Deterministic Many-to-Many Hot Potato Routing

We consider algorithms for many-to-many hot potato routing. In hot potato (deflection) routing a packet cannot be buffered, and is therefore always moving until it reaches its destination. We give optimal and nearly optimal deterministic algorithms for many-tomany packet routing in commonly occurring networks such as the hypercube, meshes and tori of various dimensions and sizes, trees and hypercubic networks such as the butterfly. All these algorithms are analyzed using a charging scheme that may be applicable to other algorithms as well. Moreover, all bounds hold in a dynamic setting in which packets can be injected at arbitrary times. ∗Dept. of Computer Science, University of Toronto, Toronto, Canada. This work was done while this author visited the Departments of Computer Science at The Hebrew University, Jerusalem and The Weizmann Institute of Science, Rehovot, Israel. E-mail: [email protected] †Most of this work was done while this author was at the Lab. for Computer Science, MIT, Cambridge, MA, supported by ARPA/Army contract DABT63-93-C-0038, and at the Dept. of Computer Science, University of Toronto, Toronto, Canada. Present address: Computer Science Dept., The Technion, Haifa 32000, Israel. Work at the Technion supported by a David and Ruth Moskowitz academic lecturship award, and by a grant from the fund for the promotion of sponsored research at the Technion. E-mail: [email protected], URL: http://www.cs.technion.ac.il/~rabani/ ‡IBM T.J. Watson Research Center, Yorktown, NY. E-mail: [email protected]