Time and Bit Optimal Broadcasting on Anonymous Unoriented Hypercubes

We consider broadcasting on asynchronous anonymous totally unoriented N node hypercubes. First we generalize a technique, introduced in [3], for partial broadcasting and orientation. Using this technique we develop a broadcasting algorithm on unoriented hypercubes that uses only linear number of bits and runs in optimal time. This gives a positive answer to the question raised in [7] whether O(N) bits are su cient for broadcasting on unoriented N -node hypercubes. It is also an improvement over the previous algorithms from [3, 1] both in time and bit complexities. As an application of broadcasting, we develop an algorithm for computing identities of all nodes in unoriented hypercubes with linear number of messages. (The question was stated in [7]). This allows every subset of nodes (such as covers, independent sets, etc) to be determined in O(N) messages.