BIT Numerical Mathematics

, Volume 28, Issue 4, pp 775–784

Encroaching lists as a measure of presortedness

  • Steven S. Skiena
Part I Computer Science


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


AMS category



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
  2. 2.Department of Computer ScienceState University of New YorkStony Brook

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