TY - JOUR A1 - Wilson, David A1 - Anglin, Carolyn A1 - Ambellan, Felix A1 - Grewe, Carl Martin A1 - Tack, Alexander A1 - Lamecker, Hans A1 - Dunbar, Michael A1 - Zachow, Stefan T1 - Validation of three-dimensional models of the distal femur created from surgical navigation point cloud data for intraoperative and postoperative analysis of total knee arthroplasty JF - International Journal of Computer Assisted Radiology and Surgery N2 - Purpose: Despite the success of total knee arthroplasty there continues to be a significant proportion of patients who are dissatisfied. One explanation may be a shape mismatch between pre and post-operative distal femurs. The purpose of this study was to investigate a method to match a statistical shape model (SSM) to intra-operatively acquired point cloud data from a surgical navigation system, and to validate it against the pre-operative magnetic resonance imaging (MRI) data from the same patients. Methods: A total of 10 patients who underwent navigated total knee arthroplasty also had an MRI scan less than 2 months pre-operatively. The standard surgical protocol was followed which included partial digitization of the distal femur. Two different methods were employed to fit the SSM to the digitized point cloud data, based on (1) Iterative Closest Points (ICP) and (2) Gaussian Mixture Models (GMM). The available MRI data were manually segmented and the reconstructed three-dimensional surfaces used as ground truth against which the statistical shape model fit was compared. Results: For both approaches, the difference between the statistical shape model-generated femur and the surface generated from MRI segmentation averaged less than 1.7 mm, with maximum errors occurring in less clinically important areas. Conclusion: The results demonstrated good correspondence with the distal femoral morphology even in cases of sparse data sets. Application of this technique will allow for measurement of mismatch between pre and post-operative femurs retrospectively on any case done using the surgical navigation system and could be integrated into the surgical navigation unit to provide real-time feedback. Y1 - 2017 UR - https://link.springer.com/content/pdf/10.1007%2Fs11548-017-1630-5.pdf U6 - https://doi.org/10.1007/s11548-017-1630-5 VL - 12 IS - 12 SP - 2097 EP - 2105 PB - Springer ER - TY - CHAP A1 - Weinhold, Carsten A1 - Lackorzynski, Adam A1 - Bierbaum, Jan A1 - Küttler, Martin A1 - Planeta, Maksym A1 - Härtig, Hermann A1 - Shiloh, Amnon A1 - Levy, Ely A1 - Ben-Nun, Tal A1 - Barak, Amnon A1 - Steinke, Thomas A1 - Schütt, Thorsten A1 - Fajerski, Jan A1 - Reinefeld, Alexander A1 - Lieber, Matthias A1 - Nagel, Wolfgang T1 - FFMK: A Fast and Fault-tolerant Microkernel-based System for Exascale Computing T2 - SPPEXA Symposium 2016 Y1 - 2016 U6 - https://doi.org/10.1007/978-3-319-40528-5_18 ER - TY - JOUR A1 - Heida, Martin A1 - Sikorski, Alexander A1 - Weber, Marcus T1 - Consistency and order 1 convergence of cell-centered finite volume discretizations of degenerate elliptic problems in any space dimension JF - SIAM Journal on Numerical Analysis N2 - We study consistency of cell-centered finite difference methods for elliptic equations with degenerate coefficients in any space dimension $d \geq 2$. This results in order of convergence estimates in the natural weighted energy norm and in the weighted discrete $L^2$-norm on admissible meshes. The cells of meshes under consideration may be very irregular in size. We particularly allow the size of certain cells to remain bounded from below even in the asymptotic limit. For uniform meshes we show that the order of convergence is at least 1 in the energy semi-norm, provided the discrete and continuous solutions exist and the continuous solution has $H^2$ regularity. Y1 - 2022 U6 - https://doi.org/10.20347/WIAS.PREPRINT.2913 ER - TY - JOUR A1 - Sikorski, Alexander A1 - Heida, Martin T1 - Voronoi Graph - Improved raycasting and integration schemes for high dimensional Voronoi diagrams N2 - The computation of Voronoi Diagrams, or their dual Delauney triangulations is difficult in high dimensions. In a recent publication Polianskii and Pokorny propose an iterative randomized algorithm facilitating the approximation of Voronoi tesselations in high dimensions. In this paper, we provide an improved vertex search method that is not only exact but even faster than the bisection method that was previously recommended. Building on this we also provide a depth-first graph-traversal algorithm which allows us to compute the entire Voronoi diagram. This enables us to compare the outcomes with those of classical algorithms like qHull, which we either match or marginally beat in terms of computation time. We furthermore show how the raycasting