19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@Proceedings{cacchiani_et_al:OASIcs.ATMOS.2019, title = {{OASIcs, Volume 75, ATMOS'19, Complete Volume}}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-128-3}, ISSN = {2190-6807}, year = {2019}, volume = {75}, editor = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019}, URN = {urn:nbn:de:0030-drops-114516}, doi = {10.4230/OASIcs.ATMOS.2019}, annote = {Keywords: Theory of computation, Design and analysis of algorithms; Mathematics of computing, Discrete mathematics; Combinatorics; Mathematical optimization;} }
19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 0:i-0:x, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{cacchiani_et_al:OASIcs.ATMOS.2019.0, author = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, title = {{Front Matter, Table of Contents, Preface, Conference Organization}}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, pages = {0:i--0:x}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-128-3}, ISSN = {2190-6807}, year = {2019}, volume = {75}, editor = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.0}, URN = {urn:nbn:de:0030-drops-114123}, doi = {10.4230/OASIcs.ATMOS.2019.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization} }
Boris Grimm, Ralf Borndörfer, Markus Reuther, and Thomas Schlechte. A Cut Separation Approach for the Rolling Stock Rotation Problem with Vehicle Maintenance. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 1:1-1:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{grimm_et_al:OASIcs.ATMOS.2019.1, author = {Grimm, Boris and Bornd\"{o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas}, title = {{A Cut Separation Approach for the Rolling Stock Rotation Problem with Vehicle Maintenance}}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, pages = {1:1--1:12}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-128-3}, ISSN = {2190-6807}, year = {2019}, volume = {75}, editor = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.1}, URN = {urn:nbn:de:0030-drops-114136}, doi = {10.4230/OASIcs.ATMOS.2019.1}, annote = {Keywords: Railway Operations Research, Integer Programming, Infeasible Path Cuts, Cut Separation, Rolling Stock Rotation Problem} }
Niels Lindner and Christian Liebchen. New Perspectives on PESP: T-Partitions and Separators. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 2:1-2:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{lindner_et_al:OASIcs.ATMOS.2019.2, author = {Lindner, Niels and Liebchen, Christian}, title = {{New Perspectives on PESP: T-Partitions and Separators}}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, pages = {2:1--2:18}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-128-3}, ISSN = {2190-6807}, year = {2019}, volume = {75}, editor = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.2}, URN = {urn:nbn:de:0030-drops-114144}, doi = {10.4230/OASIcs.ATMOS.2019.2}, annote = {Keywords: Periodic Event Scheduling Problem, Periodic Timetabling, Graph Partitioning, Graph Separators, Balanced Cuts} }
Matúš Mihalák and Marc Pont. On Sorting with a Network of Two Stacks. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 3:1-3:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{mihalak_et_al:OASIcs.ATMOS.2019.3, author = {Mihal\'{a}k, Mat\'{u}\v{s} and Pont, Marc}, title = {{On Sorting with a Network of Two Stacks}}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, pages = {3:1--3:12}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-128-3}, ISSN = {2190-6807}, year = {2019}, volume = {75}, editor = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.3}, URN = {urn:nbn:de:0030-drops-114159}, doi = {10.4230/OASIcs.ATMOS.2019.3}, annote = {Keywords: Sorting, Stacks, Optimization, Algorithms, Reduction, MinUnCut} }
Barbara Geissmann and Lukas Gianinazzi. Routing in Stochastic Public Transit Networks. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{geissmann_et_al:OASIcs.ATMOS.2019.4, author = {Geissmann, Barbara and Gianinazzi, Lukas}, title = {{Routing in Stochastic Public Transit Networks}}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, pages = {4:1--4:18}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-128-3}, ISSN = {2190-6807}, year = {2019}, volume = {75}, editor = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.4}, URN = {urn:nbn:de:0030-drops-114167}, doi = {10.4230/OASIcs.ATMOS.2019.4}, annote = {Keywords: Route Planning, Public Transit Network, Temporal Graphs} }
