@misc{MartinWeismantel1998, author = {Martin, Alexander and Weismantel, Robert}, title = {Conjunctive Cuts for Integer Programs}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3618}, number = {SC-98-18}, year = {1998}, abstract = {This paper deals with a family of conjunctive inequalities. Such inequalities are needed to describe the polyhedron associated with all the integer points that satisfy several knapsack constraints simultaneously. Here we demonstrate the strength and potential of conjunctive inequalities in connection with lifting from a computational point of view.}, language = {en} } @misc{BorndoerferEisenblaetterGroetscheletal.1997, author = {Bornd{\"o}rfer, Ralf and Eisenbl{\"a}tter, Andreas and Gr{\"o}tschel, Martin and Martin, Alexander}, title = {Frequency Assignment in Cellular Phone Networks}, doi = {10.1023/A:1018908907763}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3044}, number = {SC-97-35}, year = {1997}, abstract = {We present a graph-theoretic model for the \emph{frequency assignment problem} in Cellular Phone Networks: Obeying several technical and legal restrictions, frequencies have to be assigned to transceivers so that interference is as small as possible. This optimization problem is NP-hard. Good approximation cannot be guaranteed, unless P = NP. We describe several assignment heuristics. These heuristics are simple and not too hard to implement. We give an assessment of the heuristics' efficiency and practical usefulness. For this purpose, typical instances of frequency assignment problems with up to 4240 transceivers and 75 frequencies of a German cellular phone network operator are used. The results are satisfying from a practitioner's point of view. The best performing heuristics were integrated into a network planning system used in practice.}, language = {en} } @misc{MartinWeismantel1997, author = {Martin, Alexander and Weismantel, Robert}, title = {Contributions to General Mixed Integer Knapsack Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3075}, number = {SC-97-38}, year = {1997}, abstract = {This paper deals with a general mixed integer knapsack polyhedron for which we introduce and analyze a new family of inequalities. We discuss the value of this family both from a theoretic and a computational point of view.}, language = {en} } @misc{BrunsGubeladzeHenketal.1998, author = {Bruns, Winfried and Gubeladze, Joseph and Henk, Martin and Martin, Alexander and Weismantel, Robert}, title = {A counterexample to an integer analogue of Caratheodorys theorem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3718}, number = {SC-98-28}, year = {1998}, abstract = {For \$n\geq 6\$ we provide a counterexample to the conjecture that every integral vector of a \$n\$-dimensional integral polyhedral pointed cone \$C\$ can be written as a nonnegative integral combination of at most \$n\$ elements of the Hilbert basis of \$C\$. In fact, we show that in general at least \$\lfloor 7/6 \cdot n \rfloor\$ elements of the Hilbert basis are needed.}, language = {en} } @misc{KochMartinVoss2000, author = {Koch, Thorsten and Martin, Alexander and Voß, Stefan}, title = {SteinLib: An Updated Library on Steiner Tree Problems in Graphs}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6056}, number = {00-37}, year = {2000}, abstract = {In this paper we present the {\em SteinLib}, a library of data sets for the Steiner tree problem in graphs. This library extends former libraries on Steiner tree problems by many new interesting and difficult instances, most of them arising from real-world applications. We give a survey on the difficulty of these problem instances by giving references to state-of-the-art software packages that were the first or are currently among the best to solve these instances.}, language = {en} } @misc{EisenblaetterFuegenschuhKochetal.2002, author = {Eisenbl{\"a}tter, Andreas and F{\"u}genschuh, Armin and Koch, Thorsten and Koster, Arie M.C.A. and Martin, Alexander and Pfender, Tobias and Wegel, Oliver and Wess{\"a}ly, Roland}, title = {Modelling Feasible Network Configurations for UMTS}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6837}, number = {02-16}, year = {2002}, abstract = {A model for the optimisation of the location and configuration of base stations in a UMTS network is described. The focus is primarily on modelling the configuration problem sufficiently accurate using mixed-integer variables and (essentially) linear constraints. These constraints reflect the limited downlink code capacity in each cell, the interference limitations for successful up- and downlink transmissions, the need for sufficiently strong (cell) pilot signals, and the potential gain for mobiles from being in soft(er) hand-over. It is also explained how to use the model as a basis for rating network configurations.}, language = {en} } @misc{AchterbergKochMartin2002, author = {Achterberg, Tobias and Koch, Thorsten and Martin, Alexander}, title = {Branching on History Information}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6990}, number = {02-32}, year = {2002}, abstract = {Mixed integer programs (\$MIPs\$) are commonly solved with branch and bound algorithms based on linear programming. The success and the speed of the algorithm strongly depends on the strategy used to select the branching variables. Today's state-of-the-art strategy is called \emph{pseudocost branching} and uses information of previous branchings to determine the current branching. We propose a modification of \emph{pseudocost branching} which we call \emph{history branching}. This strategy has been implemented in \$SIP\$, a state-of-the-art \$MIP\$ solver. We give computational results that show the superiority of the new strategy.}, language = {en} } @misc{EisenblaetterFuegenschuhGeerdesetal.2003, author = {Eisenbl{\"a}tter, Andreas and F{\"u}genschuh, Armin and Geerdes, Hans-Florian and Junglas, Daniel and Koch, Thorsten and Martin, Alexander}, title = {Optimization Methods for UMTS Radio Network Planning}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7637}, number = {03-41}, year = {2003}, abstract = {The UMTS radio network planning problem poses the challenge of designing a cost-effective network that provides users with sufficient coverage and capacity. We describe an optimization model for this problem that is based on comprehensive planning data of the EU project MOMENTUM. We present heuristic mathematical methods for this realistic model, including computational results.}, language = {en} } @misc{BorndoerferEisenblaetterGroetscheletal.1998, author = {Bornd{\"o}rfer, Ralf and Eisenbl{\"a}tter, Andreas and Gr{\"o}tschel, Martin and Martin, Alexander}, title = {The Orientation Model for Frequency Assignment Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5627}, number = {TR-98-01}, year = {1998}, abstract = {Mobile telecommunication systems establish a large number of communication links with a limited number of available frequencies; reuse of the same or adjacent frequencies on neighboring links causes interference. The task to find an assignment of frequencies to channels with minimal interference is the frequency assignment problem. The frequency assignment problem is usually treated as a graph coloring problem where the number of colors is minimized, but this approach does not model interference minimization correctly. We give in this paper a new integer programming formulation of the frequency assignment problem, the orientation model, and develop a heuristic two-stage method to solve it. The algorithm iteratively solves an outer and an inner optimization problem. The outer problem decides for each pair of communication links which link gets the higher frequency and leads to an acyclic subdigraph problem with additional longest path restrictions. The inner problem to find an optimal assignment respecting an orientation leads to a min-cost flow problem.}, language = {en} } @misc{MarchandMartinWeismanteletal.1999, author = {Marchand, Hugues and Martin, Alexander and Weismantel, Robert and Wolsey, Laurence}, title = {Cutting Planes in Integer and Mixed Integer Programming}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4339}, number = {SC-99-44}, year = {1999}, abstract = {This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs. Valid inequalities for i) general integer programs, ii) problems with local structure such as knapsack constraints, and iii) problems with 0-1 coefficient matrices, such as set packing, are examined in turn. Finally the use of valid inequalities for classes of problems with structure, such as network design, is explored.}, language = {en} }