eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-11-15
75
0
0
10.4230/OASIcs.ATMOS.2019
article
OASIcs, Volume 75, ATMOS'19, Complete Volume
Cacchiani, Valentina
1
Marchetti-Spaccamela, Alberto
2
DEI, University of Bologna, Italy
Sapienza University of Rome, Italy
OASIcs, Volume 75, ATMOS'19, Complete Volume
https://drops.dagstuhl.de/storage/01oasics/oasics-vol075-atmos2019/OASIcs.ATMOS.2019/OASIcs.ATMOS.2019.pdf
Theory of computation, Design and analysis of algorithms; Mathematics of computing, Discrete mathematics; Combinatorics; Mathematical optimization;
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-11-15
75
0:i
0:x
10.4230/OASIcs.ATMOS.2019.0
article
Front Matter, Table of Contents, Preface, Conference Organization
Cacchiani, Valentina
1
Marchetti-Spaccamela, Alberto
2
DEI, University of Bologna, Italy
Sapienza University of Rome, Italy
Front Matter, Table of Contents, Preface, Conference Organization
https://drops.dagstuhl.de/storage/01oasics/oasics-vol075-atmos2019/OASIcs.ATMOS.2019.0/OASIcs.ATMOS.2019.0.pdf
Front Matter
Table of Contents
Preface
Conference Organization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-11-15
75
1:1
1:12
10.4230/OASIcs.ATMOS.2019.1
article
A Cut Separation Approach for the Rolling Stock Rotation Problem with Vehicle Maintenance
Grimm, Boris
1
Borndörfer, Ralf
1
Reuther, Markus
2
Schlechte, Thomas
2
Zuse Institute Berlin, Germany
LBW Optimization GmbH, Berlin, Germany
For providing railway services the company’s railway rolling stock is one if not the most important ingredient. It decides about the number of passenger or cargo trips the company can offer, about the quality a passenger experiences the train ride and it is often related to the image of the company itself. Thus, it is highly desired to have the available rolling stock in the best shape possible. Moreover, in many countries, as Germany where our industrial partner DB Fernverkehr AG (DBF) is located, laws enforce regular vehicle inspections to ensure the safety of the passengers. This leads to rolling stock optimization problems with complex rules for vehicle maintenance. This problem is well studied in the literature for example see [Maróti and Kroon, 2005; Gábor Maróti and Leo G. Kroon, 2007], or [Cordeau et al., 2001] for applications including vehicle maintenance. The contribution of this paper is a new algorithmic approach to solve the Rolling Stock Rotation Problem for the ICE high speed train fleet of DBF with included vehicle maintenance. It is based on a relaxation of a mixed integer linear programming model with an iterative cut generation to enforce the feasibility of a solution of the relaxation in the solution space of the original problem. The resulting mixed integer linear programming model is based on a hypergraph approach presented in [Ralf Borndörfer et al., 2015]. The new approach is tested on real world instances modeling different scenarios for the ICE high speed train network in Germany and compared to the approaches of [Reuther, 2017] that are in operation at DB Fernverkehr AG. The approach shows a significant reduction of the run time to produce solutions with comparable or even better objective function values.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol075-atmos2019/OASIcs.ATMOS.2019.1/OASIcs.ATMOS.2019.1.pdf
Railway Operations Research
Integer Programming
Infeasible Path Cuts
Cut Separation
Rolling Stock Rotation Problem
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-11-15
75
2:1
2:18
10.4230/OASIcs.ATMOS.2019.2
article
New Perspectives on PESP: T-Partitions and Separators
Lindner, Niels
1
Liebchen, Christian
2
Zuse Institute Berlin (ZIB), Takustr. 7, 14195 Berlin, Germany
Technical University of Applied Sciences Wildau, Hochschulring 1, 15745 Wildau, Germany
In the planning process of public transportation companies, designing the timetable is among the core planning steps. In particular in the case of periodic (or cyclic) services, the Periodic Event Scheduling Problem (PESP) is well-established to compute high-quality periodic timetables.
