Topology of parallel networks and computational complexity (extended abstract)
It is shown that there are such (natural) computing problems that one needs a strongly connected network topology to compute them effectively. For instance, some one-output Boolean function f (corresponding to a deterministic context-free language) requiring exponential number of processors to be computed in polylogarithmic time by unbounded-degree networks with polylogarithmic separators (for instance, trees) is presented. If one restricts the computing model to bounded-degree networks with polylogarithmic separators then f cannot be computed in polylogarithmic time (independently on the number of processors used). The results of this kind are generalized in a trade-off among time, number of processors, separator of the network and the communication complexity of the problem computed. These results are extended also for a probabilistic model of parallel networks.
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- Al86.N. Alon: Eigenvalues and expanders. Combinatorica 6 (1986), 85–95.Google Scholar
- AUY83.A. V. Aho-J. D. Ullman-M. Yanakakis: On notion of information transfer in VLSI circuits. In: Proc. 15th ACM STOC, Assoc. Comput. Mach. 1983, 133–139.Google Scholar
- BS87.A. Broder — E. Shamir: On the second eigenvalue of random regular graphs. In: Proc. 28th Annual Symp. on FOCS, IEEE 1987, 286–294.Google Scholar
- GHW92.X. Gubás, J. Hromkovič, J. Waczulík: A nonlinear lower bound on the practical combinational complexity. In: Proc. STACS '92, Lecture Notes in Computer Science 577, Springer-Verlag 1992, 281–292.Google Scholar
- H88.J. Hromkovič: The advantages of a new approach to defining the communication complexity for VLSI. Theoret. Comput. Sci 57 (1988), 97–111.Google Scholar
- Hr88.J. Hromkovič: Some complexity aspects of VLSI computations. Part 1. A framework for the study of information transfer in VLSI circuits. Comput. Artificial Intelligence 7(3) (1988), 229–252.Google Scholar
- Hr89.J. Hromkovič: Some complexity aspects of VLSI computations. Part 6. Communication complexity. Computers AI 8 (1989), No. 3, 209–225.Google Scholar
- Hr91.J. Hromkovič: Nonlinear lower bounds in the number of processors of circuits with sublinear separators. In: Proc. FCT '91, Lecture Notes on Computer Science 529, Springer-Verlag 1991, 240–247 (also: Information and Computation 95 (1991), 117–128).Google Scholar
- Ku89.G. Kumičáková-Jirásková: Chomsky hierarchy and communication complexity. Inf. Process. Cybern. EIK 25 (1989), No. 4, 157–164.Google Scholar
- PS84.Ch. Papadimitriou-M. Sipser: Communication complexity. J. Comp. Syst. Sci 28 (1984), 260–269.Google Scholar
- Ul84.J. Ullman: Computational Aspects of VLSI. Principles of Computer Science Series. Comput. Sci Press, Rochville, MD 1984.Google Scholar
- Ya81.A.C. Yao: The entropic limitation of VLSI computations. In: Proc. 13th Annual ACM STOC, Assoc. Comput. Math., New York 1981, 308–311.Google Scholar