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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 ..."
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Cited by 29 (8 self)
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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.
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 ..."
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Cited by 18 (10 self)
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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.
Bidirectional A ∗ Search for TimeDependent Fast Paths
"... Abstract. The computation of pointtopoint shortest paths on timedependent road networks has many practical applications, but there have been very few works that propose efficient algorithms for large graphs. One of the difficulties of route planning on timedependent graphs is that we do not know ..."
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Cited by 16 (10 self)
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Abstract. The computation of pointtopoint shortest paths on timedependent road networks has many practical applications, but there have been very few works that propose efficient algorithms for large graphs. One of the difficulties of route planning on timedependent graphs is that we do not know the exact arrival time at the destination, hence applying bidirectional search is not straightforward; we propose a novel approach based on A ∗ with landmarks (ALT) that starts a search from both the source and the destination node, where the backward search is used to bound the set of nodes that have to be explored by the forward search. Extensive computational results show that this approach is very effective in practice if we are willing to accept a small approximation factor, resulting in a speedup of several times with respect to Dijkstra’s algorithm while finding only slightly suboptimal solutions. 1
Timetable Information: Models and Algorithms
, 2006
"... We give an overview of models and efficient algorithms for optimally solving timetable information problems like “given a departure and an arrival station as well as a departure time, which is the connection that arrives as early as possible at the arrival station?” Two main approaches that transfor ..."
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Cited by 10 (7 self)
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We give an overview of models and efficient algorithms for optimally solving timetable information problems like “given a departure and an arrival station as well as a departure time, which is the connection that arrives as early as possible at the arrival station?” Two main approaches that transform the problems into shortest path problems are reviewed, including issues like the modeling of realistic details (e.g., train transfers) and further optimization criteria (e.g., the number of transfers). An important topic is also multicriteria optimization, where in general all attractive connections with respect to several criteria shall be determined. Finally, we discuss the performance of the described algorithms, which is crucial for their application in a real system.
Relational approach for shortest path discovery over large graphs
 Proc. VLDB Endow
"... With the rapid growth of large graphs, we cannot assume that graphs can still be fully loaded into memory, thus the diskbased graph operation is inevitable. In this paper, we take the shortest path discovery as an example to investigate the technique issues when leveraging existing infrastructure o ..."
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Cited by 9 (1 self)
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With the rapid growth of large graphs, we cannot assume that graphs can still be fully loaded into memory, thus the diskbased graph operation is inevitable. In this paper, we take the shortest path discovery as an example to investigate the technique issues when leveraging existing infrastructure of relational database (RDB) in the graph data management. Based on the observation that a variety of graph search queries can be implemented by iterative operations including selecting frontier nodes from visited nodes, making expansion from the selected frontier nodes, and merging the expanded nodes into the visited ones, we introduce a relational FEM framework with three corresponding operators to implement graph search tasks in the RDB context. We show new features such as window function and merge statement introduced by recent SQL standards can not only simplify the expression but also improve the performance of the FEM framework. In addition, we propose two optimization strategies specific to shortest path discovery inside the FEM framework. First, we take a bidirectional set Dijkstra’s algorithm in the path finding. The bidirectional strategy can reduce the search space, and set Dijkstra’s algorithm finds the shortest path in a setatatime fashion. Second, we introduce an index named SegTable to preserve the local shortest segments, and exploit SegTable to further improve the performance. The final extensive experimental results illustrate our relational approach with the optimization strategies achieves high scalability and performance. 1.
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 ..."
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Cited by 4 (2 self)
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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
A Generalization of Dijkstra’s Shortest Path Algorithm with Applications to VLSI Routing
"... We generalize Dijkstra’s algorithm for finding shortest paths in digraphs with nonnegative integral edge lengths. Instead of labeling individual vertices we label subgraphs which partition the given graph. We can achieve much better running times if the number of involved subgraphs is small compare ..."
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Cited by 3 (2 self)
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We generalize Dijkstra’s algorithm for finding shortest paths in digraphs with nonnegative integral edge lengths. Instead of labeling individual vertices we label subgraphs which partition the given graph. We can achieve much better running times if the number of involved subgraphs is small compared to the order of the original graph and the shortest path problems restricted to these subgraphs is computationally easy. As an application we consider the VLSI routing problem, where we need to find millions of shortest paths in partial grid graphs with billions of vertices. Here, our algorithm can be applied twice, once in a coarse abstraction (where the labeled subgraphs are rectangles), and once in a detailed model (where the labeled subgraphs are intervals). Using the result of the first algorithm to speed up the second one via goaloriented techniques leads to considerably reduced running time. We illustrate this with a stateoftheart routing tool on leadingedge industrial chips.
The Shortcut Problem  Complexity and Algorithms
, 2012
"... We study a graphaugmentation problem arising from a technique applied in recent approaches for route planning. Many such methods enhance the graph by inserting shortcuts, i.e., additional edges (u,v) such that the length of (u,v) is the distance from u to v. Given a weighted, directed graph G and ..."
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Cited by 2 (0 self)
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We study a graphaugmentation problem arising from a technique applied in recent approaches for route planning. Many such methods enhance the graph by inserting shortcuts, i.e., additional edges (u,v) such that the length of (u,v) is the distance from u to v. Given a weighted, directed graph G and a number c ∈ Z>0, the shortcut problem asks how to insert c shortcuts into G such that the expected number of edges that are contained in an edgeminimal shortest path from a random node s to a random node t is minimal. In this work, we study the algorithmic complexity of the problem and give approximation algorithms for a special graph class. Further, we state ILPbased exact approaches and show how to stochastically evaluate a given shortcut assignment on graphs that are too large to do so exactly.
The Shortcut Problem  Complexity and Approximation
, 2009
"... During the last years, speedup techniques for DIJKSTRA’s algorithm have been developed that make the computation of shortest paths a matter of microseconds even on huge road networks. The most sophisticated methods enhance the graph by inserting shortcuts, i.e. additional edges, that represent sh ..."
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Cited by 2 (1 self)
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During the last years, speedup techniques for DIJKSTRA’s algorithm have been developed that make the computation of shortest paths a matter of microseconds even on huge road networks. The most sophisticated methods enhance the graph by inserting shortcuts, i.e. additional edges, that represent shortest paths in the graph. Until now, all existing shortcutinsertion strategies are heuristics and no theoretical results on the topic are known. In this work, we formalize the problem of adding shortcuts as a graph augmentation problem, study the algorithmic complexity of the problem, give approximation algorithms and show how to stochastically evaluate a given shortcut assignment on graphs that are too big to evaluate it exactly.
kNearest Neighbors Queries in TimeDependent Road Networks
"... Abstract. In this article, we study the problem of processing knearest neighbors (kNN) queries in road networks considering traffic conditions, in particular the case where the speed of moving objects is timedependent. For instance, given that the user is at a given location at certain time, the q ..."
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Abstract. In this article, we study the problem of processing knearest neighbors (kNN) queries in road networks considering traffic conditions, in particular the case where the speed of moving objects is timedependent. For instance, given that the user is at a given location at certain time, the query returns the k points of interest (e.g., gas stations) that can be reached in the minimum amount of time. Previous works have proposed solutions to answer kNN queries in road networks where the moving speed in each road is constant. Obviously, these solutions cannot be simply applied to the problem we are interested in. Our approach uses the wellknown A ∗ search algorithm by applying incremental network expansion and pruning unpromising vertices. We discuss the design and correctness of our algorithm and present experimental results that show the efficiency and effectiveness of our solution.