We are considering algorithms for computing good solutions and dual bounds for the very basic PESP with no additional extra features as add-ons. The first of these algorithms generalizes several primal heuristics that have been proposed, such as single-node cuts and the modulo network simplex algorithm. We consider partitions of the graph, and identify so-called delay cuts as a structure that allows to generalize several previous heuristics. In particular, when no more improving delay cut can be found, we already know that the other heuristics could not improve either. This heuristic already had been proven to be useful in computational experiments [Ralf Borndörfer et al., 2019], and we locate it in the more general concept of what we denote T-partitions.
With the second of these algorithms we propose to turn a strategy, that has been discussed in the past, upside-down: Instead of gluing together the network line-by-line in a bottom-up way, we develop a divide-and-conquer-like top-down approach to separate the initial problem into two easier subproblems such that the information loss along their cutset edges is as small as possible.
We are aware that there may be PESP instances that do not fit well the separator setting. Yet, on the RxLy-instances of PESPlib in our experimental computations, we come up with good primal solutions and dual bounds. In particular, on the largest instance (R4L4), this new separator approach, which applies a state-of-the-art solver as subroutine, is able to come up with better dual bounds than purely applying this state-of-the-art solver in the very same time.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol075-atmos2019/OASIcs.ATMOS.2019.2/OASIcs.ATMOS.2019.2.pdf
Periodic Event Scheduling Problem
Periodic Timetabling
Graph Partitioning
Graph Separators
Balanced Cuts
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-11-15
75
3:1
3:12
10.4230/OASIcs.ATMOS.2019.3
article
On Sorting with a Network of Two Stacks
Mihalák, Matúš
1
https://orcid.org/0000-0002-1898-607X
Pont, Marc
1
Department of Data Science and Knowledge Engineering, Maastricht University, The Netherlands
Sorting with stacks is a collection of problems that deal with sorting a sequence of numbers by pushing and popping the numbers to and from a given set of stacks. Multiple concrete decision or optimization questions are formed by restricting the access to the stacks. The motivation comes, e.g., from shunting train wagons in shunting yards, shunting trams in depots, or in stacking cargo containers on cargo ships or storage yards in transshipment terminals.
We consider the problem of sorting a permutation of n integers 1,2,...,n using k >= 2 stacks. In this problem, elements from the input sequence are pushed one-by-one (in the order of the elements in the sequence) to one of the k stacks. At any time, an element from a stack can be popped and pushed to another stack; such an operation is called a shuffle. Also, at any time, an element can be popped from a stack and placed to the output sequence. We can only place the elements to the output in the increasing order of their value such that at the end the output is the ordered sequence of the elements. The problem asks to minimize the number of shuffles in the process.
It is known that for k >= 4, the problem is NP-hard, and that there is no approximation algorithm unless P=NP. For k >= 3, it is known that at most O(n log n) shuffles are needed for any input sequence. For the case when k=2, there exist input sequences that require Omega(n^{2-epsilon}) shuffles, for any epsilon>0. Nothing substantially more is known for the case of k=2. In this paper, we study the following variant of the problem with k=2 stacks: no shuffle and no placement to the output sequence can happen before every element is in one of the two stacks. We show that our problem can be seen as the MinUnCut problem by providing a polynomial-time reduction, and thus we show that there exists a randomized O(sqrt{log n})-approximation algorithm and a deterministic O(log n)-approximation algorithm for our problem.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol075-atmos2019/OASIcs.ATMOS.2019.3/OASIcs.ATMOS.2019.3.pdf
Sorting
Stacks
Optimization
Algorithms
Reduction
MinUnCut
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-11-15
75
4:1
4:18
10.4230/OASIcs.ATMOS.2019.4
article
Routing in Stochastic Public Transit Networks
Geissmann, Barbara
1
Gianinazzi, Lukas
1
Department of Computer Science, ETH Zurich, Switzerland
We present robust, adaptive routing policies for time-varying networks (temporal graphs) in the presence of random edge-failures. Such a policy answers the following question: How can a traveler navigate a time-varying network where edges fail randomly in order to maximize the traveler’s preference with respect to the arrival time? Our routing policy is computable in near-linear time in the number of edges in the network (for the case when the edges fail independently of each other).
