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16
Engineering Highway Hierarchies
, 2006
"... Highway hierarchies exploit hierarchical properties inherent in realworld road networks to allow fast and exact pointtopoint shortestpath queries. A fast preprocessing routine iteratively performs two steps: first, it removes edges that only appear on shortest paths close to source or target; s ..."
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Cited by 51 (6 self)
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Highway hierarchies exploit hierarchical properties inherent in realworld road networks to allow fast and exact pointtopoint shortestpath queries. A fast preprocessing routine iteratively performs two steps: first, it removes edges that only appear on shortest paths close to source or target; second, it identifies lowdegree nodes and bypasses them by introducing shortcut edges. The resulting hierarchy of highway networks is then used in a Dijkstralike bidirectional query algorithm to considerably reduce the search space size without losing exactness. The crucial fact is that ‘far away ’ from source and target it is sufficient to consider only highlevel edges. Various experiments with realworld road networks confirm the performance of our approach. On a 2.0 GHz machine, preprocessing the network of Western Europe, which consists of about 18 million nodes, takes 13 minutes and yields 48 bytes of additional data per node. Then, random queries take 0.61 ms on average. If we are willing to accept slower query times (1.10 ms), the memory usage can be decreased to 17 bytes per node. We can guarantee that at most 0.014 % of all nodes are visited during any query. Results for US road networks are similar. Highway hierarchies can be combined with goaldirected search, they can be extended to answer manytomany queries, and they are a crucial ingredient for other speedup techniques, namely for transitnode routing and highwaynode routing.
Engineering Route Planning Algorithms
 ALGORITHMICS OF LARGE AND COMPLEX NETWORKS. LECTURE NOTES IN COMPUTER SCIENCE
, 2009
"... Algorithms for route planning in transportation networks have recently undergone a rapid development, leading to methods that are up to three million times faster than Dijkstra’s algorithm. We give an overview of the techniques enabling this development and point out frontiers of ongoing research on ..."
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Cited by 30 (18 self)
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Algorithms for route planning in transportation networks have recently undergone a rapid development, leading to methods that are up to three million times faster than Dijkstra’s algorithm. We give an overview of the techniques enabling this development and point out frontiers of ongoing research on more challenging variants of the problem that include dynamically changing networks, timedependent routing, and flexible objective functions.
Engineering Fast Route Planning Algorithms
, 2007
"... Algorithms for route planning in transportation networks have recently undergone a rapid development, leading to methods that are up to one million times faster than Dijkstra’s algorithm. We outline ideas, algorithms, implementations, and experimental methods behind this development. We also explai ..."
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Cited by 26 (3 self)
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Algorithms for route planning in transportation networks have recently undergone a rapid development, leading to methods that are up to one million times faster than Dijkstra’s algorithm. We outline ideas, algorithms, implementations, and experimental methods behind this development. We also explain why the story is not over yet because dynamically changing networks, flexible objective functions, and new applications pose a lot of interesting challenges.
In Transit to Constant Time ShortestPath Queries in Road Networks
"... When you drive to somewhere ‘far away’, you will leave your current location via one of only a few ‘important’ traffic junctions. Starting from this informal observation, we develop an algorithmic approach—transit node routing— that allows us to reduce quickestpath queries in road networks to a sma ..."
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Cited by 11 (4 self)
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When you drive to somewhere ‘far away’, you will leave your current location via one of only a few ‘important’ traffic junctions. Starting from this informal observation, we develop an algorithmic approach—transit node routing— that allows us to reduce quickestpath queries in road networks to a small number of table lookups. We present two implementations of this idea, one based on a simple grid data structure and one based on highway hierarchies. For the road map of the United States, our best query times improve over the best previously published figures by two orders of magnitude. Our results exhibit various tradeoffs between average query time (6 µs to 63 µs), preprocessing time (62 min to 1200 min), and storage overhead (27 bytes/node to 247 bytes/node).
Graph Indexing of Road Networks for Shortest Path Queries with Label Restrictions
"... The current widespread use of locationbased services and GPS technologies has revived interest in very fast and scalable shortest path queries. We introduce a new shortest path query type in which dynamic constraints may be placed on the allowable set of edges that can appear on a valid shortest pa ..."
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Cited by 4 (0 self)
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The current widespread use of locationbased services and GPS technologies has revived interest in very fast and scalable shortest path queries. We introduce a new shortest path query type in which dynamic constraints may be placed on the allowable set of edges that can appear on a valid shortest path (e.g., dynamically restricting the type of roads or modes of travel which may be considered in a multimodal transportation network). We formalize this problem as a specific variant of formal language constrained shortest path problems, which we call the Kleene Language Constrained Shortest Paths problem. To efficiently support this type of dynamically constrained shortest path query for largescale datasets, we extend the hierarchical graph indexing technique known as Contraction Hierarchies. Our experimental evaluation using the North American road network dataset (with over 50 million edges) shows an average query speed and search space improvement of over 3 orders of magnitude compared to the naïve adaptation of the standard Dijkstra’s algorithm to support this query type. We also show an improvement of over 2 orders of magnitude compared to the only previouslyexisting indexing technique which could solve this problem without additional preprocessing. 1.
Advanced Shortest Paths Algorithms on a MassivelyMultithreaded Architecture
"... We present a study of multithreaded implementations of Thorup’s algorithm for solving the Single Source Shortest Path (SSSP) problem for undirected graphs. Our implementations leverage the fledgling MultiThreaded Graph Library (MTGL) to perform operations such as finding connected components and ext ..."
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Cited by 3 (0 self)
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We present a study of multithreaded implementations of Thorup’s algorithm for solving the Single Source Shortest Path (SSSP) problem for undirected graphs. Our implementations leverage the fledgling MultiThreaded Graph Library (MTGL) to perform operations such as finding connected components and extracting induced subgraphs. To achieve good parallel performance from this algorithm, we deviate from several theoretically optimal algorithmic steps. In this paper, we present simplifications that perform better in practice, and we describe details of the multithreaded implementation that were necessary for scalability. We study synthetic graphs that model unstructured networks, such as social networks and economic transaction networks. Most of the recent progress in shortest path algorithms relies on structure that these networks do not have. In this work, we take a step back and explore the synergy between an elegant theoretical algorithm and an elegant computer architecture. Finally, we conclude with a prediction that this work will become relevant to shortest path computation on structured networks. 1.
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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Cited by 3 (1 self)
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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.
Shortest Paths and Experimental Evaluation of Algorithms
, 2010
"... ◮ directed graph G = (V, A); ◮ arc lengths ℓ(v, w) ≥ 0; ◮ V  = n, A  = m; ◮ source s, target t. Goal: find shortest path from s to t. ◮ its length is denoted by dist(s, t). Our focus is on road networks: ◮ V: intersections; ◮ A: road segments; ◮ ℓ(·, ·): typically travel times. ..."
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◮ directed graph G = (V, A); ◮ arc lengths ℓ(v, w) ≥ 0; ◮ V  = n, A  = m; ◮ source s, target t. Goal: find shortest path from s to t. ◮ its length is denoted by dist(s, t). Our focus is on road networks: ◮ V: intersections; ◮ A: road segments; ◮ ℓ(·, ·): typically travel times.