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Transit Node Routing Reconsidered?
"... 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 ..."
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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 manytoone (or onetomany) 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 speeduptechnique that has a convenient tradeoff between preprocessing effort and query efficiency. Road network with millions of nodes
Computing Single Source Shortest Paths using SingleObjective Fitness Functions
, 2009
"... Runtime analysis of evolutionary algorithms has become an important part in the theoretical analysis of randomized search heuristics. The first combinatorial problem where rigorous runtime results have been achieved is the wellknown single source shortest path (SSSP) problem. Scharnow, Tinnefeld an ..."
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Runtime analysis of evolutionary algorithms has become an important part in the theoretical analysis of randomized search heuristics. The first combinatorial problem where rigorous runtime results have been achieved is the wellknown single source shortest path (SSSP) problem. Scharnow, Tinnefeld and Wegener [PPSN 2002, J. Math. Model. Alg. 2004] proposed a multiobjective approach which solves the problem in expected polynomial time. They also suggest a related singleobjective fitness function. However, it was left open whether this does solve the problem efficiently, and, in a broader context, whether multiobjective fitness functions for problems like the SSSP yield more efficient evolutionary algorithms. In this paper, we show that the single objective approach yields an efficient (1+1) EA with runtime bounds very close to those of the multiobjective approach.
Dynamic Multilevel Overlay Graphs for Shortest Paths
 Mathematics in Computer Science
, 2008
"... Multilevel overlay graphs represent a speedup technique for shortest paths computation which is based on a hierarchical decomposition of a weighted directed graph G. They have been shown to be experimentally efficient, especially when applied to timetable information. However, no theoretical resul ..."
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Multilevel overlay graphs represent a speedup technique for shortest paths computation which is based on a hierarchical decomposition of a weighted directed graph G. They have been shown to be experimentally efficient, especially when applied to timetable information. However, no theoretical result on the cost of constructing, maintaining and querying multilevel overlay graphs in a dynamic environment is known. In this paper, we show theoretical properties of multilevel overlay graphs that lead us to the definition of a new data structure for the computation and the maintenance of an overlay graph of G while weight decrease or weight increase operations are performed on G. Our solution is theoretically faster than the recomputation from scratch and allows queries that can be performed more efficiently than running Dijkstra’s shortest paths algorithm on G. 1
HLDB: Locationbased services in databases
 In Proceedings of the 20th ACM SIGSPATIAL International Symposium on Advances in Geographic Information Systems (GIS’12), 339–348. ACM Press. Best Paper Award
, 2012
"... This paper introduces HLDB, the first practical system that can answer exact spatial queries on continental road networks entirely within a database. HLDB is based on hub labels (HL), the fastest pointtopoint algorithm for road networks, and its queries are implemented (quite naturally) in stan ..."
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This paper introduces HLDB, the first practical system that can answer exact spatial queries on continental road networks entirely within a database. HLDB is based on hub labels (HL), the fastest pointtopoint algorithm for road networks, and its queries are implemented (quite naturally) in standard SQL. Within the database, HLDB answers exact distance queries and retrieves full shortestpath descriptions in real time, even on networks with tens of millions of vertices. The basic algorithm can be extended in a natural way (still in SQL) to answer much more sophisticated queries, such as finding the ten closest fastfood restaurants. We also introduce efficient new HLbased algorithms for even harder problems, such as best via point, ride sharing, and point of interest prediction. The HLDB framework makes it easy to implement these algorithms in SQL, enabling interactive applications on continental road networks.
PointtoPoint Shortest Path Algorithms with Preprocessing
"... This is a survey of some recent results on pointtopoint shortest path algorithms. This classical optimization problem received a lot of attention lately and significant progress has been made. After an overview of classical results, we study recent heuristics that solve the problem while examinin ..."
