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Parallel Time-Dependent Contraction Hierarchies, (2009)

by Christian Vetter
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Distributed Time-Dependent Contraction Hierarchies

by Tim Kieritz, Dennis Luxen, Peter S, Christian Vetter - In Proceedings of the 9th International Symposium on Experimental Algorithms, volume 6049 of LNCS , 2010
"... Abstract. Server based route planning in road networks is now powerful enough to find quickest paths in a matter of milliseconds, even if detailed information on time-dependent travel times is taken into account. However this requires huge amounts of memory on each query server and hours of preproce ..."
Abstract - Cited by 12 (7 self) - Add to MetaCart
Abstract. Server based route planning in road networks is now powerful enough to find quickest paths in a matter of milliseconds, even if detailed information on time-dependent travel times is taken into account. However this requires huge amounts of memory on each query server and hours of preprocessing even for a medium sized country like Germany. This is a problem since global internet companies would like to work with transcontinental networks, detailed models of intersections, and regular re-preprocessing that takes the current traffic situation into account. By giving a distributed memory parallelization of the arguably best current technique – time-dependent contraction hierarchies, we remove these bottlenecks. For example, on a medium size network 64 processes accelerate preprocessing by a factor of 28 to 160 seconds, reduce per process memory consumption by a factor of 10.5 and increase query throughput by a factor of 25. Key words: time-dependent shortest paths, distributed computation, message passing, algorithm en-gineering 1
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...er they exhibit slower query time and/or preprocessing time and distributed memory parallelization looks more difficult since the query search space is less localized around source and target. Vetter =-=[12]-=- has developed a shared memory parallelization of the preprocessing stage that is also the basis for our distributed memory parallelization. While sequential CH techniques perform node 2 ordering onli...

Route Planning with Flexible Objective Functions

by Robert Geisberger , Moritz Kobitzsch , Peter Sanders - In Proceedings of the 12th Workshop on Algorithm Engineering and Experiments (ALENEX’10), 124–137. SIAM
"... Abstract We present the first fast route planning algorithm that answers shortest paths queries for a customizable linear combination of two different metrics, e. g. travel time and energy cost, on large scale road networks. The precomputation receives as input a directed graph, two edge weight fun ..."
Abstract - Cited by 10 (4 self) - Add to MetaCart
Abstract We present the first fast route planning algorithm that answers shortest paths queries for a customizable linear combination of two different metrics, e. g. travel time and energy cost, on large scale road networks. The precomputation receives as input a directed graph, two edge weight functions t(e) and c(e), and a discrete interval [L, U ]. The resulting flexible query algorithm finds for a parameter p ∈ [L, U ] an exact shortest path for the edge weight t(e)+p·c(e). This allows for different tradeoffs between the two edge weight functions at query time. We apply precomputation based on node contraction, which adds all necessary shortcuts for any parameter choice efficiently. To improve the node ordering, we developed the new concept of gradual parameter interval splitting. Additionally, we improve performance by combining node contraction and a goaldirected technique in our flexible scenario.
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...lete. To reduce the preprocessing time, we can parallelize it. We can process different parameter intervals after a split in parallel and additionally we can apply the parallelization techniques from =-=[25]-=-. Also, our parameter splitting is efficient but leaves room for further improvements. One could possibly merge intervals later when they seem to be very similar. This could save preprocessing time si...

