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Documents authored by Vishnoi, Nisheeth K.

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Vishnoi, Nisheeth K.

Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2023.5
Algorithms in the Presence of Biased Inputs (Invited Talk)

Authors: Nisheeth K. Vishnoi

Published in: LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

Abstract
Algorithms for optimization problems such as selection, ranking, and classification typically assume that the inputs are what they are promised to be. However, in several real-world applications of these problems, the input may contain systematic biases along socially salient attributes associated with inputs such as race, gender, or political opinion. Such biases can not only lead the outputs of the current algorithms to output sub-optimal solutions with respect to true inputs but may also adversely affect opportunities for individuals in disadvantaged socially salient groups. This talk will consider the question of using optimization to solve the aforementioned problems in the presence of biased inputs. It will start with models of biases in inputs and discuss alternate ways to design algorithms for the underlying problem that can mitigate the effects of biases by taking into account knowledge about biases. This talk is based on several joint works with a number of co-authors.
Cite as

Nisheeth K. Vishnoi. Algorithms in the Presence of Biased Inputs (Invited Talk). In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 5:1-5:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{vishnoi:LIPIcs.FSTTCS.2023.5,
  author =	{Vishnoi, Nisheeth K.},
  title =	{{Algorithms in the Presence of Biased Inputs}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{5:1--5:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-304-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{284},
  editor =	{Bouyer, Patricia and Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.5},
  URN =		{urn:nbn:de:0030-drops-193788},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.5},
  annote =	{Keywords: Algorithmic Bias}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.25
On Geodesically Convex Formulations for the Brascamp-Lieb Constant

Authors: Suvrit Sra, Nisheeth K. Vishnoi, and Ozan Yildiz

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
We consider two non-convex formulations for computing the optimal constant in the Brascamp-Lieb inequality corresponding to a given datum and show that they are geodesically log-concave on the manifold of positive definite matrices endowed with the Riemannian metric corresponding to the Hessian of the log-determinant function. The first formulation is present in the work of Lieb [Lieb, 1990] and the second is new and inspired by the work of Bennett et al. [Bennett et al., 2008]. Recent work of Garg et al. [Ankit Garg et al., 2017] also implies a geodesically log-concave formulation of the Brascamp-Lieb constant through a reduction to the operator scaling problem. However, the dimension of the arising optimization problem in their reduction depends exponentially on the number of bits needed to describe the Brascamp-Lieb datum. The formulations presented here have dimensions that are polynomial in the bit complexity of the input datum.
Cite as

Suvrit Sra, Nisheeth K. Vishnoi, and Ozan Yildiz. On Geodesically Convex Formulations for the Brascamp-Lieb Constant. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 25:1-25:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{sra_et_al:LIPIcs.APPROX-RANDOM.2018.25,
  author =	{Sra, Suvrit and Vishnoi, Nisheeth K. and Yildiz, Ozan},
  title =	{{On Geodesically Convex Formulations for the Brascamp-Lieb Constant}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{25:1--25:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.25},
  URN =		{urn:nbn:de:0030-drops-94296},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.25},
  annote =	{Keywords: Geodesic convexity, positive definite cone, geodesics, Brascamp-Lieb constant}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.28
Ranking with Fairness Constraints

Authors: L. Elisa Celis, Damian Straszak, and Nisheeth K. Vishnoi

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
Ranking algorithms are deployed widely to order a set of items in applications such as search engines, news feeds, and recommendation systems. Recent studies, however, have shown that, left unchecked, the output of ranking algorithms can result in decreased diversity in the type of content presented, promote stereotypes, and polarize opinions. In order to address such issues, we study the following variant of the traditional ranking problem when, in addition, there are fairness or diversity constraints. Given a collection of items along with 1) the value of placing an item in a particular position in the ranking, 2) the collection of sensitive attributes (such as gender, race, political opinion) of each item and 3) a collection of fairness constraints that, for each k, bound the number of items with each attribute that are allowed to appear in the top k positions of the ranking, the goal is to output a ranking that maximizes the value with respect to the original rank quality metric while respecting the constraints. This problem encapsulates various well-studied problems related to bipartite and hypergraph matching as special cases and turns out to be hard to approximate even with simple constraints. Our main technical contributions are fast exact and approximation algorithms along with complementary hardness results that, together, come close to settling the approximability of this constrained ranking maximization problem. Unlike prior work on the approximability of constrained matching problems, our algorithm runs in linear time, even when the number of constraints is (polynomially) large, its approximation ratio does not depend on the number of constraints, and it produces solutions with small constraint violations. Our results rely on insights about the constrained matching problem when the objective function satisfies certain properties that appear in common ranking metrics such as discounted cumulative gain (DCG), Spearman's rho or Bradley-Terry, along with the nested structure of fairness constraints.
Cite as

