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International Workshop on Combinatorial Algorithms

IWOCA 2013: Combinatorial Algorithms pp 1–6Cite as

Weak Heaps and Friends: Recent Developments

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8288))

Abstract

A weak heap is a variant of a binary heap where, for each node, the heap ordering is enforced only for one of its two children. In 1993, Dutton showed that this data structure yields a simple worst-case-efficient sorting algorithm. In this paper we review the refinements proposed to the basic data structure that improve the efficiency even further. Ultimately, minimum and insert operations are supported in O(1) worst-case time and extract-min operation in \(O(\lg n)\) worst-case time involving at most \(\lg n + O(1)\) element comparisons. In addition, we look at several applications of weak heaps. This encompasses the creation of a sorting index and the use of a weak heap as a tournament tree leading to a sorting algorithm that is close to optimal in terms of the number of element comparisons performed. By supporting insert operation in O(1) amortized time, the weak-heap data structure becomes a valuable tool in adaptive sorting leading to an algorithm that is constant-factor optimal with respect to several measures of disorder. Also, a weak heap can be used as an intermediate step in an efficient construction of binary heaps. For graph search and network optimization, a weak-heap variant, which allows some of the nodes to violate the weak-heap ordering, is known to be provably better than a Fibonacci heap.

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Author information

Authors and Affiliations

  1. Faculty 3—Mathematics and Computer Science, University of Bremen, P.O. Box 330 440, 28334, Bremen, Germany

    Stefan Edelkamp

  2. Department of Computer Engineering and Systems, Alexandria University, Alexandria, 21544, Egypt

    Amr Elmasry

  3. Department of Computer Science, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen East, Denmark

    Jyrki Katajainen

  4. Institute for Formal Methods in Computer Science, University of Stuttgart, Universitätstraße 38, 70569, Stuttgart, Germany

    Armin Weiß

Authors
  1. Stefan Edelkamp
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  2. Amr Elmasry
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  3. Jyrki Katajainen
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  4. Armin Weiß
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Editor information

Editors and Affiliations

  1. UFR des Sciences et Techniques, LITIS, Université de Rouen, 76821, EA 4180, Mont Saint Aignan Cedex, France

    Thierry Lecroq  & Laurent Mouchard  & 

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Edelkamp, S., Elmasry, A., Katajainen, J., Weiß, A. (2013). Weak Heaps and Friends: Recent Developments. In: Lecroq, T., Mouchard, L. (eds) Combinatorial Algorithms. IWOCA 2013. Lecture Notes in Computer Science, vol 8288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45278-9_1

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  • DOI: https://doi.org/10.1007/978-3-642-45278-9_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45277-2

  • Online ISBN: 978-3-642-45278-9

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