Patent ID: 7523304

Claim:
A computer-implemented method for selecting data to form messages for transmission, the messages being associated with sets of entities, the method comprising: (1) obtaining first computer data representing: (1A) a set U of the entities; (1B) a target set P which is a subset of U; (1C) a set system CS(U), the set system being a set of subsets of U; (1D) a maximum positive number f of free riders to be allowed in constructing an f+-redundant cover CV=CV(f,P) for the target set P, wherein the cover CV(f,P) is to consist of zero or more sets S that are elements of the set system CS(U) such that a union of the sets S comprises the target set P and at most f entities from a set R=U\P, wherein the data to be selected are data pieces associated with the elements of the cover CV; (2) performing a free-rider assignment by designating at least zero and at most f entities of R as free riders, wherein performing the free-rider assignment comprises, for at least one subset v which is an element of the set system CS(U), and for at least one positive number f v ≦f, determining a cost of an f v +-redundant cover of v, wherein a cost of any cover is a non-constant, non-decreasing function of the number of elements in the cover; wherein determining the cost of the f v +-redundant cover of v comprises: (2A) determining disjoint non-empty subsets x 1 , x 2 , . . . which are subsets of v and are elements of the system CS(U); (2B) selecting two or more tuples of numbers (f 1 , f 2 , . . . ) of non-negative integers f 1 , f 2 , . . . , wherein the sum of the numbers in each tuple does not exceed f v , each tuple representing a candidate assignment of at most f i free riders to x i for each i=1, 2, . . . to obtain an f v +-redundant cover of v; (2C) selecting, from said tuples, a tuple for which the corresponding candidate assignment provides an optimality cost of an f v +-redundant cover of v, wherein an optimality cost is a cost having a predefined optimality relation to a minimum cost; wherein the method further comprises, for each set of the f+-redundant cover, using the associated piece of data to generate a message, and transmitting the message.