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SpaceEfficient SHARCRouting
, 2009
"... Accelerating the computation of quickest paths in road networks has been undergoing a rapid development during the last years. The breakthrough idea for handling road networks with tens of millions of nodes was the concept of shortcuts, i.e., additional arcs that represent long paths in the input. V ..."
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Accelerating the computation of quickest paths in road networks has been undergoing a rapid development during the last years. The breakthrough idea for handling road networks with tens of millions of nodes was the concept of shortcuts, i.e., additional arcs that represent long paths in the input. Very recently, this concept has been transferred to timedependent road networks where travel times on arcs are given by functions. Unfortunately, the concept of shortcuts yields a high increase in space consumption for timedependent road networks since the travel time functions assigned to the shortcuts may become quite complex. In this work, we present how the space overhead induced by timedependent SHARC, a technique relying on shortcuts as well, can be reduced significantely. As a result, we are able to reduce the overhead stemming from SHARC by a factor of up to 11.5 for the price of a loss in query performance of a factor of 4. The methods we present allow a flexible tradeoff between space consumption and query performance.
Contraction of Timetable Networks with Realistic Transfers
, 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 ..."
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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 onetoone 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
Engineering TimeDependent ManytoMany Shortest Paths Computation.
 In Proceedings of the 10th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS’10), OpenAccess Series in Informatics (OASIcs),
, 2010
"... Abstract Computing distance tables is important for many logistics problems like the vehicle routing problem (VRP). While shortest distances from all source nodes in S to all target nodes in T are timeindependent, travel times are not. We present the first efficient algorithms to compute timedepe ..."
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Abstract Computing distance tables is important for many logistics problems like the vehicle routing problem (VRP). While shortest distances from all source nodes in S to all target nodes in T are timeindependent, travel times are not. We present the first efficient algorithms to compute timedependent travel time tables in large timedependent road networks. Our algorithms are based on timedependent contraction hierarchies (TCH), currently the fastest timedependent speedup technique. The computation of a table is inherently in Θ(S · T ), and therefore inefficient for large tables. We provide one particular algorithm using only Θ(S + T ) time and space, being able to answer queries two orders of magnitude faster than the basic TCH implementation. If small errors are acceptable, approximate versions of our algorithms are further orders of magnitude faster. ACM Subject Classification Introduction Computing travel times between all locations in a predefined set is a known problem arising in many operations research problems, e.g. vehicle routing. More formally, given a graph G = (V, E), and a set of source nodes S ⊆ V and target nodes T ⊆ V , we want to know the travel time between each source and target node (manytomany shortest paths problem). The common approach is to compute a travel time table of size S · T , reducing subsequent travel time computations to a simple table lookup. Due to the knowledge of historical traffic data and traffic prediction models, it is possible to forecast travel times in dependence to the departure time. These timedependent travel times allow to compute more realistic routes, especially important for routing within cities with time windows. In this timedependent scenario, each cell in the travel time table corresponds to a travel time function over the departure time. In contrast to the static scenario without timedependency, such a timedependent table takes a lot longer to compute and occupies a lot more space. We refine the problem of computing a table to the problem of implementing a query interface: Given s ∈ S and t ∈ T , we want to know the earliest arrival time when we depart at time τ (or the travel time profile for all τ ). So any algorithm that previously used a table now just needs to replace its table lookups with calls to this interface. An algorithm behind this interface uses a precomputed data structure with the knowledge of G, S and T to answer these queries fast. Especially in the common case where S , T  V , such an algorithm is able to answer a query * Partially supported by DFG grant SA 933/51.
A case for timedependent shortest path computation in spatial networks
 IN: PROC. OF THE SIGSPATIAL INTL. CONF. ON ADVANCES IN GIS
, 2010
"... The problem of pointtopoint shortest path computation in spatial networks is extensively studied with many approaches proposed to speedup the computation. Most of the existing approaches make the simplifying assumption that weights (e.g., traveltime) of the network edges are constant. However, w ..."
