2 Search Results for "Lev, Shahar"


Document
Safety, Absoluteness, and Computability

Authors: Arnon Avron, Shahar Lev, and Nissan Levi

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)


Abstract
The semantic notion of dependent safety is a common generalization of the notion of absoluteness used in set theory and the notion of domain independence used in database theory for characterizing safe queries. This notion has been used in previous works to provide a unified theory of constructions and operations as they are used in different branches of mathematics and computer science, including set theory, computability theory, and database theory. In this paper we provide a complete syntactic characterization of general first-order dependent safety. We also show that this syntactic safety relation can be used for characterizing the set of strictly decidable relations on the natural numbers, as well as for characterizing rudimentary set theory and absoluteness of formulas within it.

Cite as

Arnon Avron, Shahar Lev, and Nissan Levi. Safety, Absoluteness, and Computability. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 8:1-8:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{avron_et_al:LIPIcs.CSL.2018.8,
  author =	{Avron, Arnon and Lev, Shahar and Levi, Nissan},
  title =	{{Safety, Absoluteness, and Computability}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{8:1--8:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.8},
  URN =		{urn:nbn:de:0030-drops-96754},
  doi =		{10.4230/LIPIcs.CSL.2018.8},
  annote =	{Keywords: Dependent Safety, Computability, Absoluteness, Decidability, Domain Independence}
}
Document
Improved Local Search for Geometric Hitting Set

Authors: Norbert Bus, Shashwat Garg, Nabil H. Mustafa, and Saurabh Ray

Published in: LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)


Abstract
Over the past several decades there has been steady progress towards the goal of polynomial-time approximation schemes (PTAS) for fundamental geometric combinatorial optimization problems. A foremost example is the geometric hitting set problem: given a set P of points and a set D of geometric objects, compute the minimum-sized subset of P that hits all objects in D. For the case where D is a set of disks in the plane, a PTAS was finally achieved in 2010, with a surprisingly simple algorithm based on local-search. Since then, local-search has turned out to be a powerful algorithmic approach towards achieving good approximation ratios for geometric problems (for geometric independent-set problem, for dominating sets, for the terrain guarding problem and several others). Unfortunately all these algorithms have the same limitation: local search is able to give a PTAS, but with large running times. That leaves open the question of whether a better understanding - both combinatorial and algorithmic - of local search and the problem can give a better approximation ratio in a more reasonable time. In this paper, we investigate this question for hitting sets for disks in the plane. We present tight approximation bounds for (3,2)-local search and give an (8+\epsilon)-approximation algorithm with expected running time ˜O(n^{2.34}); the previous-best result achieving a similar approximation ratio gave a 10-approximation in time O(n^{15}) -- that too just for unit disks. The techniques and ideas generalize to (4,3) local search. Furthermore, as mentioned earlier, local-search has been used for several other geometric optimization problems; for all these problems our results show that (3,2) local search gives an 8-approximation and no better \footnote{This is assuming the use of the standard framework. Improvement of the approximation factor by using additional properties specific to the problem may be possible.}. Similarly (4,3)-local search gives a 5-approximation for all these problems.

Cite as

Norbert Bus, Shashwat Garg, Nabil H. Mustafa, and Saurabh Ray. Improved Local Search for Geometric Hitting Set. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 184-196, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{bus_et_al:LIPIcs.STACS.2015.184,
  author =	{Bus, Norbert and Garg, Shashwat and Mustafa, Nabil H. and Ray, Saurabh},
  title =	{{Improved Local Search for Geometric Hitting Set}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{184--196},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Mayr, Ernst W. and Ollinger, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.184},
  URN =		{urn:nbn:de:0030-drops-49135},
  doi =		{10.4230/LIPIcs.STACS.2015.184},
  annote =	{Keywords: hitting sets, Delaunay triangulation, local search, disks, geometric algorithms}
}
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