@article{SanyalWernerZiegler2009, author = {Sanyal, Raman and Werner, Axel and Ziegler, G{\"u}nter}, title = {On Kalai's conjectures concerning centrally symmetric polytopes.}, volume = {41}, journal = {Discrete Comput. Geom.}, number = {2}, doi = {10.1007/s00454-008-9104-8}, pages = {183 -- 198}, year = {2009}, language = {en} } @inproceedings{BentzMartensOrlowskietal.2010, author = {Bentz, Winfried and Martens, Maren and Orlowski, Sebastian and Werner, Axel and Wess{\"a}ly, Roland}, title = {FTTx-PLAN}, volume = {220}, booktitle = {Breitbandversorgung in Deutschland}, publisher = {VDE-Verlag}, year = {2010}, language = {en} } @article{BrandtBrandt1999, author = {Brandt, Andreas and Brandt, Manfred}, title = {On a two-queue priority system with impatience and its application to a call center}, volume = {1}, journal = {Methodol. Comput. Appl. Probab.}, pages = {191 -- 210}, year = {1999}, language = {en} } @article{BrandtBrandt1994, author = {Brandt, Andreas and Brandt, Manfred}, title = {On the distribution of the number of packets in the fluid flow approximation of packet arrival streams}, volume = {17}, journal = {Queueing Syst.}, pages = {275 -- 315}, year = {1994}, language = {en} } @phdthesis{Werner2009, author = {Werner, Axel}, title = {Linear constraints on face numbers of polytopes}, year = {2009}, language = {en} } @phdthesis{Achterberg2009, author = {Achterberg, Tobias}, title = {Constraint Integer Programming}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11129}, year = {2009}, abstract = {This thesis introduces the novel paradigm of "constraint integer programming" (CIP), which integrates constraint programming (CP) and mixed integer programming (MIP) modeling and solving techniques. It is supplemented by the software SCIP, which is a solver and framework for constraint integer programming that also features SAT solving techniques. SCIP is freely available in source code for academic and non-commercial purposes. Our constraint integer programming approach is a generalization of MIP that allows for the inclusion of arbitrary constraints, as long as they turn into linear constraints on the continuous variables after all integer variables have been fixed. The constraints, may they be linear or more complex, are treated by any combination of CP and MIP techniques: the propagation of the domains by constraint specific algorithms, the generation of a linear relaxation and its solving by LP methods, and the strengthening of the LP by cutting plane separation. The current version of SCIP comes with all of the necessary components to solve mixed integer programs. In the thesis, we cover most of these ingredients and present extensive computational results to compare different variants for the individual building blocks of a MIP solver. We focus on the algorithms and their impact on the overall performance of the solver. In addition to mixed integer programming, the thesis deals with chip design verification, which is an important topic of electronic design automation. Chip manufacturers have to make sure that the logic design of a circuit conforms to the specification of the chip. Otherwise, the chip would show an erroneous behavior that may cause failures in the device where it is employed. An important subproblem of chip design verification is the property checking problem, which is to verify whether a circuit satisfies a specified property. We show how this problem can be modeled as constraint integer program and provide a number of problem-specific algorithms that exploit the structure of the individual constraints and the circuit as a whole. Another set of extensive computational benchmarks compares our CIP approach to the current state-of-the-art SAT methodology and documents the success of our method.}, language = {en} } @misc{BertholdHeinzVigerske2009, author = {Berthold, Timo and Heinz, Stefan and Vigerske, Stefan}, title = {Extending a CIP framework to solve MIQCPs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11371}, number = {09-23}, year = {2009}, abstract = {This paper discusses how to build a solver for mixed integer quadratically constrained programs (MIQCPs) by extending a framework for constraint integer programming (CIP). The advantage of this approach is that we can utilize the full power of advanced MIP and CP technologies. In particular, this addresses the linear relaxation and the discrete components of the problem. For relaxation, we use an outer approximation generated by linearization of convex constraints and linear underestimation of nonconvex constraints. Further, we give an overview of the reformulation, separation, and propagation techniques that are used to handle the quadratic constraints efficiently. We implemented these methods in the branch-cut-and-price framework SCIP. Computational experiments indicates the potential of the approach.}, language = {en} } @misc{BorndoerferGroetschelJaeger2009, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Jaeger, Ulrich}, title = {Planning Problems in Public Transit}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11252}, number = {09-13}, year = {2009}, abstract = {Every day, millions of people are transported by buses, trains, and airplanes in Germany. Public transit (PT) is of major importance for the quality of life of individuals as well as the productivity of entire regions. Quality and efficiency of PT systems depend on the political framework (state-run, market oriented) and the suitability of the infrastructure (railway tracks, airport locations), the existing level of service (timetable, flight schedule), the use of adequate technologies (information, control, and booking systems), and the best possible deployment of equipment and resources (energy, vehicles, crews). The decision, planning, and optimization problems arising in this context are often gigantic and "scream" for mathematical support because of their complexity. This article sketches the state and the relevance of mathematics in planning and operating public transit, describes today's challenges, and suggests a number of innovative actions. The current contribution of mathematics