@misc{Elijazyfer2018, type = {Master Thesis}, author = {Elijazyfer, Ziena}, title = {L{\"a}ngenbeschr{\"a}nkte Teilgraphenbildung zur Maut-Kontrollstreckenoptimierung}, year = {2018}, language = {de} } @misc{Schreck2018, type = {Master Thesis}, author = {Schreck, Vanessa}, title = {Algorithmic Analysis of the Graph Segmentation Problem}, year = {2018}, language = {en} } @article{Schwartz2022, author = {Schwartz, Stephan}, title = {An overview of graph covering and partitioning}, volume = {345}, journal = {Discrete Mathematics}, number = {8}, doi = {https://doi.org/10.1016/j.disc.2022.112884}, year = {2022}, abstract = {While graph covering is a fundamental and well-studied problem, this field lacks a broad and unified literature review. The holistic overview of graph covering given in this article attempts to close this gap. The focus lies on a characterization and classification of the different problems discussed in the literature. In addition, notable results and common approaches are also included. Whenever appropriate, this review extends to the corresponding partitioning problems.}, language = {en} } @misc{SchwartzBalestrieriBorndoerfer2018, author = {Schwartz, Stephan and Balestrieri, Leonardo and Bornd{\"o}rfer, Ralf}, title = {On Finding Subpaths With High Demand}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69280}, year = {2018}, abstract = {We study the problem of finding subpaths with high demand in a given network that is traversed by several users. The demand of a subpath is the number of users who completely cover this subpath during their trip. Especially with large instances, an efficient algorithm for computing all subpaths' demands is necessary. We introduce a path-graph to prevent multiple generations of the same subpath and give a recursive approach to compute the demands of all subpaths. Our runtime analysis shows, that the presented approach compares very well against the theoretical minimum runtime.}, language = {en} } @inproceedings{SchwartzBorndoerferBalestrieri2018, author = {Schwartz, Stephan and Bornd{\"o}rfer, Ralf and Balestrieri, Leonardo}, title = {On Finding Subpaths With High Demand}, booktitle = {Operations Research Proceedings 2017}, publisher = {Springer International Publishing}, pages = {355 -- 360}, year = {2018}, abstract = {We study the problem of finding subpaths with high demand in a given network that is traversed by several users. The demand of a subpath is the number of users who completely cover this subpath during their trip. Especially with large instances, an efficient algorithm for computing all subpaths' demands is necessary. We introduce a path-graph to prevent multiple generations of the same subpath and give a recursive approach to compute the demands of all subpaths. Our runtime analysis shows, that the presented approach compares very well against the theoretical minimum runtime.}, language = {en} } @inproceedings{BorndoerferSchwartzBartz2018, author = {Bornd{\"o}rfer, Ralf and Schwartz, Stephan and Bartz, Gerald}, title = {The Graph Segmentation Problem}, volume = {64}, booktitle = {INOC 2017 - 8th International Network Optimization Conference}, pages = {35 -- 44}, year = {2018}, abstract = {We investigate a graph theoretical problem arising in the automatic billing of a network toll. Given a network and a family of user paths, we study the graph segmentation problem (GSP) to cover parts of the user paths by a set of disjoint segments. The GSP is shown to be NP-hard but for special cases it can be solved in polynomial time. We also show that the marginal utility of a segment is bounded. Computational results for real-world instances show that in practice the problem is more amenable than the theoretic bounds suggest.}, language = {en} } @inproceedings{Sagnol2012, author = {Sagnol, Guillaume}, title = {Network-related problems in optimal experimental design and second order cone programming}, volume = {51}, booktitle = {Proceedings of PROBASTAT'2011, Tatra Mountains Mathematical Publications}, doi = {10.2478/v10127-012-0016-x}, pages = {161 -- 171}, year = {2012}, abstract = {In the past few years several applications of optimal experimental designs have emerged to optimize the measurements in communication networks. The optimal design problems arising from this kind of applications share three interesting properties: (i) measurements are only available at a small number of locations of the network; (ii) each monitor can simultaneously measure several quantities, which can be modeled by ``multiresponse experiments"; (iii) the observation matrices depend on the topology of the network. In this paper, we give an overview of these experimental design problems and recall recent results for the computation of optimal designs by Second Order Cone Programming (SOCP). New results for the network-monitoring of a discrete time process are presented. In particular, we show that the optimal design problem for the monitoring of an AR1 process can be reduced to the standard form and we give experimental results.}, language = {en} } @misc{Schwartz2013, type = {Master Thesis}, author = {Schwartz, Stephan}, title = {Bilevel Programming to Optimize the Use of Traffic Control Gantries for Toll Enforcement}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54180}, year = {2013}, language = {en} } @misc{BorndoerferBuwayaSagnoletal.2014, author = {Bornd{\"o}rfer, Ralf and Buwaya, Julia and Sagnol, Guillaume and Swarat, Elmar}, title = {Network Spot Checking Games: Theory and Application to Toll Enforcing in Transportation Networks}, issn = {1438-0064}, doi = {10.1002/net.21596}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-47139}, year = {2014}, abstract = {We introduce the class of spot-checking games (SC games). These games model problems where the goal is to distribute fare inspectors over a toll network. In an SC game, the pure strategies of network users correspond to paths in a graph, and the pure strategies of the inspectors are subset of edges to be controlled. Although SC games are not zero-sum, we show that a Nash equilibrium can be computed by linear programming. The computation of a strong Stackelberg equilibrium is more relevant for this problem, but we show that this is NP-hard. However, we give some bounds on the \emph{price of spite}, which measures how the payoff of the inspector degrades when committing to a Nash equilibrium. Finally, we demonstrate the quality of these bounds for a real-world application, namely the enforcement of a truck toll on German motorways.}, language = {en} } @inproceedings{SchwartzSchlechteSwarat2017, author = {Schwartz, Stephan and Schlechte, Thomas and Swarat, Elmar}, title = {Designing Inspector Rosters with Optimal Strategies}, booktitle = {Operations Research Proceedings 2016}, doi = {10.1007/978-3-319-55702-1_30}, pages = {217 -- 223}, year = {2017}, abstract = {We consider the problem of enforcing a toll on a transportation network with limited inspection resources. We formulate a game theoretic model to optimize the allocation of the inspectors, taking the reaction of the network users into account. The model includes several important aspects for practical operation of the control strategy, such as duty types for the inspectors. In contrast to an existing formulation using flows to describe the users' strategies we choose a path formulation and identify dominated user strategies to significantly reduce the problem size. Computational results suggest that our approach is better suited for practical instances.}, language = {en} }