L. Elisa Celis, Damian Straszak, and Nisheeth K. Vishnoi. Ranking with Fairness Constraints. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{celis_et_al:LIPIcs.ICALP.2018.28,
  author =	{Celis, L. Elisa and Straszak, Damian and Vishnoi, Nisheeth K.},
  title =	{{Ranking with Fairness Constraints}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{28:1--28:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.28},
  URN =		{urn:nbn:de:0030-drops-90329},
  doi =		{10.4230/LIPIcs.ICALP.2018.28},
  annote =	{Keywords: Ranking, Fairness, Optimization, Matching, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.74
Isolating a Vertex via Lattices: Polytopes with Totally Unimodular Faces

Authors: Rohit Gurjar, Thomas Thierauf, and Nisheeth K. Vishnoi

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We present a geometric approach towards derandomizing the {Isolation Lemma} by Mulmuley, Vazirani, and Vazirani. In particular, our approach produces a quasi-polynomial family of weights, where each weight is an integer and quasi-polynomially bounded, that can isolate a vertex in any 0/1 polytope for which each face lies in an affine space defined by a totally unimodular matrix. This includes the polytopes given by totally unimodular constraints and generalizes the recent derandomization of the Isolation Lemma for {bipartite perfect matching} and {matroid intersection}. We prove our result by associating a {lattice} to each face of the polytope and showing that if there is a totally unimodular kernel matrix for this lattice, then the number of vectors of length within 3/2 of the shortest vector in it is polynomially bounded. The proof of this latter geometric fact is combinatorial and follows from a polynomial bound on the number of circuits of size within 3/2 of the shortest circuit in a regular matroid. This is the technical core of the paper and relies on a variant of Seymour's decomposition theorem for regular matroids. It generalizes an influential result by Karger on the number of minimum cuts in a graph to regular matroids.
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Rohit Gurjar, Thomas Thierauf, and Nisheeth K. Vishnoi. Isolating a Vertex via Lattices: Polytopes with Totally Unimodular Faces. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 74:1-74:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{gurjar_et_al:LIPIcs.ICALP.2018.74,
  author =	{Gurjar, Rohit and Thierauf, Thomas and Vishnoi, Nisheeth K.},
  title =	{{Isolating a Vertex via Lattices: Polytopes with Totally Unimodular Faces}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{74:1--74:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.74},
  URN =		{urn:nbn:de:0030-drops-90782},
  doi =		{10.4230/LIPIcs.ICALP.2018.74},
  annote =	{Keywords: Derandomization, Isolation Lemma, Total unimodularity, Near-shortest vectors in Lattices, Regular matroids}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2017.50
Random Walks in Polytopes and Negative Dependence

Authors: Yuval Peres, Mohit Singh, and Nisheeth K. Vishnoi

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Abstract
We present a Gaussian random walk in a polytope that starts at a point inside and continues until it gets absorbed at a vertex. Our main result is that the probability distribution induced on the vertices by this random walk has strong negative dependence properties for matroid polytopes. Such distributions are highly sought after in randomized algorithms as they imply concentration properties. Our random walk is simple to implement, computationally efficient and can be viewed as an algorithm to round the starting point in an unbiased manner. The proof relies on a simple inductive argument that synthesizes the combinatorial structure of matroid polytopes with the geometric structure of multivariate Gaussian distributions. Our result not only implies a long line of past results in a unified and transparent manner, but also implies new results about constructing negatively associated distributions for all matroids.
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Yuval Peres, Mohit Singh, and Nisheeth K. Vishnoi. Random Walks in Polytopes and Negative Dependence. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 50:1-50:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{peres_et_al:LIPIcs.ITCS.2017.50,
  author =	{Peres, Yuval and Singh, Mohit and Vishnoi, Nisheeth K.},
  title =	{{Random Walks in Polytopes and Negative Dependence}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{50:1--50:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.50},
  URN =		{urn:nbn:de:0030-drops-81464},
  doi =		{10.4230/LIPIcs.ITCS.2017.50},
  annote =	{Keywords: Random walks, Matroid, Polytope, Brownian motion, Negative dependence}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.36
On the Complexity of Constrained Determinantal Point Processes

Authors: L. Elisa Celis, Amit Deshpande, Tarun Kathuria, Damian Straszak, and Nisheeth K. Vishnoi