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This is a survey of some recent results on pointtopoint shortest path algorithms. This classical optimization problem received a lot of attention lately and significant progress has been made. After an overview of classical results, we study recent heuristics that solve the problem while examining only a small portion of the input graph; the graph can be very big. Note that the algorithms we discuss find exact shortest paths. These algorithms are heuristic because they perform well only on some graph classes. While their performance has been good in experimental studies, no theoretical bounds are known to support the experimental observations. Most of these algorithms have been motivated by finding paths in large road networks. We start by reviewing the classical Dijkstra’s algorithm and its bidirectional variant, developed in 1950’s and 1960’s. Then we review A* search, an AI technique developed in 1970’s. Next we turn our attention to modern results which are based on preprocessing the graph. To be practical, preprocessing needs to be reasonably fast and not use too much space. We discuss landmark and reachbased algorithms as well as their combination.
Engineering TimeExpanded Graphs for Faster Timetable Information
, 2009
"... We present an extension of the wellknown timeexpanded approach for timetable information. By remodeling unimportant stations, we are able to obtain faster query times with less space consumption than the original model. Moreover, we show that our extensions harmonize well with speedup techniques ..."
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We present an extension of the wellknown timeexpanded approach for timetable information. By remodeling unimportant stations, we are able to obtain faster query times with less space consumption than the original model. Moreover, we show that our extensions harmonize well with speedup techniques whose adaption to timetable networks is more challenging than one might expect.
Route planning in road networks with turn costs. Studienarbeit, Universität Karlsruhe, Institut für theoretische Informatik
, 2008
"... In this paper, we will describe the use of edgebased graphs to integrate turn penalties into algorithms used for route planning in road networks. We will give a model of these turn costs and describe a way to obtain reasonable estimates. We also will describe different ways to obtain edgebased gra ..."
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Cited by 5 (0 self)
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In this paper, we will describe the use of edgebased graphs to integrate turn penalties into algorithms used for route planning in road networks. We will give a model of these turn costs and describe a way to obtain reasonable estimates. We also will describe different ways to obtain edgebased graph prior and during the runtime of a shortest path search and also present a hybrid approach. These ways come with characteristic impacts on time and space consumption. We will analyze those drawbacks theoretically and experimentally and show
Shortest paths on dynamic graphs
 International Transactions in Operational Research
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Approximate Shortest Path Queries in Graphs Using Voronoi Duals
"... We propose an approximation method to answer pointtopoint shortest path queries in undirected graphs, based on random sampling and Voronoi duals. We compute a simplification of the graph by selecting nodes independently at random with probability p. Edges are generated as the Voronoi dual of the o ..."
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Cited by 3 (2 self)
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We propose an approximation method to answer pointtopoint shortest path queries in undirected graphs, based on random sampling and Voronoi duals. We compute a simplification of the graph by selecting nodes independently at random with probability p. Edges are generated as the Voronoi dual of the original graph, using the selected nodes as Voronoi sites. This overlay graph allows for fast computation of approximate shortest paths for general, undirected graphs. The time–quality tradeoff decision can be made at query time. We provide bounds on the approximation ratio of the path lengths as well as experimental results. The theoretical worstcase approximation ratio is bounded by a logarithmic factor. Experiments show that our approximation method based on Voronoi duals has extremely fast preprocessing time and efficiently computes reasonably short paths.
Towards online shortest path computation
 IEEE Trans. Knowl. Data Eng
, 2014
"... Abstract—The online shortest path problem aims at computing the shortest path based on live traffic circumstances. This is very important in modern car navigation systems as it helps drivers to make sensible decisions. To our best knowledge, there is no efficient system/solution that can offer affor ..."
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Abstract—The online shortest path problem aims at computing the shortest path based on live traffic circumstances. This is very important in modern car navigation systems as it helps drivers to make sensible decisions. To our best knowledge, there is no efficient system/solution that can offer affordable costs at both client and server sides for online shortest path computation. Unfortunately, the conventional clientserver architecture scales poorly with the number of clients. A promising approach is to let the server collect live traffic information and then broadcast them over radio or wireless network. This approach has excellent scalability with the number of clients. Thus, we develop a new framework called live traffic index (LTI) which enables drivers to quickly and effectively collect the live traffic information on the broadcasting channel. An impressive result is that the driver can compute/update their shortest path result by receiving only a small fraction of the index. Our experimental study shows that LTI is robust to various parameters and it offers relatively short tunein cost (at client side), fast query response time (at client side), small broadcast size (at server side), and light maintenance time (at server side) for online shortest path problem. Index Terms—Spatial databases; Vehicle driving; Broadcasting F