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The problem of pointtopoint shortest path computation in spatial networks is extensively studied with many approaches proposed to speedup the computation. Most of the existing approaches make the simplifying assumption that weights (e.g., traveltime) of the network edges are constant. However, with realworld spatial networks the edge traveltimes are timedependent, where the arrivaltime to an edge determines the actual traveltime of the edge. With this paper, we study the applicability of existing shortest path algorithms to realworld large timedependent spatial networks. In addition, we evaluate the importance of considering timedependent edge traveltimes for route planning in spatial networks. We show that timedependent shortest path computation can reduce the traveltime by 36 % on average as compared to the static shortest path computation that assumes constant edge traveltimes.
Efficient route compression for hybrid route planning
 In MedAlg
, 2012
"... Abstract. We describe an algorithmic framework for lossless compression of route descriptions. This is useful for hybrid route planning where routes are computed by a server and then transmitted to a client device in a car using some mobile radio communication where bandwidth may be low. Compressed ..."
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Abstract. We describe an algorithmic framework for lossless compression of route descriptions. This is useful for hybrid route planning where routes are computed by a server and then transmitted to a client device in a car using some mobile radio communication where bandwidth may be low. Compressed routes are represented by only a few via nodes which are the connection points when the route is decomposed into unique optimal segments. To reconstruct the route efficiently a client device needs basic but fast route planning capability. Contraction hierarchies make this approach fast enough for practice: Compressing takes only a few milliseconds. And previous experiments suggest that a client can decompress each route segment virtually instantaneously. So, as the segments can be decompressed successively while driving, it is not likely that the driver experiences any delay except for the time needed by the mobile communication. 1
D.: Doing More for Less – CacheAware Parallel Contraction Hierarchies Preprocessing
, 2012
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Core Routing on Dynamic TimeDependent Road Networks
, 2010
"... Route planning in large scale timedependent road networks is an important practical application of the shortest paths problem that greatly benefits from speedup techniques. In this paper we extend a twolevel hierarchical approach for pointtopoint shortest paths computations to the timedependent ..."
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Route planning in large scale timedependent road networks is an important practical application of the shortest paths problem that greatly benefits from speedup techniques. In this paper we extend a twolevel hierarchical approach for pointtopoint shortest paths computations to the timedependent case. This method, also known as core routing in the literature for static graphs, consists in the selection of a small subnetwork where most of the computations can be carried out, thus reducing the search space. We combine this approach with bidirectional goaldirected search in order to obtain an algorithm capable of finding shortest paths in a matter of milliseconds on continental sized networks. Moreover, we tackle the dynamic scenario where the piecewise linear functions that we use to model timedependent arc costs are not fixed, but can have their coefficients updated requiring only a small computational effort.
Engineering Timedependent OneToAll Computation
"... Abstract Very recently a new algorithm to the nonnegative singlesource shortest path problem on road networks has been discovered. It is very cacheefficient, but only on static road networks. We show how to augment it to the timedependent scenario. The advantage if the new approach is that it set ..."
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Abstract Very recently a new algorithm to the nonnegative singlesource shortest path problem on road networks has been discovered. It is very cacheefficient, but only on static road networks. We show how to augment it to the timedependent scenario. The advantage if the new approach is that it settles nodes, even for a profile query, by scanning all downward edges. We improve the scanning of the downward edges with techniques developed for timedependent manytomany computations.
Shortest path algorithms techniques
, 2013
"... Shortest paths, or close to shortest paths, are commonly used in everyday situations. The paper reviews the various algorithms available for the problem. One of the famous technique Dijkstra’s algorithm solves the singlesource shortest path problem on any directed graph in O(m+nlogn) worstcase tim ..."
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Shortest paths, or close to shortest paths, are commonly used in everyday situations. The paper reviews the various algorithms available for the problem. One of the famous technique Dijkstra’s algorithm solves the singlesource shortest path problem on any directed graph in O(m+nlogn) worstcase time when a Fibonacci heap is used as the frontier set data structure.