massively Parallel Computation, AMPC, Complexity Classes, LogSpace, NL, PSPACE}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.34
Distinct Elements in Streams: An Algorithm for the (Text) Book

Authors: Sourav Chakraborty, N. V. Vinodchandran¹, and Kuldeep S. Meel

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
Given a data stream 𝒟 = ⟨ a₁, a₂, …, a_m ⟩ of m elements where each a_i ∈ [n], the Distinct Elements problem is to estimate the number of distinct elements in 𝒟. Distinct Elements has been a subject of theoretical and empirical investigations over the past four decades resulting in space optimal algorithms for it. All the current state-of-the-art algorithms are, however, beyond the reach of an undergraduate textbook owing to their reliance on the usage of notions such as pairwise independence and universal hash functions. We present a simple, intuitive, sampling-based space-efficient algorithm whose description and the proof are accessible to undergraduates with the knowledge of basic probability theory.
Cite as

Sourav Chakraborty, N. V. Vinodchandran¹, and Kuldeep S. Meel. Distinct Elements in Streams: An Algorithm for the (Text) Book. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 34:1-34:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chakraborty_et_al:LIPIcs.ESA.2022.34,
  author =	{Chakraborty, Sourav and Vinodchandran¹, N. V. and Meel, Kuldeep S.},
  title =	{{Distinct Elements in Streams: An Algorithm for the (Text) Book}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{34:1--34:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.34},
  URN =		{urn:nbn:de:0030-drops-169725},
  doi =		{10.4230/LIPIcs.ESA.2022.34},
  annote =	{Keywords: F₀ Estimation, Streaming, Sampling}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.66
Complete Problems for Multi-Pseudodeterministic Computations

Authors: Peter Dixon, A. Pavan, and N. V. Vinodchandran

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
We exhibit several computational problems that are complete for multi-pseudodeterministic computations in the following sense: (1) these problems admit 2-pseudodeterministic algorithms (2) if there exists a pseudodeterministic algorithm for any of these problems, then any multi-valued function that admits a k-pseudodeterministic algorithm for a constant k, also admits a pseudodeterministic algorithm. We also show that these computational problems are complete for Search-BPP: a pseudodeterministic algorithm for any of these problems implies a pseudodeterministic algorithm for all problems in Search-BPP.
Cite as

Peter Dixon, A. Pavan, and N. V. Vinodchandran. Complete Problems for Multi-Pseudodeterministic Computations. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 66:1-66:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{dixon_et_al:LIPIcs.ITCS.2021.66,
  author =	{Dixon, Peter and Pavan, A. and Vinodchandran, N. V.},
  title =	{{Complete Problems for Multi-Pseudodeterministic Computations}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{66:1--66:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.66},
  URN =		{urn:nbn:de:0030-drops-136050},
  doi =		{10.4230/LIPIcs.ITCS.2021.66},
  annote =	{Keywords: Pseudodeterminism, Completeness, Collision Probability, Circuit Acceptance, Entropy Approximation}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2018.61
On Pseudodeterministic Approximation Algorithms

Authors: Peter Dixon, A. Pavan, and N. V. Vinodchandran

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
We investigate the notion of pseudodeterminstic approximation algorithms. A randomized approximation algorithm A for a function f is pseudodeterministic if for every input x there is a unique value v so that A(x) outputs v with high probability, and v is a good approximation of f(x). We show that designing a pseudodeterministic version of Stockmeyer's well known approximation algorithm for the NP-membership counting problem will yield a new circuit lower bound: if such an approximation algorithm exists, then for every k, there is a language in the complexity class ZPP^{NP}_{tt} that does not have n^k-size circuits. While we do not know how to design such an algorithm for the NP-membership counting problem, we show a general result that any randomized approximation algorithm for a counting problem can be transformed to an approximation algorithm that has a constant number of influential random bits. That is, for most settings of these influential bits, the approximation algorithm will be pseudodeterministic.
Cite as

