Part I Computer Science

BIT Numerical Mathematics

, Volume 28, Issue 4, pp 775-784

First online:

Encroaching lists as a measure of presortedness

  • Steven S. SkienaAffiliated withDepartment of Computer Science, University of Illinois

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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