88,741 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
Multiple Query Optimization on the D-Wave 2X Adiabatic Quantum Computer
The D-Wave adiabatic quantum annealer solves hard combinatorial optimization
problems leveraging quantum physics. The newest version features over 1000
qubits and was released in August 2015. We were given access to such a machine,
currently hosted at NASA Ames Research Center in California, to explore the
potential for hard optimization problems that arise in the context of
databases.
In this paper, we tackle the problem of multiple query optimization (MQO). We
show how an MQO problem instance can be transformed into a mathematical formula
that complies with the restrictive input format accepted by the quantum
annealer. This formula is translated into weights on and between qubits such
that the configuration minimizing the input formula can be found via a process
called adiabatic quantum annealing. We analyze the asymptotic growth rate of
the number of required qubits in the MQO problem dimensions as the number of
qubits is currently the main factor restricting applicability. We
experimentally compare the performance of the quantum annealer against other
MQO algorithms executed on a traditional computer. While the problem sizes that
can be treated are currently limited, we already find a class of problem
instances where the quantum annealer is three orders of magnitude faster than
other approaches
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