3 Search Results for "Molina Lovett, Antonio"


Document
Computational Fun with Sturdy and Flimsy Numbers

Authors: Trevor Clokie, Thomas F. Lidbetter, Antonio J. Molina Lovett, Jeffrey Shallit, and Leon Witzman

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)


Abstract
Following Stolarsky, we say that a natural number n is flimsy in base b if some positive multiple of n has smaller digit sum in base b than n does; otherwise it is sturdy . We develop algorithmic methods for the study of sturdy and flimsy numbers. We provide some criteria for determining whether a number is sturdy. Focusing on the case of base b = 2, we study the computational problem of checking whether a given number is sturdy, giving several algorithms for the problem. We find two additional, previously unknown sturdy primes. We develop a method for determining which numbers with a fixed number of 0’s in binary are flimsy. Finally, we develop a method that allows us to estimate the number of k-flimsy numbers with n bits, and we provide explicit results for k = 3 and k = 5. Our results demonstrate the utility (and fun) of creating algorithms for number theory problems, based on methods of automata theory.

Cite as

Trevor Clokie, Thomas F. Lidbetter, Antonio J. Molina Lovett, Jeffrey Shallit, and Leon Witzman. Computational Fun with Sturdy and Flimsy Numbers. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{clokie_et_al:LIPIcs.FUN.2021.10,
  author =	{Clokie, Trevor and Lidbetter, Thomas F. and Molina Lovett, Antonio J. and Shallit, Jeffrey and Witzman, Leon},
  title =	{{Computational Fun with Sturdy and Flimsy Numbers}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{10:1--10:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.10},
  URN =		{urn:nbn:de:0030-drops-127715},
  doi =		{10.4230/LIPIcs.FUN.2021.10},
  annote =	{Keywords: sturdy number, flimsy number, context-free grammar, finite automaton, enumeration}
}
Document
A Simple Algorithm for Minimum Cuts in Near-Linear Time

Authors: Nalin Bhardwaj, Antonio J. Molina Lovett, and Bryce Sandlund

Published in: LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)


Abstract
We consider the minimum cut problem in undirected, weighted graphs. We give a simple algorithm to find a minimum cut that 2-respects (cuts two edges of) a spanning tree T of a graph G. This procedure can be used in place of the complicated subroutine given in Karger’s near-linear time minimum cut algorithm [Karger, 2000]. We give a self-contained version of Karger’s algorithm with the new procedure, which is easy to state and relatively simple to implement. It produces a minimum cut on an m-edge, n-vertex graph in O(m log³ n) time with high probability, matching the complexity of Karger’s approach.

Cite as

Nalin Bhardwaj, Antonio J. Molina Lovett, and Bryce Sandlund. A Simple Algorithm for Minimum Cuts in Near-Linear Time. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{bhardwaj_et_al:LIPIcs.SWAT.2020.12,
  author =	{Bhardwaj, Nalin and Molina Lovett, Antonio J. and Sandlund, Bryce},
  title =	{{A Simple Algorithm for Minimum Cuts in Near-Linear Time}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{12:1--12:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.12},
  URN =		{urn:nbn:de:0030-drops-122594},
  doi =		{10.4230/LIPIcs.SWAT.2020.12},
  annote =	{Keywords: minimum cut, sparsification, near-linear time, packing}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Optimal Regular Expressions for Permutations (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors: Antonio Molina Lovett and Jeffrey Shallit

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)


Abstract
The permutation language P_n consists of all words that are permutations of a fixed alphabet of size n. Using divide-and-conquer, we construct a regular expression R_n that specifies P_n. We then give explicit bounds for the length of R_n, which we find to be 4^{n}n^{-(lg n)/4+Theta(1)}, and use these bounds to show that R_n has minimum size over all regular expressions specifying P_n.

Cite as

Antonio Molina Lovett and Jeffrey Shallit. Optimal Regular Expressions for Permutations (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 121:1-121:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{molinalovett_et_al:LIPIcs.ICALP.2019.121,
  author =	{Molina Lovett, Antonio and Shallit, Jeffrey},
  title =	{{Optimal Regular Expressions for Permutations}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{121:1--121:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.121},
  URN =		{urn:nbn:de:0030-drops-106978},
  doi =		{10.4230/LIPIcs.ICALP.2019.121},
  annote =	{Keywords: regular expressions, lower bounds, divide-and-conquer}
}
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