Log-space polynomial end-to-end communication

Communication between processors is the essence of distributed computing: clearly, without communication, distributed computation is impossible. However, as networks become larger and larger, the frequency of link failures increases. The end-to-end communication problem asks how to eciently carry out fault-free communication between two processors over a network, in spite of such frequent link failures. The sole minimum assumption is that the two processors that are trying to communicate are not permanently disconnected (i.e., the communication should proceed even when there does not (ever) simultaneously exist an operational path between the two processors that are trying to communicate). We present a protocol to solve the end-to-end problem with logarithmic-space and polynomial communication at the same time. This is an exponential memory improvement to all previous polynomial communication solutions. That is, all previous polynomial communication solutions needed at least linear (in n, the size of the network) amount of memory per link. Our protocol transfers packets over the network, maintains a simple-to-compute O(logn)-bits potential function at each link in order to perform routing, and uses a novel technique of packet canceling which allows us to keep only one packet per link. The computations of both our potential function and our packet-canceling policy are totally local in nature.