Bipartite graphical connecting scheduling in time and space switch fabrics

A method of adding a new connection (c, d) to a time:space:time switch fabric. The fabric has a set I of k input elements, a set M of m switch elements, and a set O of l output elements. Each input element contributes one input to each switch element, and each output element receives one output from each switch element. A state Sm characterizes the switch elements as a set of ordered pairs (i, j), where (i, j) epsilon Sm if and only if the j output element is coupled to the i input element through one of the switch elements. The range of Sm is the set of outputs of Sm such that if j epsilon range(Sm) then (i, j) epsilon Sm for some i epsilon I. The domain of Sm is the set of inputs of Sm such that if i epsilon domain(Sm) then (i, j) epsilon Sm for some j epsilon O.