4 Search Results for "Segal, Michael"


Document
A Fine-Grained Analogue of Schaefer’s Theorem in P: Dichotomy of Exists^k-Forall-Quantified First-Order Graph Properties

Authors: Karl Bringmann, Nick Fischer, and Marvin Künnemann

Published in: LIPIcs, Volume 137, 34th Computational Complexity Conference (CCC 2019)


Abstract
An important class of problems in logics and database theory is given by fixing a first-order property psi over a relational structure, and considering the model-checking problem for psi. Recently, Gao, Impagliazzo, Kolokolova, and Williams (SODA 2017) identified this class as fundamental for the theory of fine-grained complexity in P, by showing that the (Sparse) Orthogonal Vectors problem is complete for this class under fine-grained reductions. This raises the question whether fine-grained complexity can yield a precise understanding of all first-order model-checking problems. Specifically, can we determine, for any fixed first-order property psi, the exponent of the optimal running time O(m^{c_psi}), where m denotes the number of tuples in the relational structure? Towards answering this question, in this work we give a dichotomy for the class of exists^k-forall-quantified graph properties. For every such property psi, we either give a polynomial-time improvement over the baseline O(m^k)-time algorithm or show that it requires time m^{k-o(1)} under the hypothesis that MAX-3-SAT has no O((2-epsilon)^n)-time algorithm. More precisely, we define a hardness parameter h = H(psi) such that psi can be decided in time O(m^{k-epsilon}) if h <=2 and requires time m^{k-o(1)} for h >= 3 unless the h-uniform HyperClique hypothesis fails. This unveils a natural hardness hierarchy within first-order properties: for any h >= 3, we show that there exists a exists^k-forall-quantified graph property psi with hardness H(psi)=h that is solvable in time O(m^{k-epsilon}) if and only if the h-uniform HyperClique hypothesis fails. Finally, we give more precise upper and lower bounds for an exemplary class of formulas with k=3 and extend our classification to a counting dichotomy.

Cite as

Karl Bringmann, Nick Fischer, and Marvin Künnemann. A Fine-Grained Analogue of Schaefer’s Theorem in P: Dichotomy of Exists^k-Forall-Quantified First-Order Graph Properties. In 34th Computational Complexity Conference (CCC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 137, pp. 31:1-31:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{bringmann_et_al:LIPIcs.CCC.2019.31,
  author =	{Bringmann, Karl and Fischer, Nick and K\"{u}nnemann, Marvin},
  title =	{{A Fine-Grained Analogue of Schaefer’s Theorem in P: Dichotomy of Exists^k-Forall-Quantified First-Order Graph Properties}},
  booktitle =	{34th Computational Complexity Conference (CCC 2019)},
  pages =	{31:1--31:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-116-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{137},
  editor =	{Shpilka, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2019.31},
  URN =		{urn:nbn:de:0030-drops-108533},
  doi =		{10.4230/LIPIcs.CCC.2019.31},
  annote =	{Keywords: Fine-grained Complexity, Hardness in P, Hyperclique Conjecture, Constrained Triangle Detection}
}
Document
The General Universal Property of the Propositional Truncation

Authors: Nicolai Kraus

Published in: LIPIcs, Volume 39, 20th International Conference on Types for Proofs and Programs (TYPES 2014)


Abstract
In a type-theoretic fibration category in the sense of Shulman (representing a dependent type theory with at least unit, sigma, pi, and identity types), we define the type of coherently constant functions from A to B. This involves an infinite tower of coherence conditions, and we therefore need the category to have Reedy limits of diagrams over omega^op. Our main result is that, if the category further has propositional truncations and satisfies function extensionality, the type of coherently constant function is equivalent to the type ||A|| -> B. If B is an n-type for a given finite n, the tower of coherence conditions becomes finite and the requirement of nontrivial Reedy limits vanishes. The whole construction can then be carried out in standard syntactical homotopy type theory and generalises the universal property of the truncation. This provides a way to define functions ||A|| -> B if B is not known to be propositional, and it streamlines the common approach of finding a propositional type Q with A -> Q and Q -> B.

