Route Planning in Road Networks

We present various speedup techniques for route planning in road networks. After performing some preprocessing steps, we can compute accurate quickest-path lengths in a few microseconds on a 2.0 GHz machine, using real-world road networks with several million nodes. In addition to dealing with the static point-to-point problem, we also handle dynamic scenarios (like traffic jams) and many-to-many instances

Combining Hierarchical and Goal-Directed Speed-Up Techniques for Dijkstra\u27s Algorithm

In "Combining Speed-up Techniques for Shortest-Path Computations", basic speed-up techniques for Dijkstra\u27s algorithm have been combined. The key observation in this work was that it is most promising to combine hierarchical and goal-directed speed-up techniques. However, since its publication, impressive progress has been made in the field of speed-up techniques for Dijkstra’s algorithm and huge data sets have been made available. Hence, we revisit the systematic combination of speed-up techniques in this work, which leads to the fastest known algorithms for various scenarios. Even for road networks, which have been worked on heavily during the last years, we are able to present an improvement in performance. Moreover, we gain interesting insights into the behavior of speed-up techniques when combining them

On Solving NP-complete Problems with Unconventional Models of Computation

Concentrating on the algorithmic point of view, we summarize briefly two attempts of solving NP-complete problems in polynomial time with an unconventional model of computation: • in [CPW + 01] (described in [Bal01]), Chiu, Pezzoli, Wu, Stroock, and Whitesides solve instances of the maximal clique problem (MCP) using microfluidic networks, and • in [Adl94] (described in [CPT01]), Adleman solves an instance of the directed Hamiltonian path problem using DNA Computing. We want to emphasize one common problem of these attempts that shows that we need not only new models of computation, but also new algorithms in order to be able to solve big instances of NP-complete problems. In their experiments, Chiu et al. show how to solve an instance of the maximal clique problem 1 in polynomial time. They obtain the speedup in comparison with a conventional implementation on a conventional machine by taking advantage of the possibility of parallelizing the following quite simple algorithm: 1. For each subset V ′ ⊆ V, set counter[V ′ ] = 0

quantum

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