BIT Numerical Mathematics

, Volume 28, Issue 4, pp 775–784 | Cite as

Encroaching lists as a measure of presortedness

  • Steven S. Skiena
Part I Computer Science

Abstract

Encroaching lists are a generalization of monotone sequences in permutations. Since ordered permutations contain fewer encroaching lists than random ones, the number of such listsm provides a measure of presortedness with advantages over others in the literature. Experimental and analytic results are presented to cast light on the properties of encroaching lists. Also, we describe a new sorting algorithm,melsort, with complexityO(nlogm). Thus it is linear for well ordered sets and reduces to mergesort andO(nlogn) in the worst case.

CR category

F.2.2 

AMS category

68R05 

Keywords

sorting presortedness encroaching lists melsort permutations 

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Copyright information

© BIT Foundations 1988

Authors and Affiliations

  • Steven S. Skiena
    • 1
  1. 1.Department of Computer ScienceUniversity of IllinoisUrbanaUSA

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