58 Search Results for "Suresh, S. P."

Volume

LIPIcs, Volume 29

34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)

FSTTCS 2014, December 15-17, 2014, New Delhi, India

Editors: Venkatesh Raman and S. P. Suresh

Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.20
Renyi Entropy Estimation Revisited

Authors: Maciej Obremski and Maciej Skorski

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

Abstract
We revisit the problem of estimating entropy of discrete distributions from independent samples, studied recently by Acharya, Orlitsky, Suresh and Tyagi (SODA 2015), improving their upper and lower bounds on the necessary sample size n. For estimating Renyi entropy of order alpha, up to constant accuracy and error probability, we show the following * Upper bounds n = O(1) 2^{(1-1/alpha)H_alpha} for integer alpha>1, as the worst case over distributions with Renyi entropy equal to H_alpha. * Lower bounds n = Omega(1) K^{1-1/alpha} for any real alpha>1, with the constant being an inverse polynomial of the accuracy, as the worst case over all distributions on K elements. Our upper bounds essentially replace the alphabet size by a factor exponential in the entropy, which offers improvements especially in low or medium entropy regimes (interesting for example in anomaly detection). As for the lower bounds, our proof explicitly shows how the complexity depends on both alphabet and accuracy, partially solving the open problem posted in previous works. The argument for upper bounds derives a clean identity for the variance of falling-power sum of a multinomial distribution. Our approach for lower bounds utilizes convex optimization to find a distribution with possibly worse estimation performance, and may be of independent interest as a tool to work with Le Cam’s two point method.
Cite as

Maciej Obremski and Maciej Skorski. Renyi Entropy Estimation Revisited. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{obremski_et_al:LIPIcs.APPROX-RANDOM.2017.20,
  author =	{Obremski, Maciej and Skorski, Maciej},
  title =	{{Renyi Entropy Estimation Revisited}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{20:1--20:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.20},
  URN =		{urn:nbn:de:0030-drops-75699},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.20},
  annote =	{Keywords: Renyi entropy, entropy estimation, sample complexity, convex optimization}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.FSTTCS.2014
LIPIcs, Volume 29, FSTTCS'14, Complete Volume

Authors: Venkatesh Raman and S. P. Suresh

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

Abstract
LIPIcs, Volume 29, FSTTCS'14, Complete Volume
Cite as

34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@Proceedings{raman_et_al:LIPIcs.FSTTCS.2014,
  title =	{{LIPIcs, Volume 29, FSTTCS'14, Complete Volume}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014},
  URN =		{urn:nbn:de:0030-drops-48795},
  doi =		{10.4230/LIPIcs.FSTTCS.2014},
  annote =	{Keywords: Software/Program Verification, Models of Computation, Modes of Computation, Complexity Measures and Classes, Nonnumerical Algorithms and Problems, Specifying and Verifying and Reasoning about Programs, Mathematical Logic, Formal Languages}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.FSTTCS.2014.i
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Venkatesh Raman and S. P. Suresh

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

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. i-xiv, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{raman_et_al:LIPIcs.FSTTCS.2014.i,
  author =	{Raman, Venkatesh and Suresh, S. P.},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{i--xiv},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.i},
  URN =		{urn:nbn:de:0030-drops-48258},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.i},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2014.1
New Developments in Iterated Rounding (Invited Talk)

Authors: Nikhil Bansal

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

Abstract
Iterated rounding is a relatively recent technique in algorithm design, that despite its simplicity has led to several remarkable new results and also simpler proofs of many previous results. We will briefly survey some applications of the method, including some recent developments and giving a high level overview of the ideas.
Cite as

Nikhil Bansal. New Developments in Iterated Rounding (Invited Talk). In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 1-10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{bansal:LIPIcs.FSTTCS.2014.1,
  author =	{Bansal, Nikhil},
  title =	{{New Developments in Iterated Rounding}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{1--10},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.1},
  URN =		{urn:nbn:de:0030-drops-48275},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.1},
  annote =	{Keywords: Algorithms, Approximation, Rounding}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2014.11
Reasoning About Distributed Systems: WYSIWYG (Invited Talk)

Authors: Aiswarya Cyriac and Paul Gastin

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

Abstract
There are two schools of thought on reasoning about distributed systems: one following interleaving based semantics, and one following partial-order/graph based semantics. This paper compares these two approaches and argues in favour of the latter. An introductory treatment of the split-width technique is also provided.
Cite as

