Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317) (1999)

Atlanta, Georgia

May 4, 1999 to May 6, 1999

ISSN: 1093-0159

ISBN: 0-7695-0075-7

pp: 7

Stephen J. Ponzio , Integrated Objects

Jaikumar Radhakrishnan , Tata Institute of Fundamental Research

S. Venkatesh , Tata Institute of Fundamental Research

ABSTRACT

We study the k-round two-party communication complexity of pointer chasing problem for fixed k. Damm, Jukna and Sgall showed an upper bound of O(n \log ^{(k-1)} n) for this problem. We prove a matching lower bound; this improves the lower bound of \Omega(n) shown by Nisan and Wigderson. This yields a corresponding improvement in the hierarchy results for bounded-depth monotone circuits.We consider the bit version of this problem, and show upper and lower bounds. This implies that there is an abrupt jump in complexity, from linear to superlinear, when the number of rounds is reduced below k/2. We also consider the s-paths version originally studied by Klauck and obtain upper and lower bounds.The lower bounds are based on arguments using entropy. One of the main contributions of this work is a transfer lemma for distributions with high entropy; this should be of independent interest.

INDEX TERMS

Communication complexity, pointer chasing, entropy

CITATION

J. Radhakrishnan, S. J. Ponzio and S. Venkatesh, "The Communication Complexity of Pointer Chasing Applications of Entropy and Sampling,"

*Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)(CCC)*, Atlanta, Georgia, 1999, pp. 7.

doi:10.1109/CCC.1999.766256

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