Some new results on inverse sorting problems

Abstract

In this paper, we consider two types of inverse sorting problems. The first type is an inverse sorting problem under weighted Hamming distance with bound constraints, which can be solved in O(n2) time. The second type is a family of partial inverse sorting problems which we can further divide into two kinds, with free positions and with fixed positions. We show that both types of partial inverse sorting problems can be solved by a combination of a sorting problem and an inverse sorting problem. © Springer-Verlag Berlin Heidelberg 2005.