Affiliation:
1. Nanjing University, China, Xianlin Ave., Nanjing, Jiangsu, China
Abstract
We study the complexity of parallel data structures for approximate nearest neighbor search in
d
-dimensional Hamming space {0,1}
d
. A classic model for static data structures is the cell-probe model [27]. We consider a cell-probe model with limited
adaptivity
, where given a
k
≥1, a query is resolved by making at most
k
rounds of parallel memory accesses to the data structure. We give two randomized algorithms that solve the approximate nearest neighbor search using
k
rounds of parallel memory accesses:
—a simple algorithm with
O
(
k
(log
d
)
1/
k
) total number of memory accesses for all
k
≥1;
—an algorithm with
O
(
k
+(1/
k
log
d
)
O
(1/
k
)
) total number of memory accesses for all sufficiently large
k
.
Both algorithms use data structures of polynomial size.
We prove an Ω(1/
k
(log
d
)
1/
k
) lower bound for the total number of memory accesses for any randomized algorithm solving the approximate nearest neighbor search within
k
≤log log
d
/2log log log
d
rounds of parallel memory accesses on any data structures of polynomial size. This lower bound shows that our first algorithm is asymptotically optimal when
k
=
O
(1). And our second algorithm achieves the asymptotically optimal tradeoff between number of rounds and total number of memory accesses. In the extremal case, when
k
=
O
(log log
d
/log log log
d
) is big enough, our second algorithm matches the Θ(log log
d
/log log log
d
) tight bound for fully adaptive algorithms for approximate nearest neighbor search in [11].
Funder
National Natural Science Foundation of China
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Theory and Mathematics,Computer Science Applications,Hardware and Architecture,Modelling and Simulation,Software
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献