Using our robust routing policy, we show how to travel in a public transit network where the vehicles experience delays. To validate our approach, we present experiments using real-world delay data from the public transit network of the city of Zurich. Our experiments show that we obtain significantly improved outcomes compared to a purely schedule-based policy: The traveler is on time 5-11 percentage points more often for most destinations and 20-40 percentage points more often for certain remote destinations. Our implementation shows that the approach is fast enough for real-time usage. It computes a policy for 1-hour long journeys in around 0.1 seconds.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol075-atmos2019/OASIcs.ATMOS.2019.4/OASIcs.ATMOS.2019.4.pdf
Route Planning
Public Transit Network
Temporal Graphs
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-11-15
75
5:1
5:13
10.4230/OASIcs.ATMOS.2019.5
article
Robust Network Capacity Expansion with Non-Linear Costs
Garuba, Francis
1
Goerigk, Marc
2
Jacko, Peter
1
Department of Management Science, Lancaster University, United Kingdom
Network and Data Science Management, University of Siegen, Germany, Germany
The network capacity expansion problem is a key network optimization problem practitioners regularly face. There is an uncertainty associated with the future traffic demand, which we address using a scenario-based robust optimization approach. In most literature on network design, the costs are assumed to be linear functions of the added capacity, which is not true in practice. To address this, two non-linear cost functions are investigated: (i) a linear cost with a fixed charge that is triggered if any arc capacity is modified, and (ii) its generalization to piecewise-linear costs. The resulting mixed-integer programming model is developed with the objective of minimizing the costs.
Numerical experiments were carried out for networks taken from the SNDlib database. We show that networks of realistic sizes can be designed using non-linear cost functions on a standard computer in a practical amount of time within negligible suboptimality. Although solution times increase in comparison to a linear-cost or to a non-robust model, we find solutions to be beneficial in practice. We further illustrate that including additional scenarios follows the law of diminishing returns, indicating that little is gained by considering more than a handful of scenarios. Finally, we show that the results of a robust optimization model compare favourably to the traditional deterministic model optimized for the best-case, expected, or worst-case traffic demand, suggesting that it should be used whenever computationally feasible.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol075-atmos2019/OASIcs.ATMOS.2019.5/OASIcs.ATMOS.2019.5.pdf
Robust Optimization
Mobile Network
Network Capacity Design & Expansion
Non-linear Cost
Traffic and Transport Routing
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-11-15
75
6:1
6:15
10.4230/OASIcs.ATMOS.2019.6
article
The Trickle-In Effect: Modeling Passenger Behavior in Delay Management
Schöbel, Anita
1
2
Pätzold, Julius
3
Müller, Jörg P.
4
Technical University of Kaiserslautern, Germany
Fraunhofer Institute for Industrial Mathematics ITWM, Kaiserslautern, Germany
University of Goettingen, Germany
Department of Informatics, Clausthal University of Technology, Germany
Delay management is concerned with making decisions if a train should wait for passengers from delayed trains or if it should depart on time. Models for delay management exist and can be adapted to capacities of stations, capacities of tracks, or respect vehicle and driver schedules, passengers' routes and further constraints. Nevertheless, what has been neglected so far, is that a train cannot depart as planned if passengers from another train trickle in one after another such that the doors of the departing train cannot close. This effect is often observed in real-world, but has not yet been taken into account in delay management.
We show the impact of this "trickle-in" effect to departure delays of trains under different conditions. We then modify existing delay management models to take the trickle-in effect into account. This can be done by forbidding certain intervals for departure. We present an integer programming formulation with these additional constraints resulting in a generalization of classic delay management models. We analyze the resulting model and identify parameters with which it can be best approximated by the classical delay management problem.
Experimentally, we show that the trickle-in effect has a high impact on the overall delay of public transport systems. We discuss the impact of the trickle-in effect on the objective function value and on the computation time of the delay management problem. We also analyze the trickle-in effect for timetables which have been derived without taking this particular behavioral pattern of passengers into account.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol075-atmos2019/OASIcs.ATMOS.2019.6/OASIcs.ATMOS.2019.6.pdf
Public Transport Planning
Delay Management
Integer Programming
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-11-15
75
7:1
7:14
10.4230/OASIcs.ATMOS.2019.7
article
Vehicle Capacity-Aware Rerouting of Passengers in Delay Management
Müller-Hannemann, Matthias
1
https://orcid.org/0000-0001-6976-0006
Rückert, Ralf
1
Schmidt, Sebastian S.
