40,357 research outputs found
Learning to Prune: Speeding up Repeated Computations
It is common to encounter situations where one must solve a sequence of
similar computational problems. Running a standard algorithm with worst-case
runtime guarantees on each instance will fail to take advantage of valuable
structure shared across the problem instances. For example, when a commuter
drives from work to home, there are typically only a handful of routes that
will ever be the shortest path. A naive algorithm that does not exploit this
common structure may spend most of its time checking roads that will never be
in the shortest path. More generally, we can often ignore large swaths of the
search space that will likely never contain an optimal solution.
We present an algorithm that learns to maximally prune the search space on
repeated computations, thereby reducing runtime while provably outputting the
correct solution each period with high probability. Our algorithm employs a
simple explore-exploit technique resembling those used in online algorithms,
though our setting is quite different. We prove that, with respect to our model
of pruning search spaces, our approach is optimal up to constant factors.
Finally, we illustrate the applicability of our model and algorithm to three
classic problems: shortest-path routing, string search, and linear programming.
We present experiments confirming that our simple algorithm is effective at
significantly reducing the runtime of solving repeated computations
Solving Hard Control Problems in Voting Systems via Integer Programming
Voting problems are central in the area of social choice. In this article, we
investigate various voting systems and types of control of elections. We
present integer linear programming (ILP) formulations for a wide range of
NP-hard control problems. Our ILP formulations are flexible in the sense that
they can work with an arbitrary number of candidates and voters. Using the
off-the-shelf solver Cplex, we show that our approaches can manipulate
elections with a large number of voters and candidates efficiently
Developments in GRworkbench
The software tool GRworkbench is an ongoing project in visual, numerical
General Relativity at The Australian National University. Recently, GRworkbench
has been significantly extended to facilitate numerical experimentation in
analytically-defined space-times. The numerical differential geometric engine
has been rewritten using functional programming techniques, enabling objects
which are normally defined as functions in the formalism of differential
geometry and General Relativity to be directly represented as function
variables in the C++ code of GRworkbench. The new functional differential
geometric engine allows for more accurate and efficient visualisation of
objects in space-times and makes new, efficient computational techniques
available. Motivated by the desire to investigate a recent scientific claim
using GRworkbench, new tools for numerical experimentation have been
implemented, allowing for the simulation of complex physical situations.Comment: 14 pages. To appear A. Moylan, S.M. Scott and A.C. Searle,
Developments in GRworkbench. Proceedings of the Tenth Marcel Grossmann
Meeting on General Relativity, editors M. Novello, S. Perez-Bergliaffa and R.
Ruffini. Singapore: World Scientific 200
Robust Rotation Synchronization via Low-rank and Sparse Matrix Decomposition
This paper deals with the rotation synchronization problem, which arises in
global registration of 3D point-sets and in structure from motion. The problem
is formulated in an unprecedented way as a "low-rank and sparse" matrix
decomposition that handles both outliers and missing data. A minimization
strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against
state-of-the-art algorithms on simulated and real data. The results show that
R-GoDec is the fastest among the robust algorithms.Comment: The material contained in this paper is part of a manuscript
submitted to CVI
Sparse Signal Processing Concepts for Efficient 5G System Design
As it becomes increasingly apparent that 4G will not be able to meet the
emerging demands of future mobile communication systems, the question what
could make up a 5G system, what are the crucial challenges and what are the key
drivers is part of intensive, ongoing discussions. Partly due to the advent of
compressive sensing, methods that can optimally exploit sparsity in signals
have received tremendous attention in recent years. In this paper we will
describe a variety of scenarios in which signal sparsity arises naturally in 5G
wireless systems. Signal sparsity and the associated rich collection of tools
and algorithms will thus be a viable source for innovation in 5G wireless
system design. We will discribe applications of this sparse signal processing
paradigm in MIMO random access, cloud radio access networks, compressive
channel-source network coding, and embedded security. We will also emphasize
important open problem that may arise in 5G system design, for which sparsity
will potentially play a key role in their solution.Comment: 18 pages, 5 figures, accepted for publication in IEEE Acces
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