On multi-partition communication complexity

  • Authors:

  • Pavol uriš;Juraj Hromkovič;Stasys Jukna;Martin Sauerhoff;Georg Schnitger

  • Affiliations:

  • Lehrstuhl für InformatikI, RWTH Aachen, Ahornstraíe 55, 52074 Aachen, Germany;Department of Computer Science, Swiss Federal Institute of Technology ETH Zürich, ETH Zentrum RZ F2, CH-8092 Zurich, Swizterland;Institute for Mathematics and Informatics, Akademijos 4, LT-2600 Vilnius, Lithuania;Fachbereich Informatik, Lehrstuhl 2, Universität Dortmund, 44221 Dortmund, Germany;Fachbereich Informatik, Johann Wolfgang Goethe-Universität Frankfurt, Robert-Mayer-Straíe 11-15, 60054 Frankfurt am Main, Germany

  • Venue:
  • Information and Computation
  • Year:
  • 2004

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Abstract

We study k-partition communication protocols, an extension of the standard two-party best-partition model to k input partitions. The main results are as follows.1.A strong explicit hierarchy on the degree of non-obliviousness is established by proving that, using k+1 partitions instead of k may decrease the communication complexity from @Q(n) to @Q(logk). 2.Certain linear codes are hard for k-partition protocols even when k may be exponentially large (in the input size). On the other hand, one can show that all characteristic functions of linear codes are easy for randomized OBDDs. 3.It is proved that there are subfunctions of the triangle-freeness function and the function @?Clique"3","n that are hard for multi-partition protocols. As an application, strongly exponential lower bounds on the size of nondeterministic read-once branching programs for these functions are obtained, solving an open problem of Razborov [Proceedings of eighth FCT NCS 529, Springer, 1991, pp. 47-60].