1
https://orcid.org/0000-0003-4878-2809
Institut für Informatik, Martin-Luther-Universität Halle-Wittenberg, Von-Seckendorff-Platz 1, D 06120 Halle (Saale), Germany
Due to the significant growth in passenger numbers, higher vehicle load factors and crowding become more and more of an issue in public transport. For safety reasons and because of an unsatisfactory discomfort, standing of passengers is rather limited in high-speed long-distance trains. In case of delays and (partially) cancelled trains, many passengers have to be rerouted. State-of-the-art rerouting merely focuses on minimizing delay at the destination of affected passengers but neglects limited vehicle capacities and crowding. Not considering capacities allows using highly efficient shortest path algorithms like RAPTOR or the connection scan algorithm (CSA).
In this paper, we study the more complicated scenario where passengers compete for scarce capacities. This can be modeled as a piece-wise linear, convex cost multi-source multi-commodity unsplittable flow problem where each passenger group which has to be rerouted corresponds to a commodity. We compare a path-based integer linear programming (ILP) model with a heuristic greedy approach. In experiments with instances from German long-distance train traffic, we quantify the importance of considering vehicle capacities in case of train cancellations. We observe a tradeoff: The ILP approach slightly outperforms the greedy approach and both are much better than capacity unaware rerouting in quality, while the greedy algorithm runs more than three times faster.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol075-atmos2019/OASIcs.ATMOS.2019.7/OASIcs.ATMOS.2019.7.pdf
Delay management
passenger flows
vehicle capacities
rerouting
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-11-15
75
8:1
8:14
10.4230/OASIcs.ATMOS.2019.8
article
A Priori Search Space Pruning in the Flight Planning Problem
Schienle, Adam
1
Maristany, Pedro
1
Blanco, Marco
2
Zuse Institute Berlin, Berlin, Germany
Lufthansa Systems, Raunheim, Germany
We study the Flight Planning Problem for a single aircraft, where we look for a minimum cost path in the airway network, a directed graph. Arc evaluation, such as weather computation, is computationally expensive due to non-linear functions, but required for exactness. We propose several pruning methods to thin out the search space for Dijkstra’s algorithm before the query commences. We do so by using innate problem characteristics such as an aircraft’s tank capacity, lower and upper bounds on the total costs, and in particular, we present a method to reduce the search space even in the presence of regional crossing costs.
We test all pruning methods on real-world instances, and show that incorporating crossing costs into the pruning process can reduce the number of nodes by 90% in our setting.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol075-atmos2019/OASIcs.ATMOS.2019.8/OASIcs.ATMOS.2019.8.pdf
time-dependent shortest path problem
crossing costs
flight trajectory optimization
preprocessing
search space
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-11-15
75
9:1
9:18
10.4230/OASIcs.ATMOS.2019.9
article
Exploiting Amorphous Data Parallelism to Speed-Up Massive Time-Dependent Shortest-Path Computations
Kontogiannis, Spyros
1
2
Papadopoulos, Anastasios
3
Paraskevopoulos, Andreas
3
Zaroliagis, Christos
3
2
University of Ioannina, Greece
Computer Technology Institute & Press, Rion, Greece
University of Patras, Greece
We aim at exploiting parallelism in shared-memory multiprocessing systems, in order to speed up the execution time with as small redundancy in work as possible, for an elementary task that comes up frequently as a subroutine in the daily maintenance of large-scale time-dependent graphs representing real-world relationships or technological networks: the many-to-all time-dependent shortest paths (MATDSP) problem. MATDSP requires the computation of one time-dependent shortest-path tree (TDSPT) per origin-vertex and departure-time, from an arbitrary collection of pairs of origins and departure-times, towards all reachable destinations in the graph.
