Optimal algorithms for the interval location problem with range constraints on length and average.

Let A be a sequence of n real numbers, L(1) and L(2) be two integers such that L(1) < or = L(2) , and R(1) and R(2) be two real numbers such that R(1) < or = R(2). An interval of A is feasible if its length is between L(1) and L(2) and its average is between R(1) and R(2). In this paper, we study the following problems: finding all feasible intervals of A, counting all feasible intervals of A, finding a maximum cardinality set of non-overlapping feasible intervals of A, locating a longest feasible interval of A, and locating a shortest feasible interval of A.