Abstract
Switching networks of various kinds have come to occupy a prominent position in computer science as well as communication engineering. The classical switching network technology has been spacedivision-multiplex switching, in which each switching function is performed by a spatially separate switching component (such as a crossbar switch). A recent trend in switching network technology has been the advent of time-division-multiplex switching, wherein a single switching component performs the function of many switches at successive moments of time according to a periodic schedule. This technology has the advantage that nearly all of the cost of the network is in inertial memory (such as delay lines), with the cost of switching elements growing much more slowly as a function of the capacity of the network. In order for a classical space-division-multiplex network to be adaptable to time-division-multiplex technology, its interconnection pattern must satisfy stringent requirements. For example, networks based on randomized interconnections (an important tool in determining the asymptotic complexity of optimal networks) are not suitable for time-division-multiplex implementation. Indeed, time-division-multiplex implementations have been presented for only a few of the simplest classical space-division-multiplex constructions, such as rearrangeable connection networks. This paper shows how interconnection patterns based on explicit constructions for expanding graphs can be implemented in time-division-multiplex networks. This provides time-division-multiplex implementations for switching networks that are within constant factors of optimal in memory cost, and that have asymptotically more slowly growing switching costs. These constructions are based on a metaphor involving teams of jugglers whose throwing, catching and passing patterns result in intricate permutations of the balls. This metaphor affords a convenient visualization of time-division-multiplex activities that should be of value in devising networks for a variety of switching tasks.
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M. Ajtai, J. Komlós and E. Szemerédi: Sorting in c log n parallel steps. Combinatorica 3 (1983) 1–19
M. Ajtai, J. Komlós and E. Szemerdi: An O(n log n) sorting network. Proc. ACM Symp. on Theory of Computing 15 (1983) 1–9
S. Arora, T. Leighton and B. Maggs: On-line algorithms for path selection in a nonblocking network. Proc. ACM Symp. on Theory of Computing 22 (1990) 149–158
L. A. Bassalygo and M. S. Pinsker: Complexity of an optimal nonblocking switching network without reconnections. Problems of Inform. Transm. 9 (1974) 64–66
K. E. Batcher: Sorting networks and their applications. Proc. AFIPS Spring Joint Computer Conf. 32 (1968) 307–314
V. E. Beneš: Optimal rearrangeable multistage connecting networks. Bell Sys. Tech. J. 43 (1964) 1641–1656
D. G. Cantor: On non-blocking switching networks. Networks 1 (1971) 367–377
O. Gabber and Z. Galil: Explicit constructions of linear-sized superconcentrators. J. Comp. and System Science 22 (1981) 407–420
H. Inose: Blocking probability in 3-stage time division switching network. J. IECEJ 44 (1961) 935–941
S. Jimbo and A. Maruoka: Expanders obtained from affine transformations. Combinatorica 7 (1987) 343–355
J. Lenfant: Parallel Permutations of Data: A Beneš network control algorithm for frequently used permutations. IEEE Trans. on Computers 27 (1978) 637–647
A. Lubotzky, R. Phillips and P. Sarnak: Ramanujan graphs. Combinatorica 8 (1988) 261–277
M. J. Marcus: Designs for time slot interchangers. Proc. National Electronics Conf. 26 (1970) 812–817
G. A. Margulis: Explicit construction of concentrators. Problems of Inform. Transm. 9 (1974) 71–80
G. A. Margulis: Explicit group-theoretical constructions of combinatorial schemes and their application to the design of expanders and concentrators. Problems of Inform. Transm. 24 (1988) 39–46
M. S. Pinsker: On the complexity of a concentrator. Proc. Internat. Teletraffic Congr. 7 (1973) 318/1–4
N. Pippenger: Telephone switching networks. Proc. AMS Symp. Appl. Math. 26 (1982) 101–133
N. Pippenger: Communication networks. In J. van Leeuwen (ed.), Handbook of Theoretical Computer Science — Volume A: Algorithms and Complexity, Elsevier, Amsterdam, 1990.
N. Pippenger: The blocking probability of spider-web networks. Random Structures and Algorithms 2 (1991) 121–149
N. Pippenger: The asymptotic optimality of spider-web networks. Discr. Appl. Math. 37/38 (1992) 437–450
N. Pippenger: Rearrangeable circuit-switching networks. Proc. Internat. Conf. on Graph Theory, Combinatorics, Algorithms and Applications 7 (1992) (to appear)
N. Pippenger: Self-routing superconcentrators. Proc. ACM Symp. on Theory of Computing 25 (1993) 355–361
S. V. Ramanan, H. F. Jordan and J. R. Sauer: A new time-domain, multistage permutation algorithm. IEEE Trans. Info. Theory 36 (1990) 171–173
L. G. Valiant: Graph-theoretic properties in computational complexity. J. Computer and Sys. Science 13 (1976) 278–285
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© 1994 Springer-Verlag Berlin Heidelberg
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Pippenger, N. (1994). Juggling networks. In: Cosnard, M., Ferreira, A., Peters, J. (eds) Parallel and Distributed Computing Theory and Practice. CFCP 1994. Lecture Notes in Computer Science, vol 805. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58078-6_1
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DOI: https://doi.org/10.1007/3-540-58078-6_1
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