Bernd Halstenberg
ABSTRACT
We compare the communication complexity of discrete functions under different modes of computation, unifying and extending several known models. Protocols can be deterministic, nondeterministic or probabilistic and in the last case the error probability may vary. On the other hand communication can be 1-way, 2-way or as an intermediate stage consist of a fixed number k > 1 of rounds.
The following main results are obtained. A square gap between deterministic and nondeterministic communication complexity is shown for a specific function, which is the maximal possible. This improves the results of [MS 82] and [AUY 83]. For probabilistic 1- and 2-way protocols we prove linear lower bounds for functions that satisfy certain independence conditions, extending the results of [Y 79] and [Y 83]. Further, with more technical effort an exponential gap between deterministic k-round and probabilistic (k - 1)-round communication with fixed error probability is obtained. This generalizes the main result of [DGS 84]. On contrast for arbitrary error probabilities less than 1/2 there is no difference between the complexity of 1- and 2-way protocols, extending results of [PS 84]. Finally we consider communication with fixed message length and uniform probability distributions and give simulations of arbitrary protocols by such uniform ones with little overhead.
- AUY 83.A.V. Aho, J. D. Ullman, M. Yannakakis, "On notions of information transfer in VLSI circuits", Proc. 15th ACM $TOC, 133-139, 1.983 Google Scholar
Digital Library
- DGS 84.P. Duris, Z. Galil, G. Schnitger, "Lower bounds on communication complexity", Proc. 16th ACM $TOC, 81-89, 1984 Google ScholarDigital Library
- HR 87.B. Halstenberg, R. Reischuk, "On different modes of communication", Technical Report TI-1/87, Institut f/Jr Theoretische Informa~ik, Ttt Darmstadt, 1987Google Scholar
- KS 87.B. Kalyanasundaram, G. Schnitger, "The probabilistic communication complexity of set intersection", Proc. 2rid 1EEE Structure in Complexity Theory, 41-49, 1987Google Scholar
- MS 82.K. Mehlhorn, E. M. Schmidt, "Las Vegas is better than determinism in VLSI and distributed computing", Proc. 14th ACM STOC, 330-337, 1982 Google ScholarDigital Library
- PS 84.R. Paturi, J. Simon, "Probabilistic communication complexity", Proc. 25th iEEE FOCS, 118- 126, 1984 see also J. CSS 33, 1986, 106-124 Google ScholarDigital Library
- T 84.P. Tiwari, "Lower bounds on communication complexity in distributed computer networks", Proc. 25th IEEE FOCS, 109-117, 1984 see also J. ACM 34, 1987, 921-938 Google ScholarDigital Library
- Y 79.A.C. Yao, "Some complexity questions related to distributed computing", Proc. 11th ACM STOC, 209-213, 1979 Google ScholarDigital Library
- Y 83.A.C. Yao, "Lower bounds by probabilistic arguments", Proc. 24th iEEE FOCS, 420-428, 1983Google ScholarDigital Library
Index Terms
- On different modes of communication
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