Aiswarya Cyriac and Paul Gastin. Reasoning About Distributed Systems: WYSIWYG (Invited Talk). In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 11-30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{cyriac_et_al:LIPIcs.FSTTCS.2014.11,
  author =	{Cyriac, Aiswarya and Gastin, Paul},
  title =	{{Reasoning About Distributed Systems: WYSIWYG}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{11--30},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.11},
  URN =		{urn:nbn:de:0030-drops-48283},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.11},
  annote =	{Keywords: Verification of distributed systems, Communicating recursive programs, Partial order/graph semantics, Split-width and tree interpretation}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2014.31
Colour Refinement: A Simple Partitioning Algorithm with Applications From Graph Isomorphism Testing to Machine Learning (Invited Talk)

Authors: Martin Grohe

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

Abstract
Colour refinement is a simple algorithm that partitions the vertices of a graph according their "iterated degree sequence." It has very efficient implementations, running in quasilinear time, and a surprisingly wide range of applications. The algorithm has been designed in the context of graph isomorphism testing, and it is used an important subroutine in almost all practical graph isomorphism tools. Somewhat surprisingly, other applications in machine learning, probabilistic inference, and linear programming have surfaced recently. In the first part of my talk, I will introduce the basic algorithm as well as higher dimensional extensions known as the k-dimensional Weisfeiler-Lehman algorithm. I will also discuss an unexpected connection between colour refinement and a natural linear programming approach to graph isomorphism testing. In the second part of my talk, I will discuss various applications of colour refinement.
Cite as

Martin Grohe. Colour Refinement: A Simple Partitioning Algorithm with Applications From Graph Isomorphism Testing to Machine Learning (Invited Talk). In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, p. 31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{grohe:LIPIcs.FSTTCS.2014.31,
  author =	{Grohe, Martin},
  title =	{{Colour Refinement: A Simple Partitioning Algorithm with Applications From Graph Isomorphism Testing to Machine Learning}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{31--31},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.31},
  URN =		{urn:nbn:de:0030-drops-48290},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.31},
  annote =	{Keywords: Color Refinement, Graph Isomorphism, Machine Learning}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2014.33
Properties and Utilization of Capacitated Automata (Invited Talk)

Authors: Orna Kupferman and Tami Tamir

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

Abstract
We study capacitated automata(CAs), where transitions correspond to resources and may have bounded capacities. Each transition in a CA is associated with a (possibly infinite) bound on the number of times it may be traversed. We study CAs from two points of view. The first is that of traditional automata theory, where we view CAs as recognizers of formal languages and examine their expressive power, succinctness, and determinization. The second is that of resource-allocation theory, where we view CAs as a rich description of a flow network and study their utilization.
Cite as

Orna Kupferman and Tami Tamir. Properties and Utilization of Capacitated Automata (Invited Talk). In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 33-44, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{kupferman_et_al:LIPIcs.FSTTCS.2014.33,
  author =	{Kupferman, Orna and Tamir, Tami},
  title =	{{Properties and Utilization of Capacitated Automata}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{33--44},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.33},
  URN =		{urn:nbn:de:0030-drops-48306},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.33},
  annote =	{Keywords: Automata, Capacitated transitions, Determinization, Maximum utilization}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2014.45
Algorithms, Games, and Evolution (Invited Talk)

Authors: Erick Chastain, Adi Livnat, Christos H. Papadimitriou, and Umesh V. Vazirani

