Alternative Route Techniques and their Applications to the Stochastic on-time Arrival Problem

346 Pages·2015·13.85 MB·English

by  Moritz Helge Kobitzsch

Alternative Route Techniques
and their Applications to the Stochastic on-time Arrival Problem
zur Erlangung des akademischen Grades eines
Doktors der Ingenieurwissenschaften /
Doktors der Naturwissenschaften
von der Fakultät für Informatik
des Karlsruher Instituts für Technologie (KIT)
genehmigte
Dissertation
von
Moritz Helge Kobitzsch
aus Berlin
Tag der mündlichen Prüfung: 06.11.2015
Erster Gutachter: Herr Prof. Dr. Peter Sanders
Zweiter Gutachter: Herr Andrew Goldberg, PhD
In memory of my sister.
ii
"Piled Higher and Deeper" by Jorge Cham (www.phdcomics.com)
This thesis is based on 80914 lines of code1. According to SLOCCount, this puts the
coding work alone at an estimated twenty-one years of development. The credibility
(s.a.) is backed by 90358 words, distributed over 7448 lines of LaTex code.
1Data generated using David A. Wheeler’s ’SLOCCount’
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Acknowledgements
This thesis presents not only my own work. Many of the topics discussed in this work
are strongly influenced by many different people, without whom this thesis would have
not been possible. There is no way of putting a clear number on the relevance of their
input; the order in which they are listed is purely coincidental and should not reflect
any meaning.
First, I would like to thank all of my co-authors. I owe Samitha Samaranayake, for
introducing me to the stochastic on-time arrival problem and all the fruitful discussions
we had. Dennis Schieferdecker, your input on the different topics we worked on together
as well as your support during my own endeavours are greatly appreciated. Dennis
Luxen I have to thank for his countless contributions to our work on route corridors.
Not only for the route corridors, but also for a great experience during my short stay
at Microsoft Research, I owe gratitude to Daniel Delling and Renato Werneck who
both taught me a lot. Thank you for all the help you have given me and your support,
not only in my professional but also in my personal life.
In addition, I have to thank all of my coworkers and office mates that made life at
the institute as good as it could be. I specifically am grateful to Sebastian Schlag for
all the fruitful discussions over coffee, to Timo Bingmann for his support in system
maintenance and his efforts in the office social events. I thank Christian Schulz
for supplying his partitioner and trying out adjustments to better support my own
algorithms and Jochen Speck for his general support in managing our compute servers.
Furthermore, I have to give thanks to my students that helped a great deal in
accomplishing the results presented in my thesis. Both Marcel Radermacher and
Stephan Erb have engaged me in most interesting discussions and have provided a
great deal of input. Also, Valentin Buchhold helped a great deal by implementing a lot
of useful tools and algorithms for me.
Last, but not least, I have to thank my friends and family for all the moral support
over the duration of this work. I especially owe gratitude to my mother for all her
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support in not only proofreading my publications but also this thesis. Sina Schmitt
and Vera Döttling, thank you for all your intense moral support during hard times.
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Contents
1 Introduction 1
1.1 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Algorithm Engineering in Route Planning . . . . . . . . . . . . 2
1.2 Contribution and Thesis Outline . . . . . . . . . . . . . . . . . . . . . . 3
I An Introduction to Speed-up Techniques and Alternative
Routes 7
2 Preliminaries 9
2.1 On Road Network Representations . . . . . . . . . . . . . . . . . . . . 9
2.2 Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 Graph Representation . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 Priority Queue . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3 Graph Traversal . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Shortest Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.1 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.2 SSSP Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.1 The Labelling Algorithm . . . . . . . . . . . . . . . . . . . . . . 17
2.4.2 Dijkstra’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.3 The Bellman-Ford Algorithm . . . . . . . . . . . . . . . . . . . 19
2.5 Further Concepts and Notations . . . . . . . . . . . . . . . . . . . . . . 21
3 Speeding up Dijkstra’s Algorithm 23
3.1 Goal Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Separator-Based Techniques . . . . . . . . . . . . . . . . . . . . . . . . 27
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Contents
3.3 Hierarchical Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 Additional Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4 Shortest Paths Details 33
4.1 Contraction Hierarchies . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1.1 Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1.2 Query Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.3 Batched Shortest Path using Contraction Hierarchies . . . . . . 37
4.1.4 Dynamic Implementation . . . . . . . . . . . . . . . . . . . . . . 39
4.1.5 Theoretical Results . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2 Customizable Route Planning . . . . . . . . . . . . . . . . . . . . . . . 41
4.2.1 Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2.2 Customization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.3 Query Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2.4 Real Time Customization . . . . . . . . . . . . . . . . . . . . . 46
5 Alternative Routes - a Snapshot 49
5.1 Alternative Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.1.1 Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.1.2 Recent Improvements . . . . . . . . . . . . . . . . . . . . . . . . 58
5.2 The Via-Node Paradigm . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2.1 The Concept of Viability . . . . . . . . . . . . . . . . . . . . . . 59
5.2.2 Current Implementations . . . . . . . . . . . . . . . . . . . . . . 62
5.2.3 Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6 Experimental Methodology 67
