Bipartite graphical connection 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) epsi Sm if and only if the jth output element is coupled to the ith input element through one of the switch elements. The range of Sm is the set of outputs of Sm such that if j epsi range(Sm) then (i, j) epsi Sm for some i epsiI. The domain of Sm is the set of inputs of Sm such that if i epsi domain(Sm) then (i, j) epsi Sm for some j epsi O. If a switch state Sm exists where c ∉ domain(Sm) and d ∉ range(Sm), then the new connection is added to Sm as (c, d). If no such state exists, and if no switch state Sm exists wherein c ∉ domain(Sm), then the method terminates because c is fully allocated. If there is a switch state Sm wherein c ∉ domain(Sm), and if no switch state Sn exists wherein d ∉ range(Sn), then the method terminates because d is fully allocated. If such a state Sn exists, the two states Sm, Sn are joined to form a union J with each element (i', j') in J labelled u if (i', j') epsi Sm, and each element (i', j') in J labelled v if (i', j') epsi Sn. The new connection is then added to J as (c, d). A label (u or v) is allocated to the new connection. If new connection's label has not previously been allocated to a connection (i', d) epsi J the method terminates. Otherwise, the opposite label (v or u) is reallocated to connection (i', d) epsi J. If such opposite label has not previously been allocated to a connection (i', j') epsi J the method terminates. Otherwise, the originally selected label (u or v) is reallocated to connection (i', j') epsi J and the process repeats until no label conflicts remain. The originally selected label (u or v) is chosen to minimize the number of connections requiring reallocation of labels.