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

Abstract
Even the most seasoned students of evolution, starting with Darwin himself, have occasionally expressed amazement at the fact that the mechanism of natural selection has produced the whole of Life as we see it around us. From a computational perspective, it is natural to marvel at evolution's solution to the problems of robotics, vision and theorem proving! What, then, is the complexity of evolution, viewed as an algorithm? One answer to this question is 10^{12}, roughly the number of sequential steps or generations from the earliest single celled creatures to today's Homo Sapiens. To put this into perspective, the processor of a modern cell phone can perform 10^{12} steps in less than an hour. Another answer is 10^30, the degree of parallelism, roughly the maximum number of organisms living on the Earth at any time. Perhaps the answer should be the product of the two numbers, roughly 10^42, to reflect the total work done by evolution, viewed as a parallel algorithm. Here we argue, interpreting our recently published paper, that none of the above answers is really correct. Viewing evolution as an algorithm poses an additional challenge: recombination. Even if evolution succeeds in producing a particularly good solution (a highly fit individual), its offspring would only inherit half its genes, and therefore appear unlikely to be a good solution. This is the core of the problem of explaining the role of sex in evolution, known as the "queen of problems in evolutionary biology". The starting point is the diffusion-equation-based approach of theoretical population geneticists, who analyze the changing allele frequencies (over the generations) in the gene pool, consisting of the aggregate of the genetic variants (or "alleles") over all genes (or "loci") and over all individuals in a species. Taking this viewpoint to its logical conclusion, rather than acting on individuals or species or genes, evolution acts on this gene pool, or genetic soup, by making it more "potent", in the sense that it increases the expected fitness of genotype drawn randomly from this soup. Moreover, for much genetic variation, this soup may be assumed to be in the regime of weak selection, a regime where the probability of occurrence of a certain genotype involving various alleles at different loci is simply the product of the probabilities of each of its alleles. In this regime, we show that evolution in the regime of weak selection can be formulated as a game, where the recombining loci are the players, the alleles in those loci are possible moves or actions of each player, and the expected payoff of each player-locus is precisely the organism's expected fitness across the genotypes that are present in the population. Moreover, the dynamics specified by the diffusion equations of theoretical population geneticists is closely approximated by the dynamics of multiplicative weight updates (MWUA). The algorithmic connection to MWUA brings with it new insights for evolutionary biology, specifically, into the question of how genetic diversity is maintained in the presence of natural selection. For this it is useful to consider a dual view of MWUA, which expresses "what each gene is optimizing" as it plays the game. Remarkably this turns out to be a particular convex combination of the entropy of its distribution over alleles and cumulative expected fitness. This sheds new light on the maintenance of diversity in evolution. All of this suggests that the complexity of evolution should indeed be viewed as 10^12, but for a subtle reason. It is the number of steps of multiplicative weight updates carried out on allele frequencies in the genetic soup. A closer examination of this reveals further that the accurate tracking of allele frequencies over the generations requires the simulation of a quadratic dynamical system (two parents for each offspring). Moreover the simulation of even simple quadratic dynamical systems is known to be PSPACE-hard. This suggests that the tracking of allele frequencies might require large population sizes for each species, putting into perspective the number 10^30. Finally, it is worth noting that in this view there is a primacy to recombination or sex, which serve to provide robustness to the mechanism of evolution, as well as the framework within which MWUA operates.
Cite as

Erick Chastain, Adi Livnat, Christos H. Papadimitriou, and Umesh V. Vazirani. Algorithms, Games, and Evolution (Invited Talk). In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 45-46, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{chastain_et_al:LIPIcs.FSTTCS.2014.45,
  author =	{Chastain, Erick and Livnat, Adi and Papadimitriou, Christos H. and Vazirani, Umesh V.},
  title =	{{Algorithms, Games, and Evolution}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{45--46},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.45},
  URN =		{urn:nbn:de:0030-drops-48310},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.45},
  annote =	{Keywords: evolution, recombination, coordination games, multiplicative weight updates}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2014.47
The Polynomial Method in Circuit Complexity Applied to Algorithm Design (Invited Talk)

Authors: Richard Ryan Williams

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

Abstract
In circuit complexity, the polynomial method is a general approach to proving circuit lower bounds in restricted settings. One shows that functions computed by sufficiently restricted circuits are "correlated" in some way with a low-complexity polynomial, where complexity may be measured by the degree of the polynomial or the number of monomials. Then, results limiting the capabilities of low-complexity polynomials are extended to the restricted circuits. Old theorems proved by this method have recently found interesting applications to the design of algorithms for basic problems in the theory of computing. This paper surveys some of these applications, and gives a few new ones.
Cite as

Richard Ryan Williams. The Polynomial Method in Circuit Complexity Applied to Algorithm Design (Invited Talk). In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 47-60, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{williams:LIPIcs.FSTTCS.2014.47,
  author =	{Williams, Richard Ryan},
  title =	{{The Polynomial Method in Circuit Complexity Applied to Algorithm Design}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{47--60},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.47},
  URN =		{urn:nbn:de:0030-drops-48328},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.47},
  annote =	{Keywords: algorithm design, circuit complexity, polynomial method}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2014.61
Vertex Exponential Algorithms for Connected f-Factors

