On the dynamic initialization of parallel computers

The incremental and dynamic construction of interconnection networks from smaller components often leaves the fundamental problem of assigning addresses to processors to be contended with at power-up time. The problem-called the initialization problem-is fundamental, for virtually all parallel algorithms assume that the processors know their global coordinates within the newly created entity. Rather surprisingly, the initialization problem has not received the attention it deserves. Our main contribution is to present parallel algorithms for the initialization problem on a number of network topologies, including complete binary trees, meshes of trees, pyramids, linear arrays, rings, meshes, tori, higher-dimensional meshes and tori, hypercubes, butterflies, linear arrays with a global bus, rings with a global bus and meshes with multiple broadcasting, under various assumptions about edge labels, leader existence and a priori knowledge of the number of nodes in the network.