Francis Garuba, Marc Goerigk, and Peter Jacko. Robust Network Capacity Expansion with Non-Linear Costs. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 5:1-5:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{garuba_et_al:OASIcs.ATMOS.2019.5, author = {Garuba, Francis and Goerigk, Marc and Jacko, Peter}, title = {{Robust Network Capacity Expansion with Non-Linear Costs}}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, pages = {5:1--5:13}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-128-3}, ISSN = {2190-6807}, year = {2019}, volume = {75}, editor = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.5}, URN = {urn:nbn:de:0030-drops-114175}, doi = {10.4230/OASIcs.ATMOS.2019.5}, annote = {Keywords: Robust Optimization, Mobile Network, Network Capacity Design \& Expansion, Non-linear Cost, Traffic and Transport Routing} }
Anita Schöbel, Julius Pätzold, and Jörg P. Müller. The Trickle-In Effect: Modeling Passenger Behavior in Delay Management. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{schobel_et_al:OASIcs.ATMOS.2019.6, author = {Sch\"{o}bel, Anita and P\"{a}tzold, Julius and M\"{u}ller, J\"{o}rg P.}, title = {{The Trickle-In Effect: Modeling Passenger Behavior in Delay Management}}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, pages = {6:1--6:15}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-128-3}, ISSN = {2190-6807}, year = {2019}, volume = {75}, editor = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.6}, URN = {urn:nbn:de:0030-drops-114187}, doi = {10.4230/OASIcs.ATMOS.2019.6}, annote = {Keywords: Public Transport Planning, Delay Management, Integer Programming} }
Matthias Müller-Hannemann, Ralf Rückert, and Sebastian S. Schmidt. Vehicle Capacity-Aware Rerouting of Passengers in Delay Management. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{mullerhannemann_et_al:OASIcs.ATMOS.2019.7, author = {M\"{u}ller-Hannemann, Matthias and R\"{u}ckert, Ralf and Schmidt, Sebastian S.}, title = {{Vehicle Capacity-Aware Rerouting of Passengers in Delay Management}}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, pages = {7:1--7:14}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-128-3}, ISSN = {2190-6807}, year = {2019}, volume = {75}, editor = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.7}, URN = {urn:nbn:de:0030-drops-114192}, doi = {10.4230/OASIcs.ATMOS.2019.7}, annote = {Keywords: Delay management, passenger flows, vehicle capacities, rerouting} }
Adam Schienle, Pedro Maristany, and Marco Blanco. A Priori Search Space Pruning in the Flight Planning Problem. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{schienle_et_al:OASIcs.ATMOS.2019.8, author = {Schienle, Adam and Maristany, Pedro and Blanco, Marco}, title = {{A Priori Search Space Pruning in the Flight Planning Problem}}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, pages = {8:1--8:14}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-128-3}, ISSN = {2190-6807}, year = {2019}, volume = {75}, editor = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.8}, URN = {urn:nbn:de:0030-drops-114205}, doi = {10.4230/OASIcs.ATMOS.2019.8}, annote = {Keywords: time-dependent shortest path problem, crossing costs, flight trajectory optimization, preprocessing, search space} }
Spyros Kontogiannis, Anastasios Papadopoulos, Andreas Paraskevopoulos, and Christos Zaroliagis. Exploiting Amorphous Data Parallelism to Speed-Up Massive Time-Dependent Shortest-Path Computations. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{kontogiannis_et_al:OASIcs.ATMOS.2019.9, author = {Kontogiannis, Spyros and Papadopoulos, Anastasios and Paraskevopoulos, Andreas and Zaroliagis, Christos}, title = {{Exploiting Amorphous Data Parallelism to Speed-Up Massive Time-Dependent Shortest-Path Computations}}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, pages = {9:1--9:18}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-128-3}, ISSN = {2190-6807}, year = {2019}, volume = {75}, editor = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.9}, URN = {urn:nbn:de:0030-drops-114210}, doi = {10.4230/OASIcs.ATMOS.2019.9}, annote = {Keywords: amorphous data parallelism, delta-stepping algorithm, travel-time oracle, many-to-all shortest paths, time-dependent road networks} }