to public transit is — depending on the transportation mode — of varying depth. Air traffic is already well supported by mathematics. Bus traffic made significant advances in recent years, while rail traffic still bears significant opportunities for improvements. In all areas of public transit, the existing potentials are far from being exhausted. For some PT problems, such as vehicle and crew scheduling in bus and air traffic, excellent mathematical tools are not only available, but used in many places. In other areas, such as rolling stock rostering in rail traffic, the performance of the existing mathematical algorithms is not yet sufficient. Some topics are essentially untouched from a mathematical point of view; e.g., there are (except for air traffic) no network design or fare planning models of practical relevance. PT infrastructure construction is essentially devoid of mathematics, even though enormous capital investments are made in this area. These problems lead to questions that can only be tackled by engineers, economists, politicians, and mathematicians in a joint effort. Among other things, the authors propose to investigate two specific topics, which can be addressed at short notice, are of fundamental importance not only for the area of traffic planning, should lead to a significant improvement in the collaboration of all involved parties, and, if successful, will be of real value for companies and customers: • discrete optimal control: real-time re-planning of traffic systems in case of disruptions, • model integration: service design in bus and rail traffic. Work on these topics in interdisciplinary research projects could be funded by the German ministry of research and education (BMBF), the German ministry of economics (BMWi), or the German science foundation (DFG).}, language = {en} } @misc{BrandtBrandt2009, author = {Brandt, Manfred and Brandt, Andreas}, title = {On sojourn times in M/GI systems under state-dependent processor sharing}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11366}, number = {09-22}, year = {2009}, abstract = {We consider a system with Poisson arrivals and i.i.d. service times. The requests are served according to the state-dependent processor sharing discipline, where each request receives a service capacity which depends on the actual number of requests in the system. The linear systems of PDEs describing the residual and attained sojourn times coincide for this system, which provides time reversibility including sojourn times for this system, and their minimal non negative solution gives the LST of the sojourn time \$V(\tau)\$ of a request with required service time \$\tau\$. For the case that the service time distribution is exponential in a neighborhood of zero, we derive a linear system of ODEs, whose minimal non negative solution gives the LST of \$V(\tau)\$, and which yields linear systems of ODEs for the moments of \$V(\tau)\$ in the considered neighborhood of zero. Numerical results are presented for the variance of \$V(\tau)\$. In case of an M/GI/2-PS system, the LST of \$V(\tau)\$ is given in terms of the solution of a convolution equation in the considered neighborhood of zero. For bounded from below service times, surprisingly simple expressions for the LST and variance of \$V(\tau)\$ in this neighborhood of zero are derived, which yield in particular the LST and variance of \$V(\tau)\$ in M/D/2-PS.}, language = {en} } @misc{LuceDuintjerTebbensLiesenetal.2009, author = {Luce, Robert and Duintjer Tebbens, Jurjen and Liesen, J{\"o}rg and Nabben, Robert and Gr{\"o}tschel, Martin and Koch, Thorsten and Schenk, Olaf}, title = {On the Factorization of Simplex Basis Matrices}, organization = {TU Berlin, Zuse Institute Berlin, University of Basel}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11392}, number = {09-24}, year = {2009}, abstract = {In the simplex algorithm, solving linear systems with the basis matrix and its transpose accounts for a large part of the total computation time. We investigate various methods from modern numerical linear algebra to improve the computation speed of the basis updates arising in LPs. The experiments are executed on a large real-world test set. The most widely used solution technique is sparse LU factorization, paired with an updating scheme that allows to use the factors over several iterations. Clearly, small number of fill-in elements in the LU factors is critical for the overall performance. Using a wide range of LPs we show numerically that after a simple permutation the non-triangular part of the basis matrix is so small, that the whole matrix can be factorized with (relative) fill-in close to the optimum. This permutation has been exploited by simplex practitioners for many years. But to our knowledge no systematic numerical study has been published that demonstrates the effective reduction to a surprisingly small non-triangular problem, even for large scale LPs. For the factorization of the non-triangular part most existing simplex codes use some variant of dynamic Markowitz pivoting, which originated in the late 1950s. We also show numerically that, in terms of fill-in and in the simplex context, dynamic Markowitz is quite consistently superior to other, more recently developed techniques.}, language = {en} } @misc{BorndoerferCardonha2009, author = {Bornd{\"o}rfer, Ralf and Cardonha, Carlos}, title = {A Set Partitioning Approach to Shunting}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11326}, number = {09-18}, year = {2009}, abstract = {The Vehicle Positioning Problem (VPP) is a classical combinatorial optimization problem in public transport planning. A number of models and approaches have been suggested in the literature, which work for small problems, but not for large ones. We propose in this article a novel set partitioning model and an associated column generation solution approach for the VPP. The model provides a tight linear description of the problem. The pricing problem, and hence the LP relaxation itself, can be solved in polynomial resp. pseudo-polynomial time for some versions of the problems.}, language = {en} }