A cross-bifix-free set of words is a set in which no prefix of any length of any word is the suffix of any other word in the set. A construction of cross-bifix-free sets has recently been proposed in Cheeet al.(2013) within a constant factor of optimality. We propose a Gray code for these cross-bifix-free sets and a CAT algorithm generating it. Our Gray code list is trace partitioned, that is, words with zero in the same positions are consecutive in the list.

In this paper we study the enumeration and the construction of particular binary words avoiding the pattern 1j+1 0j . By means of the theory of Riordan arrays, we solve the enumeration problem and we give a particular succession rule, called jumping

Cross-bifix-free sets are sets of words such that no prefix of any word is a suffix of any other word. In this paper, we introduce a general constructive method for the sets of cross-bifix-free binary words of fixed length. It enables us to determine a cross-bifix-free words subset which has the property to be non-expandable.

When planning a database, the problem of index selection is of particular interest. The authors examine a transaction model that includes queries, updates, insertions, and deletions, and they define a function that calculates the transaction's total cost when an index set is used. Their aim is to minimize the function cost in order to identify the optimal set. The algorithms proposed in other studies require an exponential time in the number of attributes in order to solve the problem. The authors propose a heuristic algorithm based on some properties of the cost function that produces an almost optimal set in polynomial time. In many cases, the cost function properties make it possible to prove that the solution obtained is the optimal one.>