Lower bounds on the deterministic and quantum communication complexities of hamming-distance problems

Authors:
Andris Ambainis;William Gasarch;Aravind Srinivasan;Andrey Utis
Affiliations:
Dept. of Combinatorics and Optimization and Instuitute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada;Department of Computer Science and University of Maryland Institute for Advanced Computer Studies, University of Maryland at College Park, College Park, MD;Department of Computer Science and University of Maryland Institute for Advanced Computer Studies, University of Maryland at College Park, College Park, MD;Department of Computer Science, University of Maryland at College Park, College Park, MD
Venue:
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Year:
2006

Citing 16
Cited 0

Communication complexity of computing the Hamming distance

SIAM Journal on Computing
Generating functionology

Generating functionology
Efficient Replicated Remote File Comparison

IEEE Transactions on Computers
Private vs. common random bits in communication complexity

Information Processing Letters
Interactive communication: balanced distributions, correlated files, and average-case complexity

SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
On integral zeros of Krawtchouk polynomials

Journal of Combinatorial Theory Series A
Communication complexity

Communication complexity
Communication complexity of document exchange

SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
An Optimal Strategy for Comparing File Copies

IEEE Transactions on Parallel and Distributed Systems
Quantum communication and complexity

Theoretical Computer Science - Natural computing
Secure Multiparty Computation of Approximations

ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
On the power of quantum fingerprinting

Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Las Vegas is better than determinism in VLSI and distributed computing (Extended Abstract)

STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Communication Complexity Lower Bounds by Polynomials

CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Lower Bounds for Quantum Communication Complexity

FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
The communication complexity of the Hamming distance problem

Information Processing Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

Alice and Bob want to know if two strings of length n are almost equal. That is, do they differ on at mosta bits? Let 0≤a≤n–1. We show that any deterministic protocol, as well as any error-free quantum protocol (C* version), for this problem requires at least n–2 bits of communication. We show the same bounds for the problem of determining if two strings differ in exactlya bits. We also prove a lower bound of n/2–1 for error-free Q* quantum protocols. Our results are obtained by employing basic tools from combinatorics and calculus to lower-bound the ranks of the appropriate matrices.