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An Upper Bound for Sorting \(R_n\) with LE

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Advances in Computing and Data Sciences (ICACDS 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1046))

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Abstract

A permutation on a given alphabet \(\varSigma = (1, 2, 3,\ldots , n)\) is a sequence of elements in the alphabet where every element occurs precisely once. \(S_n\) denotes the set of all such permutations on a given alphabet. \(I_n \in S_n\) be the Identity permutation where elements are in ascending order i.e. \((1, 2, 3,\ldots , n)\). \(R_n \in S_n\) is the reverse permutation where elements are in descending order, i.e. \(R_n =(n, n-1, n-2,\ldots , 2, 1)\). An operation has been defined in OEIS which consists of exactly two moves: set-rotate that we call Rotate and pair-exchange that we call Exchange. Rotate is a left rotate of all elements (moves leftmost element to the right end) and Exchange is the pair-wise exchange of the two leftmost elements. We call this operation as LE. The optimum number of moves for transforming \(R_n\) into \(I_n\) with LE operation are known for \(n \le 10\); as listed in OEIS with identity A048200. The contributions of this article are: (a) a novel upper bound for the number of moves required to sort \(R_n\) with LE has been derived; (b) the optimum number of moves to sort the next larger \(R_n\) i.e. \(R_{11}\) has been computed. Sorting permutations with various operations has applications in genomics and computer interconnection networks.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Amrita Vishwa Vidyapeetham, Amritapuri, India

    Sai Satwik Kuppili, Bhadrachalam Chitturi & T. Srinath

  2. Department of CS, University of Texas at Dallas, Richardson, Texas, USA

    Bhadrachalam Chitturi

Authors
  1. Sai Satwik Kuppili
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  2. Bhadrachalam Chitturi
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  3. T. Srinath
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Correspondence to Bhadrachalam Chitturi .

Editor information

Editors and Affiliations

  1. University of KwaZulu-Natal, Durban, South Africa

    Mayank Singh

  2. Computer Science and Engineering, Jaypee Institute of Information Technology, Waknaghat, Himachal Pradesh, India

    P.K. Gupta

  3. Department of Computer Science and Engineering, Jaypee University of Engineering and Technology, Guna, Madhya Pradesh, India

    Vipin Tyagi

  4. ÚTIA AV ČR, Institute of Information Theory and Automation, Prague 8, Praha, Czech Republic

    Jan Flusser

  5. School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, ON, Canada

    Tuncer Ören

  6. CSE Department, Inderprastha Engineering College, Ghaziabad, Uttar Pradesh, India

    Rekha Kashyap

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Kuppili, S.S., Chitturi, B., Srinath, T. (2019). An Upper Bound for Sorting \(R_n\) with LE. In: Singh, M., Gupta, P., Tyagi, V., Flusser, J., Ören, T., Kashyap, R. (eds) Advances in Computing and Data Sciences. ICACDS 2019. Communications in Computer and Information Science, vol 1046. Springer, Singapore. https://doi.org/10.1007/978-981-13-9942-8_23

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  • DOI: https://doi.org/10.1007/978-981-13-9942-8_23

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-9941-1

  • Online ISBN: 978-981-13-9942-8

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