Transit Node Routing Reconsidered?

by Julian Arz, Dennis Luxen, Peter S
"... Abstract. Transit Node Routing (TNR) is a fast and exact distance oracle for road networks. We show several new results for TNR. First, we give a surprisingly simple implementation fully based on Contraction Hierarchies that speeds up preprocessing by an order of magnitude approaching the time for j ..."
Abstract - Cited by 9 (2 self) - Add to MetaCart
Abstract. Transit Node Routing (TNR) is a fast and exact distance oracle for road networks. We show several new results for TNR. First, we give a surprisingly simple implementation fully based on Contraction Hierarchies that speeds up preprocessing by an order of magnitude approaching the time for just finding a Contraction Hierarchies (which alone has two orders of magnitude larger query time). We also develop a very effective purely graph theoretical locality filter without any compromise in query times. Finally, we show that a specialization to the online many-to-one (or one-to-many) shortest path further speeds up query time by an order of magnitude. This variant even has better query time than the fastest known previous methods which need much more space. 1 Introduction and Related Work Route planning in road networks has seen a lot of results from the algorithm engineering community in recent years. With Dijkstra’s seminal algorithm being the baseline, a number of techniques preprocess the static input graph to achieve drastic speedups. Contraction Hierarchies (CH) [1,2] is a speedup-technique that has a convenient trade-off between preprocessing effort and query efficiency. Road network with millions of nodes
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...an Intel Core i7-920, clocked at 2.67 GHz with four cores and 12 GiB of RAM. It runs Linux kernel version 2.6.34 Our CH variant implements the shared-memory parallel preprocessing algorithm of Vetter =-=[15]-=- with a hop limit of 5 and 1 000 settled nodes for witness searches and 7 hops or 2 000 settled nodes during the actual contraction of nodes. The priority function is 2 ∗ edgeQuotient + 4 ∗ originalEd...

Efficient routing in road networks with turn costs

by Robert Geisberger, Christian Vetter - In 10th Int. Symposium on Experimental Algorithms (SEA , 2011
"... Abstract. We present an efficient algorithm for shortest path compu-tation in road networks with turn costs. Each junction is modeled as a node, and each road segment as an edge in a weighted graph. Turn costs are stored in tables that are assigned to nodes. By reusing turn cost tables for identical ..."
Abstract - Cited by 9 (0 self) - Add to MetaCart
Abstract. We present an efficient algorithm for shortest path compu-tation in road networks with turn costs. Each junction is modeled as a node, and each road segment as an edge in a weighted graph. Turn costs are stored in tables that are assigned to nodes. By reusing turn cost tables for identical junctions, we improve the space efficiency. Pre-processing based on an augmented node contraction allows fast shortest path queries. Compared to an edge-based graph, we reduce preprocess-ing time by a factor of 3.4 and space by a factor of 2.4 without change in query time. Key words: route planning; banned turn; turn cost; algorithm engi-neering 1
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...n to compute the node priorities. Nodes with higher priority are more important and get contracted later. The nodes are contracted in parallel by computing independent node sets with a 2-neighborhood =-=[10]-=-. 6 Query The query computes a shortest path between two original edges, a source s→ s′ and a target t′ → t. It consists of two Dijkstra-like searches that settle original edges (cf. Section 2) one in...

Contraction of Timetable Networks with Realistic Transfers

by Robert Geisberger , 2009
"... We successfully contract timetable networks with realistic transfer times. Contraction gradually removes nodes from the graph and adds shortcuts to preserve shortest paths. This reduces query times to 1ms with preprocessing times around 6 minutes on all tested instances. We achieve this by an improv ..."
Abstract - Cited by 3 (0 self) - Add to MetaCart
We successfully contract timetable networks with realistic transfer times. Contraction gradually removes nodes from the graph and adds shortcuts to preserve shortest paths. This reduces query times to 1ms with preprocessing times around 6 minutes on all tested instances. We achieve this by an improved contraction algorithm and by using a station graph model. Every node in our graph has a one-to-one correspondence to a station and every edge has an assigned collection of connections. Our graph model does not need parallel edges. The query algorithm does not compute a single earliest arrival time at a station but a set of arriving connections that allow best transfer opportunities. 1

Advanced Route Planning in Transportation Networks zur Erlangung des akademischen Grades eines

by Doktors Der Naturwissenschaften, Erster Gutachter, Zweite Gutachterin, Prof Dr, Peter Sanders, Prof Dr, Hannah Bast Abstract
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