New type of coding problem motivated by database theory ?
The present paper is intended to survey the interaction between relational database theory and coding theory. In particular it is shown how an extremal problem for relational databases gives rise to a new type of coding problem. The former concerns minimal representation of branching dependencies that can be considered as a data mining type question. The extremal configurations involve d-distance sets  in the space of disjoint pairs of k k -element subsets of an n n -element set X X . Let X X be an n n -element finite set, 0<k<n/2 0 < k < n / 2 an integer. Suppose that {A1,B1} { A 1 , B 1 } and {A2,B2} { A 2 , B 2 } are pairs of disjoint k k -element subsets of X X (that is, | A 1 | = | B 1 | = | A 2 | = | B 2 | = k , A 1 ? B 1 = ? , A 2 ? B 2 = ? ). Define the distance of these pairs by d ( { A 1 , B 1 } , { A 2 , B 2 } ) = min { | A 1 - A 2 | + | B 1 - B 2 | , | A 1 - B 2 | + | B 1 - A 2 | } .
68p15 68r05 05d05