3,392 research outputs found
Lower Bounds for Oblivious Near-Neighbor Search
We prove an lower bound on the dynamic
cell-probe complexity of statistically
approximate-near-neighbor search () over the -dimensional
Hamming cube. For the natural setting of , our result
implies an lower bound, which is a quadratic
improvement over the highest (non-oblivious) cell-probe lower bound for
. This is the first super-logarithmic
lower bound for against general (non black-box) data structures.
We also show that any oblivious data structure for
decomposable search problems (like ) can be obliviously dynamized
with overhead in update and query time, strengthening a classic
result of Bentley and Saxe (Algorithmica, 1980).Comment: 28 page
Distributed Connectivity Decomposition
We present time-efficient distributed algorithms for decomposing graphs with
large edge or vertex connectivity into multiple spanning or dominating trees,
respectively. As their primary applications, these decompositions allow us to
achieve information flow with size close to the connectivity by parallelizing
it along the trees. More specifically, our distributed decomposition algorithms
are as follows:
(I) A decomposition of each undirected graph with vertex-connectivity
into (fractionally) vertex-disjoint weighted dominating trees with total weight
, in rounds.
(II) A decomposition of each undirected graph with edge-connectivity
into (fractionally) edge-disjoint weighted spanning trees with total
weight , in
rounds.
We also show round complexity lower bounds of
and
for the above two decompositions,
using techniques of [Das Sarma et al., STOC'11]. Moreover, our
vertex-connectivity decomposition extends to centralized algorithms and
improves the time complexity of [Censor-Hillel et al., SODA'14] from
to near-optimal .
As corollaries, we also get distributed oblivious routing broadcast with
-competitive edge-congestion and -competitive
vertex-congestion. Furthermore, the vertex connectivity decomposition leads to
near-time-optimal -approximation of vertex connectivity: centralized
and distributed . The former moves
toward the 1974 conjecture of Aho, Hopcroft, and Ullman postulating an
centralized exact algorithm while the latter is the first distributed vertex
connectivity approximation
SANNS: Scaling Up Secure Approximate k-Nearest Neighbors Search
The -Nearest Neighbor Search (-NNS) is the backbone of several
cloud-based services such as recommender systems, face recognition, and
database search on text and images. In these services, the client sends the
query to the cloud server and receives the response in which case the query and
response are revealed to the service provider. Such data disclosures are
unacceptable in several scenarios due to the sensitivity of data and/or privacy
laws.
In this paper, we introduce SANNS, a system for secure -NNS that keeps
client's query and the search result confidential. SANNS comprises two
protocols: an optimized linear scan and a protocol based on a novel sublinear
time clustering-based algorithm. We prove the security of both protocols in the
standard semi-honest model. The protocols are built upon several
state-of-the-art cryptographic primitives such as lattice-based additively
homomorphic encryption, distributed oblivious RAM, and garbled circuits. We
provide several contributions to each of these primitives which are applicable
to other secure computation tasks. Both of our protocols rely on a new circuit
for the approximate top- selection from numbers that is built from comparators.
We have implemented our proposed system and performed extensive experimental
results on four datasets in two different computation environments,
demonstrating more than faster response time compared to
optimally implemented protocols from the prior work. Moreover, SANNS is the
first work that scales to the database of 10 million entries, pushing the limit
by more than two orders of magnitude.Comment: 18 pages, to appear at USENIX Security Symposium 202
Geometry-Oblivious FMM for Compressing Dense SPD Matrices
We present GOFMM (geometry-oblivious FMM), a novel method that creates a
hierarchical low-rank approximation, "compression," of an arbitrary dense
symmetric positive definite (SPD) matrix. For many applications, GOFMM enables
an approximate matrix-vector multiplication in or even time,
where is the matrix size. Compression requires storage and work.
In general, our scheme belongs to the family of hierarchical matrix
approximation methods. In particular, it generalizes the fast multipole method
(FMM) to a purely algebraic setting by only requiring the ability to sample
matrix entries. Neither geometric information (i.e., point coordinates) nor
knowledge of how the matrix entries have been generated is required, thus the
term "geometry-oblivious." Also, we introduce a shared-memory parallel scheme
for hierarchical matrix computations that reduces synchronization barriers. We
present results on the Intel Knights Landing and Haswell architectures, and on
the NVIDIA Pascal architecture for a variety of matrices.Comment: 13 pages, accepted by SC'1
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