151 research outputs found
Route Planning in Transportation Networks
We survey recent advances in algorithms for route planning in transportation
networks. For road networks, we show that one can compute driving directions in
milliseconds or less even at continental scale. A variety of techniques provide
different trade-offs between preprocessing effort, space requirements, and
query time. Some algorithms can answer queries in a fraction of a microsecond,
while others can deal efficiently with real-time traffic. Journey planning on
public transportation systems, although conceptually similar, is a
significantly harder problem due to its inherent time-dependent and
multicriteria nature. Although exact algorithms are fast enough for interactive
queries on metropolitan transit systems, dealing with continent-sized instances
requires simplifications or heavy preprocessing. The multimodal route planning
problem, which seeks journeys combining schedule-based transportation (buses,
trains) with unrestricted modes (walking, driving), is even harder, relying on
approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4,
previously published by Microsoft Research. This work was mostly done while
the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at
Microsoft Research Silicon Valle
Fast Exact Shortest-Path Distance Queries on Large Networks by Pruned Landmark Labeling
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 combination of these two techniques is
efficient and robust on various kinds of large-scale real-world networks. In
particular, 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.Comment: To appear in SIGMOD 201
PReaCH: A Fast Lightweight Reachability Index using Pruning and Contraction Hierarchies
We develop the data structure PReaCH (for Pruned Reachability Contraction
Hierarchies) which supports reachability queries in a directed graph, i.e., it
supports queries that ask whether two nodes in the graph are connected by a
directed path. PReaCH adapts the contraction hierarchy speedup techniques for
shortest path queries to the reachability setting. The resulting approach is
surprisingly simple and guarantees linear space and near linear preprocessing
time. Orthogonally to that, we improve existing pruning techniques for the
search by gathering more information from a single DFS-traversal of the graph.
PReaCH-indices significantly outperform previous data structures with
comparable preprocessing cost. Methods with faster queries need significantly
more preprocessing time in particular for the most difficult instances
Transit Node Routing Reconsidered
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
CH (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.Comment: 19 pages, submitted to SEA'201
Algorithms for Landmark Hub Labeling
Landmark-based routing and Hub Labeling (HL) are shortest path planning techniques, both of which rely on storing shortest path distances between selected pairs of nodes in a preprocessing phase to accelerate query answering. In Landmark-based routing, stored distances to landmark nodes are used to obtain distance lower bounds that guide A* search from node s to node t. With HL, tight upper bounds for shortest path distances between any s-t-pair can be interfered from their stored node labels, making HL an efficient distance oracle. However, for shortest path retrieval, the oracle has to be called once per edge in said path. Furthermore, HL often suffers from a large space consumption as many node pair distances have to be stored in the labels to allow for correct query answering. In this paper, we propose a novel technique, called Landmark Hub Labeling (LHL), which integrates the landmark concept into HL. We prove better worst-case path retrieval times for LHL in case it is path-consistent (a new labeling property we introduce). Moreover, we design efficient (approximation) algorithms that produce path-consistent LHL with small label size and provide parametrized upper bounds, depending on the highway dimension h or the geodesic transversal number gt of the graph. Finally, we show that the space consumption of LHL is smaller than that of (hierarchical) HL, both in theory and in experiments on real-world road networks
枝刈りラベリング法による大規模グラフ上の体系的なクエリ処理
学位の種別: 課程博士審査委員会委員 : (主査)東京大学教授 小林 直樹, 東京大学教授 萩谷 昌己, 東京大学教授 須田 礼仁, 東京大学准教授 渋谷 哲朗, 東京大学教授 定兼 邦彦, 東京大学教授 岩田 覚University of Tokyo(東京大学
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