Our goal is to explore the potential and highlight the limitations of amorphous data parallelism, when dealing with MATDSP in multicore computing environments with a given amount of processing elements and a shared memory to exploit. Apart from speeding-up execution time, consumption of resources (and energy) is also critical. Therefore, we aim at limiting the work overhead for solving a MATDSP instance, as measured by the overall number of arc relaxations in shortest-path computations, while trying to minimize the overall execution time. Towards this direction, we provide several algorithmic engineering interventions for solving MATDSP concerning: (i) the compact representation of the instance; (ii) the choice and the improvement of the time-dependent single-source shortest path algorithm that is used as a subroutine; (iii) the way according to which the overall work is allocated to the processing elements; (iv) the adoption of the amorphous data parallelism rationale, in order to avoid costly synchronization among the processing elements while doing their own part of the work.
Our experimental evaluations, both on real-world and on synthetic benchmark instances of time-dependent road networks, provide insight how one should organize heavy MATDSP computations, depending on the application scenario. This insight is in some cases rather unexpected. For instance, it is not always the case that pure data parallelism (among otherwise totally independent processors) is the best choice for minimizing execution times. In certain cases it may be worthwhile to limit the level of data parallelism in favor of algorithmic parallelism, in order to achieve more efficient MATDSP computations.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol075-atmos2019/OASIcs.ATMOS.2019.9/OASIcs.ATMOS.2019.9.pdf
amorphous data parallelism
delta-stepping algorithm
travel-time oracle
many-to-all shortest paths
time-dependent road networks
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-11-15
75
10:1
10:14
10.4230/OASIcs.ATMOS.2019.10
article
More Hierarchy in Route Planning Using Edge Hierarchies
Hespe, Demian
1
2
Sanders, Peter
1
2
Karlsruhe Institute of Technology, Germany
www.kit.edu
A highly successful approach to route planning in networks (particularly road networks) is to identify a hierarchy in the network that allows faster queries after some preprocessing that basically inserts additional "shortcut"-edges into a graph. In the past there has been a succession of techniques that infer a more and more fine grained hierarchy enabling increasingly more efficient queries. This appeared to culminate in contraction hierarchies that assign one hierarchy level to each vertex.
In this paper we show how to identify an even more fine grained hierarchy that assigns one level to each edge of the network. Our findings indicate that this can lead to considerably smaller search spaces in terms of visited edges. Currently, this rarely implies improved query times so that it remains an open question whether edge hierarchies can lead to consistently improved performance. However, we believe that the technique as such is a noteworthy enrichment of the portfolio of available techniques that might prove useful in the future.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol075-atmos2019/OASIcs.ATMOS.2019.10/OASIcs.ATMOS.2019.10.pdf
shortest path
hierarchy
road networks
preprocessing
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-11-15
75
11:1
11:15
10.4230/OASIcs.ATMOS.2019.11
article
Maximizing the Number of Rides Served for Dial-a-Ride
Anthony, Barbara M.
1
https://orcid.org/0000-0002-2493-1251
Birnbaum, Ricky
2
Boyd, Sara
1
Christman, Ananya
3
https://orcid.org/0000-0001-9445-1475
Chung, Christine
2
https://orcid.org/0000-0003-3580-9275
Davis, Patrick
2
Dhimar, Jigar
2
Yuen, David
4
Southwestern University, Georgetown TX 78626, USA
Connecticut College, New London CT 06320, USA
Middlebury College, Middlebury VT 05753, USA
Kapolei HI 96707, USA
We study a variation of offline Dial-a-Ride, where each request has not only a source and destination, but also a revenue that is earned for serving the request. We investigate this problem for the uniform metric space with uniform revenues. While we present a study on a simplified setting of the problem that has limited practical applications, this work provides the theoretical foundation for analyzing the more general forms of the problem. Since revenues are uniform the problem is equivalent to maximizing the number of served requests. We show that the problem is NP-hard and present a 2/3 approximation algorithm. We also show that a natural generalization of this algorithm has an approximation ratio at most 7/9.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol075-atmos2019/OASIcs.ATMOS.2019.11/OASIcs.ATMOS.2019.11.pdf
