On the Comparison Cost of Partial Orders

Abstract

A great deal of e ort has been directed towards determining the minimumnumber of binary comparisons su cient to produce various partial orders given some partial order For example the sorting problem considers the minimum number of comparisons su cient to construct a total order starting from n elements The merging problem considers the minimum number of comparisons su cient to construct a total order from two total orders The searching problem can be seen as a special case of the merging problem in which one of the total orders is a singleton The selection problem considers the minimum number of comparisons su cient to select the i largest of n elements Little however is known about the minimum number of comparisons su cient to produce an arbitrary partial order In this paper we brie y survey the known results on this problem and we present some rst results on partial orders which can be produced using either restricted types of comparisons or a limited number of comparisons