6.1 Hardware and Environment . . . . . . . . . . . . . . . . . . . . . . . . 67
6.2 Instances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.3 Queries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.4 Specialized Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.4.1 Bi-Criteria Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.4.2 Stochastic Travel Times . . . . . . . . . . . . . . . . . . . . . . 74
6.4.3 Arc Expanded Graphs . . . . . . . . . . . . . . . . . . . . . . . 76
6.5 Comparing Alternative Route Quality . . . . . . . . . . . . . . . . . . . 76
6.6 Quality Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.6.1 Classic Measures . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.6.2 An Additional Measure . . . . . . . . . . . . . . . . . . . . . . . 78
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II Contributions 81
7 Parallel Pareto Optimal Routes 83
7.1 Multi-Criteria Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
7.2 paPaSearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
7.2.1 A Parallel Pareto Queue . . . . . . . . . . . . . . . . . . . . . . 86
7.2.2 Vertex Local Operations . . . . . . . . . . . . . . . . . . . . . . 89
7.3 An Efficient Implementation . . . . . . . . . . . . . . . . . . . . . . . . 90
7.3.1 B-Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.3.2 Further Parallel Queues . . . . . . . . . . . . . . . . . . . . . . 94
7.3.3 A Practical Parallel Pareto-queue . . . . . . . . . . . . . . . . . 95
7.3.4 Engineering paPaSearch . . . . . . . . . . . . . . . . . . . . . . 100
7.3.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.3.6 Increasing Parallelism . . . . . . . . . . . . . . . . . . . . . . . 103
7.4 Experimental Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.4.1 Pareto Queue . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.4.2 Label Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.4.3 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
7.4.4 Delta-Stepping . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
7.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8 Engineering the Penalty Method 117
8.1 Adjusting the Penalty Method . . . . . . . . . . . . . . . . . . . . . . . 119
8.1.1 Penalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
8.1.2 A New Stopping Criterion . . . . . . . . . . . . . . . . . . . . . 121
8.1.3 Selecting Feasible Paths . . . . . . . . . . . . . . . . . . . . . . 122
8.2 Experimental Evaluation – Modifications . . . . . . . . . . . . . . . . . 124
8.2.1 Parameterization Influences. . . . . . . . . . . . . . . . . . . . . 124
8.2.2 Quality Considerations . . . . . . . . . . . . . . . . . . . . . . . 125
8.3 Customizing a Single Query . . . . . . . . . . . . . . . . . . . . . . . . 129
8.3.1 Omitting Origin and Destination Cells. . . . . . . . . . . . . . . 130
8.3.2 Alternative Route Extraction . . . . . . . . . . . . . . . . . . . 133
8.4 Experimental Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 133
8.4.1 Penalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
8.4.2 Parallel Execution . . . . . . . . . . . . . . . . . . . . . . . . . 138
8.4.3 Final Configuration . . . . . . . . . . . . . . . . . . . . . . . . . 141
8.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
9 A new Approach to Via-Alternatives 147
9.1 Alternative Graphs via Plateaux . . . . . . . . . . . . . . . . . . . . . . 148
9.1.1 Building Shortest Path Trees . . . . . . . . . . . . . . . . . . . 149
9.1.2 Discovering Plateaux . . . . . . . . . . . . . . . . . . . . . . . . 152
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9.1.3 Generating a Compact Representation and Actually Finding the
Plateaux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
9.1.4 Direct Alternative Graph Compaction . . . . . . . . . . . . . . 157
9.1.5 Artificial Shortcuts . . . . . . . . . . . . . . . . . . . . . . . . . 161
9.1.6 Additional Processing . . . . . . . . . . . . . . . . . . . . . . . . 161
9.2 Experimental Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 164
9.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
10 Alternative Routes via Segment Exclusion 171
10.1 The Concept of Segment Exclusion . . . . . . . . . . . . . . . . . . . . 172
10.1.1 Implementation Details . . . . . . . . . . . . . . . . . . . . . . . 176
10.1.2 Potential Problems . . . . . . . . . . . . . . . . . . . . . . . . . 180
10.1.3 Constructing an Alternative Graph . . . . . . . . . . . . . . . . 180
10.2 Experimental Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 181
10.2.1 Running Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
10.2.2 Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
10.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
11 On a Hybrid Navigation Scenario 191
11.1 A General View on Corridors . . . . . . . . . . . . . . . . . . . . . . . 192
11.2 Search Space Corridors . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
11.2.1 Goal Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
11.2.2 Hierarchical Techniques . . . . . . . . . . . . . . . . . . . . . . 194
11.3 Turn Corridors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
11.3.1 Theoretical Discussions . . . . . . . . . . . . . . . . . . . . . . . 196
11.4 Detour Corridors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
11.4.1 Attached Components . . . . . . . . . . . . . . . . . . . . . . . 199
11.5 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
11.5.1 The Random Drive Concept . . . . . . . . . . . . . . . . . . . . 201
11.5.2 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
11.6 Attached Component Filtering . . . . . . . . . . . . . . . . . . . . . . . 208
11.6.1 Corridor Size Reduction . . . . . . . . . . . . . . . . . . . . . . 208
11.6.2 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
11.7 Corridor Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
11.7.1 Conceptual Approaches . . . . . . . . . . . . . . . . . . . . . . . 212
11.7.2 Contraction Hierarchies-Based Corridors . . . . . . . . . . . . . 219
11.8 Turn Corridor Contraction Hierarchies . . . . . . . . . . . . . . . . . . 219
11.9 Experimental Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 223
11.9.1 Corridor-based Alternative Routes . . . . . . . . . . . . . . . . 226
11.9.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
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