dial-a-ride
revenue maximization
approximation algorithm
vehicle routing
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-11-15
75
12:1
12:15
10.4230/OASIcs.ATMOS.2019.12
article
A Graph- and Monoid-Based Framework for Price-Sensitive Routing in Local Public Transportation Networks
Euler, Ricardo
1
https://orcid.org/0000-0001-5112-4191
Borndörfer, Ralf
1
Zuse Institute Berlin, Germany
We present a novel framework to mathematically describe the fare systems of local public transit companies. The model allows the computation of a provably cheapest itinerary even if prices depend on a number of parameters and non-linear conditions. Our approach is based on a ticket graph model to represent tickets and their relation to each other. Transitions between tickets are modeled via transition functions over partially ordered monoids and a set of symbols representing special properties of fares (e.g. surcharges). Shortest path algorithms rely on the subpath optimality property. This property is usually lost when dealing with complicated fare systems. We restore it by relaxing domination rules for tickets depending on the structure of the ticket graph. An exemplary model for the fare system of Mitteldeutsche Verkehrsbetriebe (MDV) is provided. By integrating our framework in the multi-criteria RAPTOR algorithm we provide a price-sensitive algorithm for the earliest arrival problem and assess its performance on data obtained from MDV. We discuss three preprocessing techniques that improve run times enough to make the algorithm applicable for real-time queries.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol075-atmos2019/OASIcs.ATMOS.2019.12/OASIcs.ATMOS.2019.12.pdf
shortest path
public transit
optimization
price-sensitive
raptor
fare
operations research
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-11-15
75
13:1
13:15
10.4230/OASIcs.ATMOS.2019.13
article
Mode Personalization in Trip-Based Transit Routing
Lehoux, Vassilissa
1
Drakulic, Darko
1
NAVER LABS Europe, Meylan, France
We study the problem of finding bi-criteria Pareto optimal journeys in public transit networks. We extend the Trip-Based Public Transit Routing (TB) approach [Sascha Witt, 2015] to allow for users to select modes of interest at query time. As a first step, we modify the preprocessing of the TB method for it to be correct for any set of selected modes. Then, we change the bi-criteria earliest arrival time queries, and propose a similar algorithm for latest departure time queries, that can handle the definition of the allowed mode set at query time. Experiments are run on 3 networks of different sizes to evaluate the cost of allowing for mode personalization. They show that although preprocessing times are increased, query times are similar when all modes are allowed and lower when some part of the network is removed by mode selection.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol075-atmos2019/OASIcs.ATMOS.2019.13/OASIcs.ATMOS.2019.13.pdf
Public transit
Route planning
Personalization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-11-15
75
14:1
14:15
10.4230/OASIcs.ATMOS.2019.14
article
An Asymptotically Optimal Approximation Algorithm for the Travelling Car Renter Problem
Pedrosa, Lehilton L. C.
1
https://orcid.org/0000-0003-1001-082X
Quesquén, Greis Y. O.
1
https://orcid.org/0000-0003-0112-8009
Schouery, Rafael C. S.
1
https://orcid.org/0000-0002-0472-4810
Institute of Computing, University of Campinas, SP, Brazil
In the classical Travelling Salesman Problem (TSP), one wants to find a route that visits a set of n cities, such that the total travelled distance is minimum. An often considered generalization is the Travelling Car Renter Problem (CaRS), in which the route is travelled by renting a set of cars and the cost to travel between two given cities depends on the car that is used. The car renter may choose to swap vehicles at any city, but must pay a fee to return the car to its pickup location. This problem appears in logistics and urban transportation when the vehicles can be provided by multiple companies, such as in the tourism sector. In this paper, we consider the case in which the return fee is some fixed number g >= 0, which we call the Uniform CaRS (UCaRS). We show that, already for this version, there is no o(log n)-approximation algorithm unless P = NP. The main contribution is an O(log n)-approximation algorithm for the problem, which is based on the randomized rounding of an exponentially large LP-relaxation.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol075-atmos2019/OASIcs.ATMOS.2019.14/OASIcs.ATMOS.2019.14.pdf
Approximation Algorithm
Travelling Car Renter Problem
LP-rounding
Separation Problem