Cite as

Nicolai Kraus. The General Universal Property of the Propositional Truncation. In 20th International Conference on Types for Proofs and Programs (TYPES 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 39, pp. 111-145, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{kraus:LIPIcs.TYPES.2014.111,
  author =	{Kraus, Nicolai},
  title =	{{The General Universal Property of the Propositional Truncation}},
  booktitle =	{20th International Conference on Types for Proofs and Programs (TYPES 2014)},
  pages =	{111--145},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-88-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{39},
  editor =	{Herbelin, Hugo and Letouzey, Pierre and Sozeau, Matthieu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2014.111},
  URN =		{urn:nbn:de:0030-drops-54944},
  doi =		{10.4230/LIPIcs.TYPES.2014.111},
  annote =	{Keywords: coherence conditions, propositional truncation, Reedy limits, universal property, well-behaved constancy}
}
Document
Simplified Lower Bounds on the Multiparty Communication Complexity of Disjointness

Authors: Anup Rao and Amir Yehudayoff

Published in: LIPIcs, Volume 33, 30th Conference on Computational Complexity (CCC 2015)


Abstract
We show that the deterministic number-on-forehead communication complexity of set disjointness for k parties on a universe of size n is Omega(n/4^k). This gives the first lower bound that is linear in n, nearly matching Grolmusz's upper bound of O(log^2(n) + k^2n/2^k). We also simplify the proof of Sherstov's Omega(sqrt(n)/(k2^k)) lower bound for the randomized communication complexity of set disjointness.

Cite as

Anup Rao and Amir Yehudayoff. Simplified Lower Bounds on the Multiparty Communication Complexity of Disjointness. In 30th Conference on Computational Complexity (CCC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 33, pp. 88-101, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{rao_et_al:LIPIcs.CCC.2015.88,
  author =	{Rao, Anup and Yehudayoff, Amir},
  title =	{{Simplified Lower Bounds on the Multiparty Communication Complexity of Disjointness}},
  booktitle =	{30th Conference on Computational Complexity (CCC 2015)},
  pages =	{88--101},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-81-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{33},
  editor =	{Zuckerman, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2015.88},
  URN =		{urn:nbn:de:0030-drops-50769},
  doi =		{10.4230/LIPIcs.CCC.2015.88},
  annote =	{Keywords: communication complexity, set disjointness, number on forehead, lower bounds}
}
Document
Locating Battery Charging Stations to Facilitate Almost Shortest Paths

Authors: Esther M. Arkin, Paz Carmi, Matthew J. Katz, Joseph S. B. Mitchell, and Michael Segal

Published in: OASIcs, Volume 42, 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2014)


Abstract
We study a facility location problem motivated by requirements pertaining to the distribution of charging stations for electric vehicles: Place a minimum number of battery charging stations at a subset of nodes of a network, so that battery-powered electric vehicles will be able to move between destinations using "t-spanning" routes, of lengths within a factor t > 1 of the length of a shortest path, while having sufficient charging stations along the way. We give constant-factor approximation algorithms for minimizing the number of charging stations, subject to the t-spanning constraint. We study two versions of the problem, one in which the stations are required to support a single ride (to a single destination), and one in which the stations are to support multiple rides through a sequence of destinations, where the destinations are revealed one at a time.

Cite as

Esther M. Arkin, Paz Carmi, Matthew J. Katz, Joseph S. B. Mitchell, and Michael Segal. Locating Battery Charging Stations to Facilitate Almost Shortest Paths. In 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 42, pp. 25-33, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2014)


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@InProceedings{arkin_et_al:OASIcs.ATMOS.2014.25,
  author =	{Arkin, Esther M. and Carmi, Paz and Katz, Matthew J. and Mitchell, Joseph S. B. and Segal, Michael},
  title =	{{Locating Battery Charging Stations to Facilitate Almost Shortest Paths}},
  booktitle =	{14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{25--33},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-75-0},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{42},
  editor =	{Funke, Stefan and Mihal\'{a}k, Mat\'{u}s},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2014.25},
  URN =		{urn:nbn:de:0030-drops-47500},
  doi =		{10.4230/OASIcs.ATMOS.2014.25},
  annote =	{Keywords: approximation algorithms; geometric spanners; transportation networks}
}
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