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21
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 82 (39 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.
TimeDependent Route Planning
 Robust and Online LargeScale Optimization, LNCS
, 2009
"... Abstract. In this paper, we present an overview over existing speedup techniques for timedependent route planning. Apart from only explaining each technique one by one, we follow a more systematic approach. We identify basic ingredients of these recent techniques and show how they need to be augmen ..."
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Cited by 44 (17 self)
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Abstract. In this paper, we present an overview over existing speedup techniques for timedependent route planning. Apart from only explaining each technique one by one, we follow a more systematic approach. We identify basic ingredients of these recent techniques and show how they need to be augmented to guarantee correctness in timedependent networks. With the ingredients adapted, three efficient speedup techniques can be set up: CoreALT, SHARC, and Contraction Hierarchies. Experiments on realworld data deriving from road networks and public transportation confirm that these techniques allow the fast computation of timedependent shortest paths. 1
Highway dimension, shortest paths, and provably efficient algorithms
 IN ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA’10) JANUARY 1719, 2010
, 2010
"... Computing driving directions has motivated many shortest path heuristics that answer queries on continental scale networks, with tens of millions of intersections, literally instantly, and with very low storage overhead. In this paper we complement the experimental evidence with the first rigorous p ..."
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Cited by 40 (3 self)
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Computing driving directions has motivated many shortest path heuristics that answer queries on continental scale networks, with tens of millions of intersections, literally instantly, and with very low storage overhead. In this paper we complement the experimental evidence with the first rigorous proofs of efficiency for many of the heuristics suggested over the past decade. We introduce the notion of highway dimension and show how low highway dimension gives a unified explanation for several seemingly different algorithms.
Graph Partitioning with Natural Cuts
 In IPDPS. IEEE Computer Society
, 2011
"... Abstract. We present a novel approach to graph partitioning based on the notion of natural cuts. Our algorithm, called PUNCH, has two phases. The first phase performs a series of minimumcut computations to identify and contract dense regions of the graph. This reduces the graph size, but preserves ..."
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Cited by 23 (9 self)
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Abstract. We present a novel approach to graph partitioning based on the notion of natural cuts. Our algorithm, called PUNCH, has two phases. The first phase performs a series of minimumcut computations to identify and contract dense regions of the graph. This reduces the graph size, but preserves its general structure. The second phase uses a combination of greedy and local search heuristics to assemble the final partition. The algorithm performs especially well on road networks, which have an abundance of natural cuts (such as bridges, mountain passes, and ferries). In a few minutes, it obtains excellent partitions for continentalsized networks. 1
PHAST: hardwareaccelerated shortest path trees
 J. PARALLEL DISTRIB. COMPUT
, 2013
"... We present a novel algorithm to solve the nonnegative singlesource shortest path problem on road networks and graphs with low highway dimension. After a quick preprocessing phase, we can compute all distances from a given source in the graph with essentially a linear sweep over all vertices. Becaus ..."
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Cited by 20 (4 self)
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We present a novel algorithm to solve the nonnegative singlesource shortest path problem on road networks and graphs with low highway dimension. After a quick preprocessing phase, we can compute all distances from a given source in the graph with essentially a linear sweep over all vertices. Because this sweep is independent of the source, we are able to reorder vertices in advance to exploit locality. Moreover, our algorithm takes advantage of features of modern CPU architectures, such as SSE and multiple cores. Compared to Dijkstra’s algorithm, our method needs fewer operations, has better locality, and is better able to exploit parallelism at multicore and instruction levels. We gain additional speedup when implementing our algorithm on a GPU, where it is up to three orders of magnitude faster than Dijkstra’s algorithm on a highend CPU. This makes applications based on allpairs shortestpaths practical for continentalsized road networks. Several algorithms, such as computing the graph diameter, arc flags, or exact reaches, can be greatly accelerated by our method.
VCdimension and shortest path algorithms
"... We explore the relationship between VCdimension and graph algorithm design. In particular, we show that set systems induced by sets of vertices on shortest paths have VCdimension at most two. This allows us to use a result from learning theory to improve time bounds on query algorithms for the p ..."
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Cited by 17 (5 self)
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We explore the relationship between VCdimension and graph algorithm design. In particular, we show that set systems induced by sets of vertices on shortest paths have VCdimension at most two. This allows us to use a result from learning theory to improve time bounds on query algorithms for the pointtopoint shortest path problem in networks of low highway dimension, such as road networks. We also refine the definitions of highway dimension and related concepts, making them more general and potentially more relevant to practice. In particular, we define highway dimension in terms of set systems induced by shortest paths, and give cardinalitybased and average case definitions.
Faster Customization of Road Networks
 In Proc. SEA, LNCS
, 2013
"... Abstract. A wide variety of algorithms can answer exact shortestpath queries in real time on continental road networks, but they typically require significant preprocessing effort. Recently, the customizable route planning (CRP) approach has reduced the time to process a new cost function to a frac ..."
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Cited by 15 (5 self)
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Abstract. A wide variety of algorithms can answer exact shortestpath queries in real time on continental road networks, but they typically require significant preprocessing effort. Recently, the customizable route planning (CRP) approach has reduced the time to process a new cost function to a fraction of a minute. We reduce customization time even further, by an order of magnitude. This makes it worthwhile even when a single query is to be run, enabling a host of new applications. 1
On kskip Shortest Paths
"... Given two vertices s, t in a graph, let P be the shortest path (SP) from s to t, and P ⋆ a subset of the vertices in P. P ⋆ is a kskip shortest path from s to t, if it includes at least a vertex out of every k consecutive vertices in P. In general, P ⋆ succinctly describes P by sampling the vertice ..."
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Cited by 11 (0 self)
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Given two vertices s, t in a graph, let P be the shortest path (SP) from s to t, and P ⋆ a subset of the vertices in P. P ⋆ is a kskip shortest path from s to t, if it includes at least a vertex out of every k consecutive vertices in P. In general, P ⋆ succinctly describes P by sampling the vertices in P with a rate of at least 1/k. This makes P ⋆ a natural substitute in scenarios where reporting every single vertex of P is unnecessary or even undesired. This paper studies kskip SP computation in the context of spatial network databases (SNDB). Our technique has two properties crucial for realtime query processing in SNDB. First, our solution is able to answer kskip queries significantly faster than finding the original SPs in their entirety. Second, the previous objective is achieved with a structure that occupies less space than storing the underlying road network. The proposed algorithms are the outcome of a careful theoretical analysis that reveals valuable insight into the characteristics of the kskip SP problem. Their efficiency has been confirmed by extensive experiments with real data.
Alternative Routes in Road Networks
"... Abstract. We study the problem of finding good alternative routes in road networks. We look for routes that are substantially different from the shortest path, have small stretch, and are locally optimal. We formally define the problem of finding alternative routes with a single via vertex, develop ..."
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Cited by 10 (3 self)
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Abstract. We study the problem of finding good alternative routes in road networks. We look for routes that are substantially different from the shortest path, have small stretch, and are locally optimal. We formally define the problem of finding alternative routes with a single via vertex, develop efficient algorithms for it, and evaluate them experimentally. Our algorithms are efficient enough for practical use and compare favorably with previous methods in both speed and solution quality. 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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Cited by 7 (4 self)
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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.