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22
Y.: Fast exact shortest-path distance queries on large networks by pruned landmark labeling
- In: SIGMOD 2013
, 2013
"... We propose a new exact method for shortest-path distance queries on large-scale networks. Our method precomputes distance labels for vertices by performing a breadth-first search from every vertex. Seemingly too obvious and too inefficient at first glance, the key ingredient introduced here is pruni ..."
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Cited by 22 (1 self)
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We propose a new exact method for shortest-path distance queries on large-scale networks. Our method precomputes distance labels for vertices by performing a breadth-first search from every vertex. Seemingly too obvious and too inefficient at first glance, the key ingredient introduced here is pruning during breadth-first searches. While we can still answer the correct distance for any pair of vertices from the labels, it surprisingly reduces the search space and sizes of labels. Moreover, we show that we can perform 32 or 64 breadth-first searches simultaneously exploiting bitwise operations. We experimentally demonstrate that the com-bination of these two techniques is efficient and robust on various kinds of large-scale real-world networks. In particu-lar, our method can handle social networks and web graphs with hundreds of millions of edges, which are two orders of magnitude larger than the limits of previous exact methods, with comparable query time to those of previous methods.
Faster Customization of Road Networks
- In Proc. SEA, LNCS
, 2013
"... Abstract. A wide variety of algorithms can answer exact shortest-path 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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Abstract. A wide variety of algorithms can answer exact shortest-path 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
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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Cited by 9 (2 self)
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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 many-to-one (or one-to-many) 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 speedup-technique that has a convenient trade-off between preprocessing effort and query efficiency. Road network with millions of nodes
HLDB: Location-based 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 net-works entirely within a database. HLDB is based on hub la-bels (HL), the fastest point-to-point algorithm for road net-works, 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 net-works entirely within a database. HLDB is based on hub la-bels (HL), the fastest point-to-point algorithm for road net-works, and its queries are implemented (quite naturally) in standard SQL. Within the database, HLDB answers exact distance queries and retrieves full shortest-path descriptions in real time, even on networks with tens of millions of ver-tices. 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 fast-food restaurants. We also introduce efficient new HL-based 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.
IS-LABEL: an Independent-Set based Labeling Scheme for Point-to-Point Distance Querying
"... We study the problem of computing shortest path or distance between two query vertices in a graph, which has numerous important applications. Quite a number of indexes have been proposed to answer such distance queries. However, all of these indexes can only process graphs of size barely up to 1 mil ..."
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Cited by 7 (2 self)
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We study the problem of computing shortest path or distance between two query vertices in a graph, which has numerous important applications. Quite a number of indexes have been proposed to answer such distance queries. However, all of these indexes can only process graphs of size barely up to 1 million vertices, which is rather small in view of many of the fast-growing real-world graphs today such as social networks and Web graphs. We propose an efficient index, which is a novel labeling scheme based on the independent set of a graph. We show that our method can handle graphs of size orders of magnitude larger than existing indexes. 1.
Scalable similarity estimation in social networks: closeness, node labels, and random edge lengths
- In COSN
, 2013
"... Similarity estimation between nodes based on structural properties of graphs is a basic building block used in the analysis of massive networks for diverse purposes such as link prediction, product rec-ommendations, advertisement, collaborative filtering, and commu-nity discovery. While local simila ..."
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Cited by 6 (4 self)
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Similarity estimation between nodes based on structural properties of graphs is a basic building block used in the analysis of massive networks for diverse purposes such as link prediction, product rec-ommendations, advertisement, collaborative filtering, and commu-nity discovery. While local similarity measures, based on proper-ties of immediate neighbors, are easy to compute, those relying on global properties have better recall. Unfortunately, this better qual-ity comes with a computational price tag. Aiming for both accuracy and scalability, we make several contributions. First, we define closeness similarity, a natural measure that compares two nodes based on the similarity of their relations to all other nodes. Second, we show how the all-distances sketch (ADS) node labels, which are efficient to compute, can support the estimation of closeness sim-ilarity and shortest-path (SP) distances in logarithmic query time. Third, we propose the randomized edge lengths (REL) technique and define the corresponding REL distance, which captures both path length and path multiplicity and therefore improves over the SP distance as a similarity measure. The REL distance can also be the basis of closeness similarity and can be estimated using SP computation or the ADS labels. We demonstrate the effectiveness of our measures and the accuracy of our estimates through experi-ments on social networks with up to tens of millions of nodes.
