License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ICALP.2018.81
URN: urn:nbn:de:0030-drops-90858
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Besa, Juan Jose ; Devanny, William E. ; Eppstein, David ; Goodrich, Michael T. ; Johnson, Timothy

Optimally Sorting Evolving Data

LIPIcs-ICALP-2018-81.pdf (0.6 MB)


We give optimal sorting algorithms in the evolving data framework, where an algorithm's input data is changing while the algorithm is executing. In this framework, instead of producing a final output, an algorithm attempts to maintain an output close to the correct output for the current state of the data, repeatedly updating its best estimate of a correct output over time. We show that a simple repeated insertion-sort algorithm can maintain an O(n) Kendall tau distance, with high probability, between a maintained list and an underlying total order of n items in an evolving data model where each comparison is followed by a swap between a random consecutive pair of items in the underlying total order. This result is asymptotically optimal, since there is an Omega(n) lower bound for Kendall tau distance for this problem. Our result closes the gap between this lower bound and the previous best algorithm for this problem, which maintains a Kendall tau distance of O(n log log n) with high probability. It also confirms previous experimental results that suggested that insertion sort tends to perform better than quicksort in practice.

BibTeX - Entry

  author =	{Juan Jose Besa and William E. Devanny and David Eppstein and Michael T. Goodrich and Timothy Johnson},
  title =	{{Optimally Sorting Evolving Data}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{81:1--81:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-90858},
  doi =		{10.4230/LIPIcs.ICALP.2018.81},
  annote =	{Keywords: Sorting, Evolving data, Insertion sort}

Keywords: Sorting, Evolving data, Insertion sort
Collection: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue Date: 2018
Date of publication: 04.07.2018

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