Peter Dixon, A. Pavan, and N. V. Vinodchandran. On Pseudodeterministic Approximation Algorithms. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 61:1-61:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{dixon_et_al:LIPIcs.MFCS.2018.61,
  author =	{Dixon, Peter and Pavan, A. and Vinodchandran, N. V.},
  title =	{{On Pseudodeterministic Approximation Algorithms}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{61:1--61:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.61},
  URN =		{urn:nbn:de:0030-drops-96431},
  doi =		{10.4230/LIPIcs.MFCS.2018.61},
  annote =	{Keywords: Approximation Algorithms, Circuit lower bounds, Pseudodeterminism}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2018.22
New Algorithms for Distributed Sliding Windows

Authors: Sutanu Gayen and N. V. Vinodchandran

Published in: LIPIcs, Volume 101, 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)

Abstract
Computing functions over a distributed stream of data is a significant problem with practical applications. The distributed streaming model is a natural computational model to deal with such scenarios. The goal in this model is to maintain an approximate value of a function of interest over a data stream distributed across several computational nodes. These computational nodes have a two-way communication channel with a coordinator node that maintains an approximation of the function over the entire data stream seen so far. The resources of interest, which need to be minimized, are communication (primary), space, and update time. A practical variant of this model is that of distributed sliding window (dsw), where the computation is limited to the last W items, where W is the window size. Important problems such as sampling and counting have been investigated in this model. However, certain problems including computing frequency moments and metric clustering, that are well studied in other streaming models, have not been considered in the distributed sliding window model. We give the first algorithms for computing the frequency moments and metric clustering problems in the distributed sliding window model. Our algorithms for these problems are a result of a general transfer theorem we establish that transforms any algorithm in the distributed infinite window model to an algorithm in the distributed sliding window model, for a large class of functions. In particular, we show an efficient adaptation of the smooth histogram technique of Braverman and Ostrovsky, to the distributed streaming model. Our construction allows trade-offs between communication and space. If we optimize for communication, we get algorithms that are as communication efficient as their infinite window counter parts (upto polylogarithmic factors).
Cite as

Sutanu Gayen and N. V. Vinodchandran. New Algorithms for Distributed Sliding Windows. In 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 101, pp. 22:1-22:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{gayen_et_al:LIPIcs.SWAT.2018.22,
  author =	{Gayen, Sutanu and Vinodchandran, N. V.},
  title =	{{New Algorithms for Distributed Sliding Windows}},
  booktitle =	{16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)},
  pages =	{22:1--22:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-068-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{101},
  editor =	{Eppstein, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2018.22},
  URN =		{urn:nbn:de:0030-drops-88481},
  doi =		{10.4230/LIPIcs.SWAT.2018.22},
  annote =	{Keywords: distributed streaming, distributed functional monitoring, distributed sliding window, frequency moments, k-median clustering, k-center clustering}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2016.31
A Note on the Advice Complexity of Multipass Randomized Logspace

Authors: Peter Dixon, Debasis Mandal, A. Pavan, and N. V. Vinodchandran

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract
Investigating the complexity of randomized space-bounded machines that are allowed to make multiple passes over the random tape has been of recent interest. In particular, it has been shown that derandomizing such probabilistic machines yields a weak but new derandomization of probabilistic time-bounded classes. In this paper we further explore the complexity of such machines. In particular, as our main result we show that for any epsilon<1, every language that is accepted by an O(n^epsilon)-pass, randomized logspace machine can be simulated in deterministic logspace with linear amount of advice. This result extends an earlier result of Fortnow and Klivans who showed that RL is in deterministic logspace with linear advice.
Cite as

Peter Dixon, Debasis Mandal, A. Pavan, and N. V. Vinodchandran. A Note on the Advice Complexity of Multipass Randomized Logspace. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 31:1-31:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{dixon_et_al:LIPIcs.MFCS.2016.31,
  author =	{Dixon, Peter and Mandal, Debasis and Pavan, A. and Vinodchandran, N. V.},
  title =	{{A Note on the Advice Complexity of Multipass Randomized Logspace}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{31:1--31:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.31},
  URN =		{urn:nbn:de:0030-drops-65003},
  doi =		{10.4230/LIPIcs.MFCS.2016.31},
  annote =	{Keywords: space-bounded computations, randomized machines, advice}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2014.585
New Time-Space Upperbounds for Directed Reachability in High-genus and H-minor-free Graphs

