Generating successive incomplete blocks with each pair of elements in at least one block

This paper examines solutions to the following combinatorial problem: Produce an ordered set of blocks of M elements chosen from N such that (i) any pair of the N elements occurs together in at least one block, and (ii) the total number of element changes in forming each new block from the previous one is minimised. For certain values of N and M, the only known solutions have no known generalisation. However, several general algorithms are described that produce sets of blocks satisfying (i) and either satisfying or nearly satisfying (ii). Other, related, combinatorial problems are outlined; all are relevant to organizing a certain type of data in a computer.