Authors: Geevarghese Philip and M. S. Ramanujan

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

Abstract
Given a graph G and a function f:V(G) -> [V(G)], an f-factor is a subgraph H of G such that deg_H(v)=f(v) for every vertex v in V(G); we say that H is a connected f-factor if, in addition, the subgraph H is connected. Tutte (1954) showed that one can check whether a given graph has a specified f-factor in polynomial time. However, detecting a connected f-factor is NP-complete, even when f is a constant function - a foremost example is the problem of checking whether a graph has a Hamiltonian cycle; here f is a function which maps every vertex to 2. The current best algorithm for this latter problem is due to Björklund (FOCS 2010), and runs in randomized O^*(1.657^n) time (the O^*() notation hides polynomial factors). This was the first superpolynomial improvement, in nearly fifty years, over the previous best algorithm of Bellman, Held and Karp (1962) which checks for a Hamiltonian cycle in deterministic O(2^n*n^2) time. In this paper we present the first vertex-exponential algorithms for the more general problem of finding a connected f-factor. Our first result is a randomized algorithm which, given a graph G on n vertices and a function f:V(G) -> [n], checks whether G has a connected f-factor in O^*(2^n) time. We then extend our result to the case when f is a mapping from V(G) to {0,1} and the degree of every vertex v in the subgraph H is required to be f(v)(mod 2). This generalizes the problem of checking whether a graph has an Eulerian subgraph; this is a connected subgraph whose degrees are all even (f(v) equiv 0). Furthermore, we show that the min-cost editing and edge-weighted versions of these problems can be solved in randomized O^*(2^n) time as long as the costs/weights are bounded polynomially in n.
Cite as

Geevarghese Philip and M. S. Ramanujan. Vertex Exponential Algorithms for Connected f-Factors. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 61-71, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{philip_et_al:LIPIcs.FSTTCS.2014.61,
  author =	{Philip, Geevarghese and Ramanujan, M. S.},
  title =	{{Vertex Exponential Algorithms for Connected f-Factors}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{61--71},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.61},
  URN =		{urn:nbn:de:0030-drops-48337},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.61},
  annote =	{Keywords: Exact Exponential Time Algorithms, f-Factors}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2014.73
Connecting Vertices by Independent Trees

Authors: Manu Basavaraju, Fedor V. Fomin, Petr A. Golovach, and Saket Saurabh

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

Abstract
We study the paramereteized complexity of the following connectivity problem. For a vertex subset U of a graph G, trees T_1,...,T_s of G are completely independent spanning trees of U if each of them contains U, and for every two distinct vertices u,v in U, the paths from u to v in T_1,...,T_s are pairwise vertex disjoint except for end-vertices u and v. Then for a given s >= 2 and a parameter k, the task is to decide if a given n-vertex graph G contains a set U of size at least k such that there are s completely independent spanning trees of U. The problem is known to be NP-complete already for s=2. We prove the following results: (*) For s=2 the problem is solvable in time 2^{O(k)}*n^{O(1)}. (*) For s=2 the problem does not admit a polynomial kernel unless NP subseteq coNP/poly. (*) For arbitrary s, we show that the problem is solvable in time f(s,k)n^{O(1)} for some function f of s and k only.
Cite as

Manu Basavaraju, Fedor V. Fomin, Petr A. Golovach, and Saket Saurabh. Connecting Vertices by Independent Trees. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 73-84, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{basavaraju_et_al:LIPIcs.FSTTCS.2014.73,
  author =	{Basavaraju, Manu and Fomin, Fedor V. and Golovach, Petr A. and Saurabh, Saket},
  title =	{{Connecting Vertices by Independent Trees}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{73--84},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.73},
  URN =		{urn:nbn:de:0030-drops-48340},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.73},
  annote =	{Keywords: Parameterized complexity, FPT-algorithms, completely independent spanning trees}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2014.85
Tree Deletion Set Has a Polynomial Kernel (but no OPT^O(1) Approximation)

Authors: Archontia C. Giannopoulou, Daniel Lokshtanov, Saket Saurabh, and Ondrej Suchy

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

Abstract
In the Tree Deletion Set problem the input is a graph G together with an integer k. The objective is to determine whether there exists a set S of at most k vertices such that G \ S is a tree. The problem is NP-complete and even NP-hard to approximate within any factor of OPT^c for any constant c. In this paper we give an O(k^5) size kernel for the Tree Deletion Set problem. An appealing feature of our kernelization algorithm is a new reduction rule, based on system of linear equations, that we use to handle the instances on which Tree Deletion Set is hard to approximate.
Cite as

