19,803 research outputs found
Speeding up Martins' algorithm for multiple objective shortest path problems
The latest transportation systems require the best routes in a large network with respect to multiple objectives simultaneously to be calculated in a very short time. The label setting algorithm of Martins efficiently finds this set of Pareto optimal paths, but sometimes tends to be slow, especially for large networks such as transportation networks. In this article we investigate a number of speedup measures, resulting in new algorithms. It is shown that the calculation time to find the Pareto optimal set can be reduced considerably. Moreover, it is mathematically proven that these algorithms still produce the Pareto optimal set of paths
On the Necessity of Entanglement for the Explanation of Quantum Speedup
In this paper I argue that entanglement is a necessary component for any
explanation of quantum speedup and I address some purported counter-examples
that some claim show that the contrary is true. In particular, I address Biham
et al.'s mixed-state version of the Deutsch-Jozsa algorithm, and Knill &
Laflamme's deterministic quantum computation with one qubit (DQC1) model of
quantum computation. I argue that these examples do not demonstrate that
entanglement is unnecessary for the explanation of quantum speedup, but that
they rather illuminate and clarify the role that entanglement does play.Comment: Many clarificatory changes, and improved argumentation. Comments and
criticisms are still welcom
Symmetry-Based Search Space Reduction For Grid Maps
In this paper we explore a symmetry-based search space reduction technique
which can speed up optimal pathfinding on undirected uniform-cost grid maps by
up to 38 times. Our technique decomposes grid maps into a set of empty
rectangles, removing from each rectangle all interior nodes and possibly some
from along the perimeter. We then add a series of macro-edges between selected
pairs of remaining perimeter nodes to facilitate provably optimal traversal
through each rectangle. We also develop a novel online pruning technique to
further speed up search. Our algorithm is fast, memory efficient and retains
the same optimality and completeness guarantees as searching on an unmodified
grid map
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