Mesh-Connected Computers with Broadcasting

We consider the effects of augmenting an arbitrary mesh-connected computer with a second communication system called broadcasting. In broadcasting, a processor sends a value to all the other processors simultaneously, taking unit time, with the restriction that only one broadcast occurs at any one time. We show that this significantly decreases the time to do sample problems such as semigroup calculations or finding the median, but it cannot significantly improve sorting. For example, in a one-dimensional mesh-connected computer without broadcasting, if there are n numbers, each stored separately in consecutive processors, then θ(n) time is needed to find their minimum, find their median, or sort them, while with broadcasting, this can be done in θ(n
^1/2
), θ((n log n)
^1/2
), and θ(n) time, respectively.