Authors: Diptarka Chakraborty, A. Pavan, Raghunath Tewari, N. V. Vinodchandran, and Lin Forrest Yang

Published in: LIPIcs, Volume 29, 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)

Abstract
We obtain the following new simultaneous time-space upper bounds for the directed reachability problem. (1) A polynomial-time, O(n^{2/3} * g^{1/3})-space algorithm for directed graphs embedded on orientable surfaces of genus g. (2) A polynomial-time, O(n^{2/3})-space algorithm for all H-minor-free graphs given the tree decomposition, and (3) for K_{3,3}-free and K_5-free graphs, a polynomial-time, O(n^{1/2 + epsilon})-space algorithm, for every epsilon > 0. For the general directed reachability problem, the best known simultaneous time-space upper bound is the BBRS bound, due to Barnes, Buss, Ruzzo, and Schieber, which achieves a space bound of O(n/2^{k * sqrt(log(n))}) with polynomial running time, for any constant k. It is a significant open question to improve this bound for reachability over general directed graphs. Our algorithms beat the BBRS bound for graphs embedded on surfaces of genus n/2^{omega(sqrt(log(n))}, and for all H-minor-free graphs. This significantly broadens the class of directed graphs for which the BBRS bound can be improved.
Cite as

Diptarka Chakraborty, A. Pavan, Raghunath Tewari, N. V. Vinodchandran, and Lin Forrest Yang. New Time-Space Upperbounds for Directed Reachability in High-genus and H-minor-free Graphs. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 585-595, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{chakraborty_et_al:LIPIcs.FSTTCS.2014.585,
  author =	{Chakraborty, Diptarka and Pavan, A. and Tewari, Raghunath and Vinodchandran, N. V. and Yang, Lin Forrest},
  title =	{{New Time-Space Upperbounds for Directed Reachability in High-genus and H-minor-free Graphs}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{585--595},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-77-4},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{29},
  editor =	{Raman, Venkatesh and Suresh, S. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.585},
  URN =		{urn:nbn:de:0030-drops-48730},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.585},
  annote =	{Keywords: Reachability, Space complexity, Time-Space Efficient Algorithms, Graphs on Surfaces, Minor Free Graphs, Savitch's Algorithm, BBRS Bound}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2009.2320
Kolmogorov Complexity in Randomness Extraction

Authors: John M. Hitchcock, Aduri Pavan, and N. V. Vinodchandran

Published in: LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

Abstract
We clarify the role of Kolmogorov complexity in the area of randomness extraction. We show that a computable function is an almost randomness extractor if and only if it is a Kolmogorov complexity extractor, thus establishing a fundamental equivalence between two forms of extraction studied in the literature: Kolmogorov extraction and randomness extraction. We present a distribution ${\cal M}_k$ based on Kolmogorov complexity that is complete for randomness extraction in the sense that a computable function is an almost randomness extractor if and only if it extracts randomness from ${\cal M}_k$.
Cite as

John M. Hitchcock, Aduri Pavan, and N. V. Vinodchandran. Kolmogorov Complexity in Randomness Extraction. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 215-226, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{hitchcock_et_al:LIPIcs.FSTTCS.2009.2320,
  author =	{Hitchcock, John M. and Pavan, Aduri and Vinodchandran, N. V.},
  title =	{{Kolmogorov Complexity in Randomness Extraction}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{215--226},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-13-2},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{4},
  editor =	{Kannan, Ravi and Narayan Kumar, K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2320},
  URN =		{urn:nbn:de:0030-drops-23201},
  doi =		{10.4230/LIPIcs.FSTTCS.2009.2320},
  annote =	{Keywords: Extractors, Kolmogorov extractors, randomness}
}
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