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

Abstract
Determinantal Point Processes (DPPs) are probabilistic models that arise in quantum physics and random matrix theory and have recently found numerous applications in theoretical computer science and machine learning. DPPs define probability distributions over subsets of a given ground set, they exhibit interesting properties such as negative correlation, and, unlike other models of negative correlation such as Markov random fields, have efficient algorithms for sampling. When applied to kernel methods in machine learning, DPPs favor subsets of the given data with more diverse features. However, many real-world applications require efficient algorithms to sample from DPPs with additional constraints on the sampled subset, e.g., partition or matroid constraints that are important from the viewpoint of ensuring priors, resource or fairness constraints on the sampled subset. Whether one can efficiently sample from DPPs in such constrained settings is an important problem that was first raised in a survey of DPPs for machine learning by Kulesza and Taskar and studied in some recent works. The main contribution of this paper is the first resolution of the complexity of sampling from DPPs with constraints. On the one hand, we give exact efficient algorithms for sampling from constrained DPPs when the description of the constraints is in unary; this includes special cases of practical importance such as a small number of partition, knapsack or budget constraints. On the other hand, we prove that when the constraints are specified in binary, this problem is #P-hard via a reduction from the problem of computing mixed discriminants; implying that it may be unlikely that there is an FPRAS. Technically, our algorithmic result benefits from viewing the constrained sampling problem via the lens of polynomials and we obtain our complexity results by providing an equivalence between computing mixed discriminants and sampling from partition constrained DPPs. As a consequence, we obtain a few corollaries of independent interest: 1) An algorithm to count, sample (and, hence, optimize) over the base polytope of regular matroids when there are additional (succinct) budget constraints and, 2) An algorithm to evaluate and compute mixed characteristic polynomials, that played a central role in the resolution of the Kadison-Singer problem, for certain special cases.
Cite as

L. Elisa Celis, Amit Deshpande, Tarun Kathuria, Damian Straszak, and Nisheeth K. Vishnoi. On the Complexity of Constrained Determinantal Point Processes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 36:1-36:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{celis_et_al:LIPIcs.APPROX-RANDOM.2017.36,
  author =	{Celis, L. Elisa and Deshpande, Amit and Kathuria, Tarun and Straszak, Damian and Vishnoi, Nisheeth K.},
  title =	{{On the Complexity of Constrained Determinantal Point Processes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{36:1--36:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.36},
  URN =		{urn:nbn:de:0030-drops-75851},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.36},
  annote =	{Keywords: determinantal point processes, constraints, matroids, sampling and counting, polynomials, mixed discriminant}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.63
Mixing Time of Markov Chains, Dynamical Systems and Evolution

Authors: Ioannis Panageas and Nisheeth K. Vishnoi

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
In this paper we study the mixing time of evolutionary Markov chains over populations of a fixed size (N) in which each individual can be one of m types. These Markov chains have the property that they are guided by a dynamical system from the m-dimensional probability simplex to itself. Roughly, given the current state of the Markov chain, which can be viewed as a probability distribution over the m types, the next state is generated by applying this dynamical system to this distribution, and then sampling from it N times. Many processes in nature, from biology to sociology, are evolutionary and such chains can be used to model them. In this study, the mixing time is of particular interest as it determines the speed of evolution and whether the statistics of the steady state can be efficiently computed. In a recent result [Panageas, Srivastava, Vishnoi, Soda, 2016], it was suggested that the mixing time of such Markov chains is connected to the geometry of this guiding dynamical system. In particular, when the dynamical system has a fixed point which is a global attractor, then the mixing is fast. The limit sets of dynamical systems, however, can exhibit more complex behavior: they could have multiple fixed points that are not necessarily stable, periodic orbits, or even chaos. Such behavior arises in important evolutionary settings such as the dynamics of sexual evolution and that of grammar acquisition. In this paper we prove that the geometry of the dynamical system can also give tight mixing time bounds when the dynamical system has multiple fixed points and periodic orbits. We show that the mixing time continues to remain small in the presence of several unstable fixed points and is exponential in N when there are two or more stable fixed points. As a consequence of our results, we obtain a phase transition result for the mixing time of the sexual/grammar model mentioned above. We arrive at the conclusion that in the interesting parameter regime for these models, i.e., when there are multiple stable fixed points, the mixing is slow. Our techniques strengthen the connections between Markov chains and dynamical systems and we expect that the tools developed in this paper should have a wider applicability.
Cite as

Ioannis Panageas and Nisheeth K. Vishnoi. Mixing Time of Markov Chains, Dynamical Systems and Evolution. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 63:1-63:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{panageas_et_al:LIPIcs.ICALP.2016.63,
  author =	{Panageas, Ioannis and Vishnoi, Nisheeth K.},
  title =	{{Mixing Time of Markov Chains, Dynamical Systems and Evolution}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{63:1--63:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.63},
  URN =		{urn:nbn:de:0030-drops-62213},
  doi =		{10.4230/LIPIcs.ICALP.2016.63},
  annote =	{Keywords: Markov chains, Mixing time, Dynamical Systems, Evolutionary dynamics, Language evolution}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.CCC.2016.21
Evolution and Computation (Invited Talk)