Archontia C. Giannopoulou, Daniel Lokshtanov, Saket Saurabh, and Ondrej Suchy. Tree Deletion Set Has a Polynomial Kernel (but no OPT^O(1) Approximation). In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 85-96, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{giannopoulou_et_al:LIPIcs.FSTTCS.2014.85,
  author =	{Giannopoulou, Archontia C. and Lokshtanov, Daniel and Saurabh, Saket and Suchy, Ondrej},
  title =	{{Tree Deletion Set Has a Polynomial Kernel (but no OPT^O(1) Approximation)}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{85--96},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.85},
  URN =		{urn:nbn:de:0030-drops-48261},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.85},
  annote =	{Keywords: Tree Deletion Set, Feedback Vertex Set, Kernelization, Linear Equations}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2014.97
Editing to Eulerian Graphs

Authors: Konrad K. Dabrowski, Petr A. Golovach, Pim van 't Hof, and Daniel Paulusma

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

Abstract
We investigate the problem of modifying a graph into a connected graph in which the degree of each vertex satisfies a prescribed parity constraint. Let ea, ed and vd denote the operations edge addition, edge deletion and vertex deletion respectively. For any S subseteq {ea,ed,vd}, we define Connected Degree Parity Editing (S) (CDPE(S)) to be the problem that takes as input a graph G, an integer k and a function delta: V(G) -> {0,1}, and asks whether G can be modified into a connected graph H with d_H(v) = delta(v)(mod 2) for each v in V(H), using at most k operations from S. We prove that (*) if S={ea} or S={ea,ed}, then CDPE(S) can be solved in polynomial time; (*) if {vd} subseteq S subseteq {ea,ed,vd}, then CDPE(S) is NP-complete and W-hard when parameterized by k, even if delta = 0. Together with known results by Cai and Yang and by Cygan, Marx, Pilipczuk, Pilipczuk and Schlotter, our results completely classify the classical and parameterized complexity of the CDPE(S) problem for all S subseteq {ea,ed,vd}. We obtain the same classification for a natural variant of the cdpe(S) problem on directed graphs, where the target is a weakly connected digraph in which the difference between the in- and out-degree of every vertex equals a prescribed value. As an important implication of our results, we obtain polynomial-time algorithms for Eulerian Editing problem and its directed variant. To the best of our knowledge, the only other natural non-trivial graph class H for which the H-Editing problem is known to be polynomial-time solvable is the class of split graphs.
Cite as

Konrad K. Dabrowski, Petr A. Golovach, Pim van 't Hof, and Daniel Paulusma. Editing to Eulerian 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. 97-108, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{dabrowski_et_al:LIPIcs.FSTTCS.2014.97,
  author =	{Dabrowski, Konrad K. and Golovach, Petr A. and van 't Hof, Pim and Paulusma, Daniel},
  title =	{{Editing to Eulerian Graphs}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{97--108},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.97},
  URN =		{urn:nbn:de:0030-drops-48356},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.97},
  annote =	{Keywords: Eulerian graphs, graph editing, polynomial algorithm}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2014.109
Parameterized Complexity of Fixed Variable Logics

Authors: Christoph Berkholz and Michael Elberfeld

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

Abstract
We study the complexity of model checking formulas in first-order logic parameterized by the number of distinct variables in the formula. This problem, which is not known to be fixed-parameter tractable, resisted to be properly classified in the context of parameterized complexity. We show that it is complete for a newly-defined complexity class that we propose as an analog of the classical class PSPACE in parameterized complexity. We support this intuition by the following findings: First, the proposed class admits a definition in terms of alternating Turing machines in a similar way as PSPACE can be defined in terms of polynomial-time alternating machines. Second, we show that parameterized versions of other PSPACE-complete problems, like winning certain pebble games and finding restricted resolution refutations, are complete for this class.
Cite as

Christoph Berkholz and Michael Elberfeld. Parameterized Complexity of Fixed Variable Logics. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 109-120, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{berkholz_et_al:LIPIcs.FSTTCS.2014.109,
  author =	{Berkholz, Christoph and Elberfeld, Michael},
  title =	{{Parameterized Complexity of Fixed Variable Logics}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{109--120},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.109},
  URN =		{urn:nbn:de:0030-drops-48367},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.109},
  annote =	{Keywords: Parameterized complexity, polynomial space, first-order logic, pebble games, regular resolutions}
}
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