Maximal boasting

We introduce the boasting problem, wherein useful trends in historical ordinal data (rankings) are discovered. Claims of the form "our object was ranked r or better in x of the last t time units," are formalized, and maximal claims (boasts) of this form are defined under two natural partial orders. For the first partial order, we give an efficient and optimal algorithm for finding all such maximal claims. For the second, we apply a classical result from computational geometry to achieve an algorithm whose running time is significantly more efficient than that of a naïve one. Finally, we connect this boasting problem to a novel variation of the problem of finding optimized confidence association rules as originally posed by Fukuda, et al. [2], and give an efficient algorithm for solving a simplification of the new problem.