21,520 research outputs found
XOR-Sampling for Network Design with Correlated Stochastic Events
Many network optimization problems can be formulated as stochastic network
design problems in which edges are present or absent stochastically.
Furthermore, protective actions can guarantee that edges will remain present.
We consider the problem of finding the optimal protection strategy under a
budget limit in order to maximize some connectivity measurements of the
network. Previous approaches rely on the assumption that edges are independent.
In this paper, we consider a more realistic setting where multiple edges are
not independent due to natural disasters or regional events that make the
states of multiple edges stochastically correlated. We use Markov Random Fields
to model the correlation and define a new stochastic network design framework.
We provide a novel algorithm based on Sample Average Approximation (SAA)
coupled with a Gibbs or XOR sampler. The experimental results on real road
network data show that the policies produced by SAA with the XOR sampler have
higher quality and lower variance compared to SAA with Gibbs sampler.Comment: In Proceedings of the Twenty-sixth International Joint Conference on
Artificial Intelligence (IJCAI-17). The first two authors contribute equall
Faster Clustering via Preprocessing
We examine the efficiency of clustering a set of points, when the
encompassing metric space may be preprocessed in advance. In computational
problems of this genre, there is a first stage of preprocessing, whose input is
a collection of points ; the next stage receives as input a query set
, and should report a clustering of according to some
objective, such as 1-median, in which case the answer is a point
minimizing .
We design fast algorithms that approximately solve such problems under
standard clustering objectives like -center and -median, when the metric
has low doubling dimension. By leveraging the preprocessing stage, our
algorithms achieve query time that is near-linear in the query size ,
and is (almost) independent of the total number of points .Comment: 24 page
Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable
There has been significant recent interest in parallel graph processing due
to the need to quickly analyze the large graphs available today. Many graph
codes have been designed for distributed memory or external memory. However,
today even the largest publicly-available real-world graph (the Hyperlink Web
graph with over 3.5 billion vertices and 128 billion edges) can fit in the
memory of a single commodity multicore server. Nevertheless, most experimental
work in the literature report results on much smaller graphs, and the ones for
the Hyperlink graph use distributed or external memory. Therefore, it is
natural to ask whether we can efficiently solve a broad class of graph problems
on this graph in memory.
This paper shows that theoretically-efficient parallel graph algorithms can
scale to the largest publicly-available graphs using a single machine with a
terabyte of RAM, processing them in minutes. We give implementations of
theoretically-efficient parallel algorithms for 20 important graph problems. We
also present the optimizations and techniques that we used in our
implementations, which were crucial in enabling us to process these large
graphs quickly. We show that the running times of our implementations
outperform existing state-of-the-art implementations on the largest real-world
graphs. For many of the problems that we consider, this is the first time they
have been solved on graphs at this scale. We have made the implementations
developed in this work publicly-available as the Graph-Based Benchmark Suite
(GBBS).Comment: This is the full version of the paper appearing in the ACM Symposium
on Parallelism in Algorithms and Architectures (SPAA), 201
The -Center Problem in Tree Networks Revisited
We present two improved algorithms for weighted discrete -center problem
for tree networks with vertices. One of our proposed algorithms runs in
time. For all values of , our algorithm
thus runs as fast as or faster than the most efficient time
algorithm obtained by applying Cole's speed-up technique [cole1987] to the
algorithm due to Megiddo and Tamir [megiddo1983], which has remained
unchallenged for nearly 30 years. Our other algorithm, which is more practical,
runs in time, and when it is
faster than Megiddo and Tamir's time algorithm
[megiddo1983]
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