Demian Hespe and Peter Sanders. More Hierarchy in Route Planning Using Edge Hierarchies. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{hespe_et_al:OASIcs.ATMOS.2019.10, author = {Hespe, Demian and Sanders, Peter}, title = {{More Hierarchy in Route Planning Using Edge Hierarchies}}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, pages = {10:1--10:14}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-128-3}, ISSN = {2190-6807}, year = {2019}, volume = {75}, editor = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.10}, URN = {urn:nbn:de:0030-drops-114228}, doi = {10.4230/OASIcs.ATMOS.2019.10}, annote = {Keywords: shortest path, hierarchy, road networks, preprocessing} }
Barbara M. Anthony, Sara Boyd, Ricky Birnbaum, Ananya Christman, Christine Chung, Patrick Davis, Jigar Dhimar, and David Yuen. Maximizing the Number of Rides Served for Dial-a-Ride. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{anthony_et_al:OASIcs.ATMOS.2019.11, author = {Anthony, Barbara M. and Birnbaum, Ricky and Boyd, Sara and Christman, Ananya and Chung, Christine and Davis, Patrick and Dhimar, Jigar and Yuen, David}, title = {{Maximizing the Number of Rides Served for Dial-a-Ride}}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, pages = {11:1--11:15}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-128-3}, ISSN = {2190-6807}, year = {2019}, volume = {75}, editor = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.11}, URN = {urn:nbn:de:0030-drops-114237}, doi = {10.4230/OASIcs.ATMOS.2019.11}, annote = {Keywords: dial-a-ride, revenue maximization, approximation algorithm, vehicle routing} }
Ricardo Euler and Ralf Borndörfer. A Graph- and Monoid-Based Framework for Price-Sensitive Routing in Local Public Transportation Networks. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{euler_et_al:OASIcs.ATMOS.2019.12, author = {Euler, Ricardo and Bornd\"{o}rfer, Ralf}, title = {{A Graph- and Monoid-Based Framework for Price-Sensitive Routing in Local Public Transportation Networks}}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, pages = {12:1--12:15}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-128-3}, ISSN = {2190-6807}, year = {2019}, volume = {75}, editor = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.12}, URN = {urn:nbn:de:0030-drops-114243}, doi = {10.4230/OASIcs.ATMOS.2019.12}, annote = {Keywords: shortest path, public transit, optimization, price-sensitive, raptor, fare, operations research} }
Vassilissa Lehoux and Darko Drakulic. Mode Personalization in Trip-Based Transit Routing. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 13:1-13:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{lehoux_et_al:OASIcs.ATMOS.2019.13, author = {Lehoux, Vassilissa and Drakulic, Darko}, title = {{Mode Personalization in Trip-Based Transit Routing}}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, pages = {13:1--13:15}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-128-3}, ISSN = {2190-6807}, year = {2019}, volume = {75}, editor = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.13}, URN = {urn:nbn:de:0030-drops-114256}, doi = {10.4230/OASIcs.ATMOS.2019.13}, annote = {Keywords: Public transit, Route planning, Personalization} }
Lehilton L. C. Pedrosa, Greis Y. O. Quesquén, and Rafael C. S. Schouery. An Asymptotically Optimal Approximation Algorithm for the Travelling Car Renter Problem. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{pedrosa_et_al:OASIcs.ATMOS.2019.14, author = {Pedrosa, Lehilton L. C. and Quesqu\'{e}n, Greis Y. O. and Schouery, Rafael C. S.}, title = {{An Asymptotically Optimal Approximation Algorithm for the Travelling Car Renter Problem}}, booktitle = {19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)}, pages = {14:1--14:15}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-128-3}, ISSN = {2190-6807}, year = {2019}, volume = {75}, editor = {Cacchiani, Valentina and Marchetti-Spaccamela, Alberto}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.14}, URN = {urn:nbn:de:0030-drops-114263}, doi = {10.4230/OASIcs.ATMOS.2019.14}, annote = {Keywords: Approximation Algorithm, Travelling Car Renter Problem, LP-rounding, Separation Problem} }
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