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DOI: 10.4230/LIPIcs.ICALP.2017.135

Saving Critical Nodes with Firefighters is FPT

Authors: Jayesh Choudhari, Anirban Dasgupta, Neeldhara Misra, and M. S. Ramanujan

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract

We consider the problem of firefighting to save a critical subset of nodes. The firefighting game is a turn-based game played on a graph, where the fire spreads to vertices in a breadth-first manner from a source, and firefighters can be placed on yet unburnt vertices on alternate rounds to block the fire. In this work, we consider the problem of saving a critical subset of nodes from catching fire, given a total budget on the number of firefighters. We show that the problem is para-NP-hard when parameterized by the size of the critical set. We also show that it is fixed-parameter tractable on general graphs when parameterized by the number of firefighters. We also demonstrate improved running times on trees and establish that the problem is unlikely to admit a polynomial kernelization (even when restricted to trees). Our work is the first to exploit the connection between the firefighting problem and the notions of important separators and tight separator sequences. Finally, we consider the spreading model of the firefighting game, a closely related problem, and show that the problem of saving a critical set parameterized by the number of firefighters is W[2]-hard, which contrasts our FPT result for the non-spreading model.

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Jayesh Choudhari, Anirban Dasgupta, Neeldhara Misra, and M. S. Ramanujan. Saving Critical Nodes with Firefighters is FPT. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 135:1-135:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{choudhari_et_al:LIPIcs.ICALP.2017.135,
  author =	{Choudhari, Jayesh and Dasgupta, Anirban and Misra, Neeldhara and Ramanujan, M. S.},
  title =	{{Saving Critical Nodes with Firefighters is FPT}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{135:1--135:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.135},
  URN =		{urn:nbn:de:0030-drops-74968},
  doi =		{10.4230/LIPIcs.ICALP.2017.135},
  annote =	{Keywords: firefighting, cuts, FPT, kernelization}
}

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DOI: 10.4230/LIPIcs.ICDT.2016.6

A Framework for Estimating Stream Expression Cardinalities

Authors: Anirban Dasgupta, Kevin J. Lang, Lee Rhodes, and Justin Thaler

Published in: LIPIcs, Volume 48, 19th International Conference on Database Theory (ICDT 2016)

Abstract

Given m distributed data streams A_1,..., A_m, we consider the problem of estimating the number of unique identifiers in streams defined by set expressions over A_1,..., A_m. We identify a broad class of algorithms for solving this problem, and show that the estimators output by any algorithm in this class are perfectly unbiased and satisfy strong variance bounds. Our analysis unifies and generalizes a variety of earlier results in the literature. To demonstrate its generality, we describe several novel sampling algorithms in our class, and show that they achieve a novel tradeoff between accuracy, space usage, update speed, and applicability.

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Anirban Dasgupta, Kevin J. Lang, Lee Rhodes, and Justin Thaler. A Framework for Estimating Stream Expression Cardinalities. In 19th International Conference on Database Theory (ICDT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 48, pp. 6:1-6:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{dasgupta_et_al:LIPIcs.ICDT.2016.6,
  author =	{Dasgupta, Anirban and Lang, Kevin J. and Rhodes, Lee and Thaler, Justin},
  title =	{{A Framework for Estimating Stream Expression Cardinalities}},
  booktitle =	{19th International Conference on Database Theory (ICDT 2016)},
  pages =	{6:1--6:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-002-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{48},
  editor =	{Martens, Wim and Zeume, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2016.6},
  URN =		{urn:nbn:de:0030-drops-57754},
  doi =		{10.4230/LIPIcs.ICDT.2016.6},
  annote =	{Keywords: sketching, data stream algorithms, mergeability, distinct elements, set operations}
}

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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.604

On Reconstructing a Hidden Permutation

Authors: Flavio Chierichetti, Anirban Dasgupta, Ravi Kumar, and Silvio Lattanzi

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

Abstract

The Mallows model is a classical model for generating noisy perturbations of a hidden permutation, where the magnitude of the perturbations is determined by a single parameter. In this work we consider the following reconstruction problem: given several perturbations of a hidden permutation that are generated according to the Mallows model, each with its own parameter, how to recover the hidden permutation? When the parameters are approximately known and satisfy certain conditions, we obtain a simple algorithm for reconstructing the hidden permutation; we also show that these conditions are nearly inevitable for reconstruction. We then provide an algorithm to estimate the parameters themselves. En route we obtain a precise characterization of the swapping probability in the Mallows model.

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Flavio Chierichetti, Anirban Dasgupta, Ravi Kumar, and Silvio Lattanzi. On Reconstructing a Hidden Permutation. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 604-617, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{chierichetti_et_al:LIPIcs.APPROX-RANDOM.2014.604,
  author =	{Chierichetti, Flavio and Dasgupta, Anirban and Kumar, Ravi and Lattanzi, Silvio},
  title =	{{On Reconstructing a Hidden Permutation}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{604--617},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.604},
  URN =		{urn:nbn:de:0030-drops-47251},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.604},
  annote =	{Keywords: Mallows model; Rank aggregation; Reconstruction}
}

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Saving Critical Nodes with Firefighters is FPT

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A Framework for Estimating Stream Expression Cardinalities

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On Reconstructing a Hidden Permutation

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