Results 1  10
of
10
Engineering multilevel overlay graphs for shortestpath queries
 IN: PROCEEDINGS OF THE EIGHT WORKSHOP ON ALGORITHM ENGINEERING AND EXPERIMENTS (ALENEX06), SIAM
, 2006
"... An overlay graph of a given graph G =(V,E) on a subset S ⊆ V is a graph with vertex set S that preserves some property of G. In particular, we consider variations of the multilevel overlay graph used in [21] to speed up shortestpath computations. In this work, we follow up and present general verte ..."
Abstract

Cited by 22 (6 self)
 Add to MetaCart
An overlay graph of a given graph G =(V,E) on a subset S ⊆ V is a graph with vertex set S that preserves some property of G. In particular, we consider variations of the multilevel overlay graph used in [21] to speed up shortestpath computations. In this work, we follow up and present general vertex selection criteria and strategies of applying these criteria to determine a subset S inducing an overlay graph. The main contribution is a systematic experimental study where we investigate the impact of selection criteria and strategies on multilevel overlay graphs and the resulting speedup achieved for shortestpath queries. Depending on selection strategy and graph type, a centrality index criterion, a criterion based on planar separators, and vertex degree turned out to be good selection criteria.
Landmarkbased routing in dynamic graphs
 IN: 6TH WORKSHOP ON EXPERIMENTAL ALGORITHMS
, 2007
"... Many speedup techniques for route planning in static graphs exist, only few of them are proven to work in a dynamic scenario. Most of them use preprocessed information, which has to be updated whenever the graph is changed. However, goal directed search based on landmarks (ALT) still performs cor ..."
Abstract

Cited by 17 (6 self)
 Add to MetaCart
Many speedup techniques for route planning in static graphs exist, only few of them are proven to work in a dynamic scenario. Most of them use preprocessed information, which has to be updated whenever the graph is changed. However, goal directed search based on landmarks (ALT) still performs correct queries as long as an edge weight does not drop below its initial value. In this work, we evaluate the robustness of ALT with respect to traffic jams. It turns out that—by increasing the efficiency of ALT—we are able to perform fast (down to 20 ms on the Western European network) random queries in a dynamic scenario without updating the preprocessing as long as the changes in the network are moderate. Furthermore, we present how to update the preprocessed data without any additional space consumption and how to adapt the ALT algorithm to a timedependent scenario. A timedependent scenario models predictable changes in the network, e.g. traffic jams due to rush hour.
Computing ManytoMany Shortest Paths Using Highway Hierarchies
, 2007
"... We present a fast algorithm for computing all shortest paths between source nodes s ∈ S and target nodes t ∈ T. This problem is important as an initial step for many operations research problems (e.g., the vehicle routing problem), which require the distances between S and T as input. Our approach i ..."
Abstract

Cited by 16 (5 self)
 Add to MetaCart
We present a fast algorithm for computing all shortest paths between source nodes s ∈ S and target nodes t ∈ T. This problem is important as an initial step for many operations research problems (e.g., the vehicle routing problem), which require the distances between S and T as input. Our approach is based on highway hierarchies, which are also used for the currently fastest speedup techniques for shortest path queries in road networks. We show how to use highway hierarchies so that for example, a 10 000 × 10 000 distance table in the European road network can be computed in about one minute. These results are based on a simple basic idea, several refinements, and careful engineering of the approach. We also explain how the approach can be parallelized and how the computation can be restricted to computing only the k closest connections.
TRANSIT— ultrafast shortestpath queries with lineartime preprocessing
 In 9th DIMACS Implementation Challenge [1
, 2006
"... {bast,funke,dmatijev} at mpiinf dot mpg dot de We introduce the concept of transit nodes, as a means for preprocessing a road network, with given coordinates for each node and a travel time for each edge, such that pointtopoint shortestpath queries can be answered extremely fast. The transit nod ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
{bast,funke,dmatijev} at mpiinf dot mpg dot de We introduce the concept of transit nodes, as a means for preprocessing a road network, with given coordinates for each node and a travel time for each edge, such that pointtopoint shortestpath queries can be answered extremely fast. The transit nodes are a set of nodes, as small as possible, with the property that every shortest path that is nonlocal in the sense that it covers a certain not too small euclidean distance passes through at least on of these nodes. With such a set and precomputed distances from each node in the graph to its few, closest transit nodes, every nonlocal shortest path query becomes a simple matter of combining information from a few table lookups. For the US road network, which has about 24 million nodes and 58 million edges, we achieve a worstcase query processing time of about 10 microseconds (not milliseconds) for 99 % of all queries. This improves over the best previously reported times by two orders of magnitude. 1
Better landmarks within reach
 IN THE 9TH DIMACS IMPLEMENTATION CHALLENGE: SHORTEST PATHS
, 2007
"... We present significant improvements to a practical algorithm for the pointtopoint shortest path problem on road networks that combines A∗ search, landmarkbased lower bounds, and reachbased pruning. Through reachaware landmarks, better use of cache, and improved algorithms for reach computation ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
We present significant improvements to a practical algorithm for the pointtopoint shortest path problem on road networks that combines A∗ search, landmarkbased lower bounds, and reachbased pruning. Through reachaware landmarks, better use of cache, and improved algorithms for reach computation, we make preprocessing and queries faster while reducing the overall space requirements. On the road networks of the USA or Europe, the shortest path between two random vertices can be found in about one millisecond after one or two hours of preprocessing. The algorithm is also effective on twodimensional grids.
Experimental Study on SpeedUp Techniques for Timetable Information Systems
 PROCEEDINGS OF THE 7TH WORKSHOP ON ALGORITHMIC APPROACHES FOR TRANSPORTATION MODELING, OPTIMIZATION, AND SYSTEMS (ATMOS 2007
, 2007
"... During the last years, impressive speedup techniques for DIJKSTRA’s algorithm have been developed. Unfortunately, recent research mainly focused on road networks. However, fast algorithms are also needed for other applications like timetable information systems. Even worse, the adaption of recentl ..."
Abstract

