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.
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This work was partially supported by National Science Foundation Grant CCSR-8714565.
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Skiena, S.S. Encroaching lists as a measure of presortedness. BIT 28, 775–784 (1988). https://doi.org/10.1007/BF01954897
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DOI: https://doi.org/10.1007/BF01954897