Authors: Nisheeth K. Vishnoi

Published in: LIPIcs, Volume 50, 31st Conference on Computational Complexity (CCC 2016)

Abstract
Over the last two centuries there have been tremendous scientific and mathematical advances in our understanding of evolution, life and its mysteries. Recently, the relatively new and powerful tool of computation has joined forces to develop this understanding further: the underlying tenet is that several natural processes, including evolution itself, can be viewed as computing or optimizing something - evolution is computation. Furthermore, as in computation, efficiency is an important consideration in evolution. As many of these evolutionary processes are described using the language of dynamical systems, this entails understanding how quickly such systems can attain their equilibria. This endeavor not only has the potential to give us fundamental insights into life, it holds the promise that we will unveil new computational models and techniques. In this talk we will see some vignettes of this interplay between evolution and computation.
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Nisheeth K. Vishnoi. Evolution and Computation (Invited Talk). In 31st Conference on Computational Complexity (CCC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 50, p. 21:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{vishnoi:LIPIcs.CCC.2016.21,
  author =	{Vishnoi, Nisheeth K.},
  title =	{{Evolution and Computation}},
  booktitle =	{31st Conference on Computational Complexity (CCC 2016)},
  pages =	{21:1--21:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-008-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{50},
  editor =	{Raz, Ran},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2016.21},
  URN =		{urn:nbn:de:0030-drops-58576},
  doi =		{10.4230/LIPIcs.CCC.2016.21},
  annote =	{Keywords: Evolution, Dynamical Systems, Algorithms, Complexity}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.FSTTCS.2013
LIPIcs, Volume 24, FSTTCS'13, Complete Volume

Authors: Anil Seth and Nisheeth K. Vishnoi

Published in: LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)

Abstract
LIPIcs, Volume 24, FSTTCS'13, Complete Volume
Cite as

IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@Proceedings{seth_et_al:LIPIcs.FSTTCS.2013,
  title =	{{LIPIcs, Volume 24, FSTTCS'13, Complete Volume}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-64-4},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{24},
  editor =	{Seth, Anil and Vishnoi, Nisheeth K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013},
  URN =		{urn:nbn:de:0030-drops-44358},
  doi =		{10.4230/LIPIcs.FSTTCS.2013},
  annote =	{Keywords: Software/Program Verification, Models of Computation, Modes of Computation, Complexity Measures and Classes, Nonnumerical Algorithms and Problems, Spe Programs, Mathematical Logic, Formal Languages}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.FSTTCS.2013.i
Frontmatter, Table of Contents, Preface, Conference Organization

Authors: Anil Seth and Nisheeth K. Vishnoi

Published in: LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)

Abstract
Frontmatter, Table of Contents, Preface, Conference Organization
Cite as

IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. i-xiv, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{seth_et_al:LIPIcs.FSTTCS.2013.i,
  author =	{Seth, Anil and Vishnoi, Nisheeth K.},
  title =	{{Frontmatter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
  pages =	{i--xiv},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-64-4},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{24},
  editor =	{Seth, Anil and Vishnoi, Nisheeth K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.i},
  URN =		{urn:nbn:de:0030-drops-44041},
  doi =		{10.4230/LIPIcs.FSTTCS.2013.i},
  annote =	{Keywords: Frontmatter, Table of Contents, Preface, Conference Organization}
}

Vishnoi, Nisheeth

Document
DOI: 10.4230/DagRep.6.1.1
Evolution and Computing (Dagstuhl Seminar 16011)

Authors: Nick Barton, Per Kristian Lehre, and Nisheeth Vishnoi

Published in: Dagstuhl Reports, Volume 6, Issue 1 (2016)

Abstract
This report documents the talks and discussions at the Dagstuhl seminar 16011 “Evolution and Computing”. The seminar brought together several research disciplines studying evolution, including population genetics and mathematical biology, theoretical computer science, and evolutionary computation.
Cite as

Nick Barton, Per Kristian Lehre, and Nisheeth Vishnoi. Evolution and Computing (Dagstuhl Seminar 16011). In Dagstuhl Reports, Volume 6, Issue 1, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@Article{barton_et_al:DagRep.6.1.1,
  author =	{Barton, Nick and Lehre, Per Kristian and Vishnoi, Nisheeth},
  title =	{{Evolution and Computing (Dagstuhl Seminar 16011)}},
  pages =	{1--14},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2016},
  volume =	{6},
  number =	{1},
  editor =	{Barton, Nick and Lehre, Per Kristian and Vishnoi, Nisheeth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.6.1.1},
  URN =		{urn:nbn:de:0030-drops-58064},
  doi =		{10.4230/DagRep.6.1.1},
  annote =	{Keywords: Evolution, Evolutionary Computation, Natural Algorithms, Theory of Computation}
}
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