Abstract: The communications network includes a plurality of interconnected nodes and communication links between nodes. Computing apparatus in provided for determining a shortest path from a starting node to a destination node. The computing apparatus is adapted so that each node forms a routing tree having nodes with indentities, branches with weights, and a distinguished node called a root. The routing tree is the estimated shortest path to all of the nodes and each node communicates its routing tree to each adjacent node. Upon receipt of a routing tree by a reference node from an adjacent node, the reference node stores the routing tree and produces a large tree having roots and branches by placing the reference node as the root of the large tree and creating branches from the reference node to the roots of the routing trees of the adjacent nodes. The lengths of the branches are equal to the lengths of the links from the reference node to the adjacent nodes.

Abstract: Data flow in a communications network is controlled by a downstream node specifying the maximum average speeds of a plurality of data streams sent from an upstream node on a plurality of data paths.

Abstract: A stream of source characters, which occur with varying relative frequencies, is encoded into a compressed stream of codewords, each having one, two or three subwords, by ranking the source characters by their current frequency of appearance, encoding the source characters having ranks no higher than a first number as one sub-word codewords, source characters having ranks higher than the first number but no higher than a second number as two sub-word codewords, and the remaining source characters as three sub-word codewords. The first number is changed and the second number is recalculated as required by the changing frequencies of the source characters to minimize the length of the stream of codewords.