Two-Dimensional Partitioning Problems

We study the complexity of a class of partitioning problems which arise in storage organization and scheduling. All our problems are variants of the 2-Dimensional Consecutive Sets problem. The 2-Dimensional Consecutive Sets problem is to find for a given set L of strings over an alphabet Z a partition of Z into a sequence of sets such that the characters of each string S in L occur in exactly ISI consecutive sets of the sequence. All our problems are investigated with respect to restrictions concerning the length of the strings in L as well as the size and the number of sets in the partition of the alphabet.