3 Search Results for "Compton, Spencer"

Document
DOI: 10.4230/LIPIcs.CSL.2025.12
First-Order Logic with Equicardinality in Random Graphs

Authors: Simi Haber, Tal Hershko, Mostafa Mirabi, and Saharon Shelah

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
We answer a question of Blass and Harary about the validity of the zero-one law in random graphs for extensions of first-order logic (FOL). For a given graph property P, the Lindström extension of FOL by P is defined as the minimal (regular) extension of FOL able to express P. For several graph properties P (e.g. Hamiltonicity), it is known that the Lindström extension by P is also able to interpret a segment of arithmetic, and thus strongly disobeys the zero-one law. Common to all these properties is the ability to express the Härtig quantifier, a natural extension of FOL testing if two definable sets are of the same size. We prove that the Härtig quantifier is sufficient for the interpretation of arithmetic, thus providing a general result which implies all known cases of Lindström extensions which are able to interpret a segment of arithmetic.
Cite as

Simi Haber, Tal Hershko, Mostafa Mirabi, and Saharon Shelah. First-Order Logic with Equicardinality in Random Graphs. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{haber_et_al:LIPIcs.CSL.2025.12,
  author =	{Haber, Simi and Hershko, Tal and Mirabi, Mostafa and Shelah, Saharon},
  title =	{{First-Order Logic with Equicardinality in Random Graphs}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.12},
  URN =		{urn:nbn:de:0030-drops-227694},
  doi =		{10.4230/LIPIcs.CSL.2025.12},
  annote =	{Keywords: finite model theory, first-order logic, monadic second-order logic, random graphs, zero-one laws, generalized quantifiers, equicardinality}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.45
New Partitioning Techniques and Faster Algorithms for Approximate Interval Scheduling

Authors: Spencer Compton, Slobodan Mitrović, and Ronitt Rubinfeld

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
Interval scheduling is a basic problem in the theory of algorithms and a classical task in combinatorial optimization. We develop a set of techniques for partitioning and grouping jobs based on their starting and ending times, that enable us to view an instance of interval scheduling on many jobs as a union of multiple interval scheduling instances, each containing only a few jobs. Instantiating these techniques in dynamic and local settings of computation leads to several new results. For (1+ε)-approximation of job scheduling of n jobs on a single machine, we develop a fully dynamic algorithm with O((log n)/ε) update and O(log n) query worst-case time. Further, we design a local computation algorithm that uses only O((log N)/ε) queries when all jobs are length at least 1 and have starting/ending times within [0,N]. Our techniques are also applicable in a setting where jobs have rewards/weights. For this case we design a fully dynamic deterministic algorithm whose worst-case update and query time are poly(log n,1/ε). Equivalently, this is the first algorithm that maintains a (1+ε)-approximation of the maximum independent set of a collection of weighted intervals in poly(log n,1/ε) time updates/queries. This is an exponential improvement in 1/ε over the running time of a randomized algorithm of Henzinger, Neumann, and Wiese [SoCG, 2020], while also removing all dependence on the values of the jobs' starting/ending times and rewards, as well as removing the need for any randomness. We also extend our approaches for interval scheduling on a single machine to examine the setting with M machines.
Cite as

Spencer Compton, Slobodan Mitrović, and Ronitt Rubinfeld. New Partitioning Techniques and Faster Algorithms for Approximate Interval Scheduling. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 45:1-45:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{compton_et_al:LIPIcs.ICALP.2023.45,
  author =	{Compton, Spencer and Mitrovi\'{c}, Slobodan and Rubinfeld, Ronitt},
  title =	{{New Partitioning Techniques and Faster Algorithms for Approximate Interval Scheduling}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{45:1--45:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.45},
  URN =		{urn:nbn:de:0030-drops-180978},
  doi =		{10.4230/LIPIcs.ICALP.2023.45},
  annote =	{Keywords: interval scheduling, dynamic algorithms, local computation algorithms}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.54
New Approximation Algorithms for Touring Regions

Authors: Benjamin Qi and Richard Qi

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
We analyze the touring regions problem: find a (1+ε)-approximate Euclidean shortest path in d-dimensional space that starts at a given starting point, ends at a given ending point, and visits given regions R₁, R₂, R₃, … , R_n in that order. Our main result is an O (n/√ε log{1/ε} + 1/ε)-time algorithm for touring disjoint disks. We also give an O(min(n/ε, n²/√ε))-time algorithm for touring disjoint two-dimensional convex fat bodies. Both of these results naturally generalize to larger dimensions; we obtain O(n/{ε^{d-1}} log²1/ε + 1/ε^{2d-2}) and O(n/ε^{2d-2})-time algorithms for touring disjoint d-dimensional balls and convex fat bodies, respectively.
Cite as

Benjamin Qi and Richard Qi. New Approximation Algorithms for Touring Regions. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 54:1-54:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{qi_et_al:LIPIcs.SoCG.2023.54,
  author =	{Qi, Benjamin and Qi, Richard},
  title =	{{New Approximation Algorithms for Touring Regions}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{54:1--54:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.54},
  URN =		{urn:nbn:de:0030-drops-179047},
  doi =		{10.4230/LIPIcs.SoCG.2023.54},
  annote =	{Keywords: shortest paths, convex bodies, fat objects, disks}
}
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