Hop Doubling Label Indexing for Point-to-Point Distance Querying on Scale-Free Networks
"... We study the problem of point-to-point distance querying for massive scale-free graphs, which is important for numerous applications. Given a directed or undirected graph, we propose to build an index for answering such queries based on a novel hop-doubling labeling technique. We derive bounds on th ..."
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Cited by 5 (0 self)
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We study the problem of point-to-point distance querying for massive scale-free graphs, which is important for numerous applications. Given a directed or undirected graph, we propose to build an index for answering such queries based on a novel hop-doubling labeling technique. We derive bounds on the index size, the computation costs and I/O costs based on the properties of unweighted scale-free graphs. We show that our method is much more efficient and effective compared to the state-of-the-art techniques, in terms of both querying time and indexing costs. Our empirical study shows that our method can handle graphs that are orders of magnitude larger than existing methods. 1.
Hub labels: Theory and practice
- In SEA
, 2014
"... Abstract. The Hub Labeling algorithm (HL) is an exact shortest path algorithm with excellent query performance on some classes of problems. It precomputes some auxiliary information (stored as a label) for each vertex, and its query performance depends only on the label size. While there are polynom ..."
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Cited by 4 (0 self)
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Abstract. The Hub Labeling algorithm (HL) is an exact shortest path algorithm with excellent query performance on some classes of problems. It precomputes some auxiliary information (stored as a label) for each vertex, and its query performance depends only on the label size. While there are polynomial-time approximation algorithms to find labels of ap-proximately optimal size, practical solutions use hierarchical hub labels (HHL), which are faster to compute but offer no guarantee on the la-bel size. We improve the theoretical and practical performance of the HL approximation algorithms, enabling us to compute such labels for moderately large problems. Our comparison shows that HHL algorithms scale much better and find labels that usually are not much bigger than the theoretically justified HL labels. 1
R.: Separating hierarchical and general hub labelings
- MFCS 2013, LNCS
, 2013
"... Abstract. In the context of distance oracles, a labeling algorithm computes vertex labels during preprocessing. An s, t query computes the corresponding distance using the labels of s and t only, without looking at the input graph. Hub labels is a class of labels that has been extensively studied. ..."
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Cited by 3 (3 self)
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Abstract. In the context of distance oracles, a labeling algorithm computes vertex labels during preprocessing. An s, t query computes the corresponding distance using the labels of s and t only, without looking at the input graph. Hub labels is a class of labels that has been extensively studied. Performance of the hub label query depends on the label size. Hierarchical labels are a natural special kind of hub labels. These labels are related to other problems and can be computed more efficiently. This brings up a natural question of the quality of hierarchical labels. We show that there is a gap: optimal hierarchical labels can be polynomially bigger than the general hub labels. To prove this result, we give tight upper and lower bounds on the size of hierarchical and general labels for hypercubes.
Optimizing landmark-based routing and preprocessing
- In Proceedings of the 6th ACM SIGSPATIAL International Workshop on Computational Transportation Science, IWCTS ’13
, 2013
"... Many acceleration techniques exist for the single-pair shortest path problem on road networks. Most of them have been significantly improved over the years to achieve faster preprocessing times and superior performance. In this spirit, our current work significantly improves the classic ALT (A ∗ + L ..."
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Cited by 3 (3 self)
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Many acceleration techniques exist for the single-pair shortest path problem on road networks. Most of them have been significantly improved over the years to achieve faster preprocessing times and superior performance. In this spirit, our current work significantly improves the classic ALT (A ∗ + Landmarks + Triangle equality) algorithm. By carefully optimizing both preprocessing and query phases, we managed to effectively minimize preprocessing time to a few seconds, making the ALT algorithm also suitable for dynamic scenarios, i.e., road networks with changing edge weights due to traffic updates. We also accelerated the query phase for both unidi-rectional and bidirectional versions of the ALT algorithm, provid-ing fast enough query times (including full-path unpacking) suit-able for real-time services and continental road networks. Categories and Subject Descriptors
