17 research outputs found
Accelerated filtering on graphs using Lanczos method
Signal-processing on graphs has developed into a very active field of
research during the last decade. In particular, the number of applications
using frames constructed from graphs, like wavelets on graphs, has
substantially increased. To attain scalability for large graphs, fast
graph-signal filtering techniques are needed. In this contribution, we propose
an accelerated algorithm based on the Lanczos method that adapts to the
Laplacian spectrum without explicitly computing it. The result is an accurate,
robust, scalable and efficient algorithm. Compared to existing methods based on
Chebyshev polynomials, our solution achieves higher accuracy without increasing
the overall complexity significantly. Furthermore, it is particularly well
suited for graphs with large spectral gaps
A fast and tight heuristic for A∗ in road networks
We study exact, efficient and practical algorithms for route planning in large road networks. Routing applications often require integrating the current traffic situation, planning ahead with traffic predictions for the future, respecting forbidden turns, and many other features depending on the exact application. While Dijkstra’s algorithm can be used to solve these problems, it is too slow for many applications. A* is a classical approach to accelerate Dijkstra’s algorithm. A* can support many extended scenarios without much additional implementation complexity. However, A*’s performance depends on the availability of a good heuristic that estimates distances. Computing tight distance estimates is a challenge on its own. On road networks, shortest paths can also be quickly computed using hierarchical speedup techniques. They achieve speed and exactness but sacrifice A*’s flexibility. Extending them to certain practical applications can be hard. In this paper, we present an algorithm to efficiently extract distance estimates for A* from Contraction Hierarchies (CH), a hierarchical technique. We call our heuristic CH-Potentials. Our approach allows decoupling the supported extensions from the hierarchical speed-up technique. Additionally, we describe A* optimizations to accelerate the processing of low degree nodes, which often occur in road networks