A Lower Bound for Nearly Minimal Adaptive and Hot Potato Algorithms

Recently, Chinn et al. [10] presented lower bounds for store-and-forward permutation routing algorithms on the n \times n mesh with bounded buffer size and where a packet must take a shortest (or minimal ) path to its destination. We extend their analysis to algorithms that are nearly minimal. We also apply this technique to the domain of hot potato algorithms, where there is no storage of packets and the shortest path to a destination is not assumed (and is in general impossible). We show that ``natural'' variants and ``improvements'' of several algorithms in the literature perform poorly in the worst case. As a result, we identify algorithmic features that are undesirable for worst-case hot potato permutation routing.

[1]  P. Baran,et al.  On Distributed Communications Networks , 1964 .

[2]  Rene L. Cruz,et al.  Bounds on Maximum Delay in Networks with Deflection Routing , 1995, IEEE Trans. Parallel Distributed Syst..

[3]  Satish Rao,et al.  Hot-potato routing on processor arrays , 1993, ACM Symposium on Parallelism in Algorithms and Architectures.

[4]  Anthony S. Acampora,et al.  Multihop lightwave networks: a comparison of store-and-forward and hot-potato routing , 1992, IEEE Trans. Commun..

[5]  Charles L. Seitz,et al.  A framework for adaptive routing in multicomputer networks , 1989, CARN.

[6]  Heiko Schröder,et al.  Fast Deterministic Hot-Potato Routing on Processor Arrays , 1994, ISAAC.

[7]  Frank Thomson Leighton,et al.  Minimal Adaptive Routing on the Mesh with Bounded Queue Size , 1996, J. Parallel Distributed Comput..

[8]  Uriel Feige,et al.  Observations on hot potato routing , 1995, Proceedings Third Israel Symposium on the Theory of Computing and Systems.

[9]  Nicholas F. Maxemchuk,et al.  Comparison of deflection and store-and-forward techniques in the Manhattan Street and Shuffle-Exchange Networks , 1989, IEEE INFOCOM '89, Proceedings of the Eighth Annual Joint Conference of the IEEE Computer and Communications Societies.

[10]  Leslie G. Valiant,et al.  Optimality of a Two-Phase Strategy for Routing in Interconnection Networks , 1983, IEEE Transactions on Computers.

[11]  Allan Borodin,et al.  Routing, Merging, and Sorting on Parallel Models of Computation , 1985, J. Comput. Syst. Sci..

[12]  Assaf Schuster,et al.  Randomized Single-Target Hot-Potato Routing , 1997, J. Algorithms.

[13]  Assaf Schuster,et al.  Hot-Potato Algorithms for Permutation Routing , 1995, IEEE Trans. Parallel Distributed Syst..

[14]  Albert G. Greenberg,et al.  Deflection routing in hypercube networks , 1992, IEEE Trans. Commun..

[15]  Burton J. Smith.  Architecture And Applications Of The HEP Multiprocessor Computer System , 1982, Optics & Photonics.

[16]  J. Y. Ngai,et al.  A framework for adaptive routing in multicomputer networks , 1989, CARN.

[17]  Zhensheng Zhang,et al.  Performance analysis of multihop lightwave networks with hot potato routing and distance-age-priorities , 1991, IEEE INFCOM '91. The conference on Computer Communications. Tenth Annual Joint Comference of the IEEE Computer and Communications Societies Proceedings.

[18]  Baruch Schieber,et al.  Fast deflection routing for packets and worms , 1993, PODC '93.

[19]  Uriel Feige,et al.  Exact analysis of hot-potato routing , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[20]  Allan Borodin,et al.  Deterministic Many-to-Many Hot Potato Routing , 1997, IEEE Trans. Parallel Distributed Syst..

[21]  Ted H. Szymanski.  An analysis of 'hot-potato' routing in a fiber optic packet switched hypercube , 1990, Proceedings. IEEE INFOCOM '90: Ninth Annual Joint Conference of the IEEE Computer and Communications Societies@m_The Multiple Facets of Integration.