19,625 research outputs found
Improved Quantum Communication Complexity Bounds for Disjointness and Equality
We prove new bounds on the quantum communication complexity of the
disjointness and equality problems. For the case of exact and non-deterministic
protocols we show that these complexities are all equal to n+1, the previous
best lower bound being n/2. We show this by improving a general bound for
non-deterministic protocols of de Wolf. We also give an O(sqrt{n}c^{log^*
n})-qubit bounded-error protocol for disjointness, modifying and improving the
earlier O(sqrt{n}log n) protocol of Buhrman, Cleve, and Wigderson, and prove an
Omega(sqrt{n}) lower bound for a large class of protocols that includes the
BCW-protocol as well as our new protocol.Comment: 11 pages LaTe
Optimal Error Rates for Interactive Coding II: Efficiency and List Decoding
We study coding schemes for error correction in interactive communications.
Such interactive coding schemes simulate any -round interactive protocol
using rounds over an adversarial channel that corrupts up to
transmissions. Important performance measures for a coding scheme are its
maximum tolerable error rate , communication complexity , and
computational complexity.
We give the first coding scheme for the standard setting which performs
optimally in all three measures: Our randomized non-adaptive coding scheme has
a near-linear computational complexity and tolerates any error rate with a linear communication complexity. This improves over
prior results which each performed well in two of these measures.
We also give results for other settings of interest, namely, the first
computationally and communication efficient schemes that tolerate adaptively, if only one party is required to
decode, and if list decoding is allowed. These are the
optimal tolerable error rates for the respective settings. These coding schemes
also have near linear computational and communication complexity.
These results are obtained via two techniques: We give a general black-box
reduction which reduces unique decoding, in various settings, to list decoding.
We also show how to boost the computational and communication efficiency of any
list decoder to become near linear.Comment: preliminary versio
Approximate Two-Party Privacy-Preserving String Matching with Linear Complexity
Consider two parties who want to compare their strings, e.g., genomes, but do
not want to reveal them to each other. We present a system for
privacy-preserving matching of strings, which differs from existing systems by
providing a deterministic approximation instead of an exact distance. It is
efficient (linear complexity), non-interactive and does not involve a third
party which makes it particularly suitable for cloud computing. We extend our
protocol, such that it mitigates iterated differential attacks proposed by
Goodrich. Further an implementation of the system is evaluated and compared
against current privacy-preserving string matching algorithms.Comment: 6 pages, 4 figure
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