Cited by 11 (7 self)
 Add to MetaCart
During the last years, impressive speedup techniques for DIJKSTRA’s algorithm have been developed. Unfortunately, recent research mainly focused on road networks. However, fast algorithms are also needed for other applications like timetable information systems. Even worse, the adaption of recently developed techniques to timetable information is more complicated than expected. In this work, we check whether results from road networks are transferable to timetable information. To this end, we present an extensive experimental study of the most prominent speedup techniques on different types of inputs. It turns out that recently developed techniques are much slower on graphs derived from timetable information than on road networks. In addition, we gain amazing insights into the behavior of speedup techniques in general.
Timetable information updating in case of delays: Modeling issues
, 2008
"... Abstract. The timetable information problem can be solved by computing shortest paths in special graphs built from timetable data. In general, two models exist: the timedependent and timeexpanded network. In a recent work, both models are compared with respect to advantages and disadvantages on a ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Abstract. The timetable information problem can be solved by computing shortest paths in special graphs built from timetable data. In general, two models exist: the timedependent and timeexpanded network. In a recent work, both models are compared with respect to advantages and disadvantages on a theoretical and a practical framework. In addition, an extensive experimental evaluation reveals further differences with respect to query performance. However, delays – which occur very frequently in railway systems – are not covered. In this work, we show how the timedependent and the timeexpanded models should be updated in order to capture delays. It turns out that delays can be incorporated in the timedependent model without changing the topology of the network. This is not true for the timeexpanded model, whose updating involves a (sometimes large) sequence of edge insertions, deletions, and cost modifications. 1
Robust, almost constant time shortestpath queries on road networks
 IN: 9TH DIMACS IMPLEMENTATION CHALLENGE
, 2006
"... When you drive to somewhere ‘far away’, you will leave your current location via one of only a few ‘important ’ traffic junctions. Recently, other research groups and we have largely independently developed this informal observation into transit node routing, a technique for reducing quickestpath ..."
Abstract
 Add to MetaCart
When you drive to somewhere ‘far away’, you will leave your current location via one of only a few ‘important ’ traffic junctions. Recently, other research groups and we have largely independently developed this informal observation into transit node routing, a technique for reducing quickestpath queries in road networks to a small number of table lookups. The contribution of our paper is twofold. First, we present a generic framework for transit node routing that allows almost constant time routing for both global and local queries. Second, we develop a highly tuned implementation using highway hierarchies. For the road maps of Western Europe and the United States, our best query times improve over the best previously published figures by two orders of magnitude. This is more than one million times faster than the best known algorithm for general networks. We also explain how to compute complete descriptions of shortest paths (and not only their lengths) very efficiently.
Maintenance of Multilevel Overlay Graphs for Timetable Queries ⋆
"... Abstract. In railways systems the timetable is typically represented as a weighted digraph on which itinerary queries are answered by shortest path algorithms, usually running Dijkstra’s algorithm. Due to the continuously growing size of realworld graphs, there is a constant need for faster algorit ..."
Abstract
 Add to MetaCart
Abstract. In railways systems the timetable is typically represented as a weighted digraph on which itinerary queries are answered by shortest path algorithms, usually running Dijkstra’s algorithm. Due to the continuously growing size of realworld graphs, there is a constant need for faster algorithms and many techniques have been devised to heuristically speed up Dijkstra’s algorithm. One of these techniques is the multilevel overlay graph, that has been recently introduced and shown to be experimentally efficient, especially when applied to timetable information. In many practical application major disruptions to the normal operation cannot be completely avoided because of the complexity of the underlying systems. Timetable information update after disruptions is considered one of the weakest points in current railway systems. This determines the need for an effective online redesign and update of the shortest paths information as a consequence of disruptions. In this paper, we make a step forward toward this direction by showing some theoretical properties of multilevel overlay graphs that lead us to the definition of a new data structure for the dynamic maintenance of a multilevel overlay graph of a given graph G while weight decrease or weight increase operations are performed on G. Our solution is theoretically faster than the recomputation from scratch and allows fast queries. Keywords. Timetable Queries, Speedup techniques for shortest paths 1
Simple, Fast, and Scalable Reachability Oracle
"... A reachability oracle (or hop labeling) assigns each vertex v two sets of vertices: Lout(v) and Lin(v), such that u reaches v iff Lout(u) ∩ Lin(v) = ∅. Despite their simplicity and elegance, reachability oracles have failed to achieve efficiency in more than ten years since their introduction: The ..."
Abstract
 Add to MetaCart
A reachability oracle (or hop labeling) assigns each vertex v two sets of vertices: Lout(v) and Lin(v), such that u reaches v iff Lout(u) ∩ Lin(v) = ∅. Despite their simplicity and elegance, reachability oracles have failed to achieve efficiency in more than ten years since their introduction: The main problem is high construction cost, which stems from a setcover framework and the need to materialize transitive closure. In this paper, we present two simple and efficient labeling algorithms, HierarchicalLabeling and DistributionLabeling, which can work on massive realworld graphs: Their construction time is an order of magnitude faster than the setcover based labeling approach, and transitive closure materialization is not needed. On large graphs, their index sizes and their query performance can now beat the stateoftheart transitive closure compression and online search approaches.