algorithm naturally lends to a Monte Carlo approximation for the volume and boundary integrals of the Voronoi cells, both of which are of importance for finite Volume methods. We compare the Monte-Carlo methods to the exact polygonal integration, as well as a hybrid approximation scheme. Y1 - 2024 ER - TY - JOUR A1 - Xie, Kunpeng A1 - Gruber, Lennart Johannes A1 - Crampen, Martin A1 - Li, Yao A1 - Ferreira, André A1 - Tappeiner, Elias A1 - Gillot, Maxime A1 - Schepers, Jan A1 - Xu, Jiangchang A1 - Pankert, Tobias A1 - Beyer, Michel A1 - Shahamiri, Negar A1 - ten Brink, Reinier A1 - Dot, Gauthier A1 - Weschke, Charlotte A1 - van Nistelrooij, Niels A1 - Verhelst, Pieter-Jan A1 - Guo, Yan A1 - Xu, Zhibin A1 - Bienzeisler, Jonas A1 - Rashad, Ashkan A1 - Flügge, Tabea A1 - Cotton, Ross A1 - Vinayahalingam, Shankeeth A1 - Ilesan, Robert A1 - Raith, Stefan A1 - Madsen, Dennis A1 - Seibold, Constantin A1 - Xi, Tong A1 - Bergé, Stefaan A1 - Nebelung, Sven A1 - Kodym, Oldřich A1 - Sundqvist, Osku A1 - Thieringer, Florian A1 - Lamecker, Hans A1 - Coppens, Antoine A1 - Potrusil, Thomas A1 - Kraeima, Joep A1 - Witjes, Max A1 - Wu, Guomin A1 - Chen, Xiaojun A1 - Lambrechts, Adriaan A1 - Cevidanes, Lucia H Soares A1 - Zachow, Stefan A1 - Hermans, Alexander A1 - Truhn, Daniel A1 - Alves, Victor A1 - Egger, Jan A1 - Röhrig, Rainer A1 - Hölzle, Frank A1 - Puladi, Behrus T1 - Beyond Benchmarks: Towards Robust Artificial Intelligence Bone Segmentation in Socio-Technical Systems JF - Expert Systems With Applications N2 - Despite the advances in automated medical image segmentation, AI models still underperform in various clinical settings, challenging real-world integration. In this multicenter evaluation, we analyzed 20 state-of-the-art mandibular segmentation models across 19,218 segmentations of 1,000 clinically resampled CT/CBCT scans. We show that segmentation accuracy varies by up to 25% depending on socio-technical factors such as voxel size, bone orientation, and patient conditions such as osteosynthesis or pathology. Higher sharpness, isotropic smaller voxels, and neutral orientation significantly improved results, while metallic osteosynthesis and anatomical complexity led to significant degradation. Our findings challenge the common view of AI models as “plug-and-play” tools and suggest evidence-based optimization recommendations for both clinicians and developers. This will in turn boost the integration of AI segmentation tools in routine healthcare. Y1 - 2025 UR - https://www.medrxiv.org/content/10.1101/2025.06.11.25329022v1 U6 - https://doi.org/10.1016/j.eswa.2025.130031 VL - 299 IS - Part D ER - TY - JOUR A1 - Bärmann, Andreas A1 - Martin, Alexander A1 - Pokutta, Sebastian A1 - Schneider, Oskar T1 - An Online-Learning Approach to Inverse Optimization Y1 - 2018 ER - TY - JOUR A1 - Eisenblätter, Andreas A1 - Geerdes, Hans-Florian A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Wessäly, Roland T1 - UMTS Radio Network Evaluation and Optimization beyond Snapshots JF - Mathematical Methods of Operations Research Y1 - 2005 UR - http://opus.kobv.de/zib/volltexte/2004/791/ U6 - https://doi.org/10.1007/s00186-005-0002-z VL - 63 IS - 1 SP - 1 EP - 29 ER - TY - CHAP A1 - Fügenschuh, Armin A1 - Hess, Wolfgang A1 - Martin, Alexander A1 - Ulbrich, Stefan ED - Groche, P. T1 - Diskrete und kontinuierliche Modelle zur Topologie- und Geometrie-Optimierung von Blechprofilen T2 - Sonderforschungsbereich 666 Y1 - 2007 SP - 37 EP - 47 ER - TY - BOOK A1 - Grötschel, Martin A1 - Lovász, Lászlo A1 - Schrijver, Alexander T1 - Geometric Algorithms and Combinatorial Optimization T3 - Algorithms and Combinatorics Y1 - 1993 SN - 3-540-56740-2, 0-387-56740-2 (U.S.) VL - 2 PB - Springer ET - Second corrected edition ER - TY - CHAP A1 - Eisenblätter, Andreas A1 - Fügenschuh, Armin A1 - Koch, Thorsten A1 - Koster, Arie M.C.A. A1 - Martin, Alexander A1 - Pfender, Tobias A1 - Wegel, Oliver A1 - Wessäly, Roland ED - G. Anandalingam, S. T1 - Mathematical Model of Feasible Network Configurations for UMTS T2 - Telecommunications network design and management Y1 - 2002 SP - 1 EP - 24 PB - Kluwer ER - TY - CHAP A1 - Fügenschuh, Armin A1 - Martin, Alexander A1 - Stöveken, Peter ED - Bixby, Robert E. ED - Simchi-Levi, D. ED - Martin, Alexander ED - Zimmermann, U. T1 - Integrated Optimization of School Starting Times and Public Bus Services T2 - Mathematics in the Supply Chain Y1 - 2004 ER - TY - CHAP A1 - Eisenblätter, Andreas A1 - Fügenschuh, Armin A1 - Geerdes, Hans-Florian A1 - Junglas, Daniel A1 - Koch, Thorsten A1 - Martin, Alexander T1 - Integer Programming Methods for UMTS Radio Network Planning T2 - Proceedings of the WiOpt’04, Cambridge, UK Y1 - 2004 ER - TY - CHAP A1 - Fügenschuh, Armin A1 - Martin, Alexander ED - Aardal, Karen I. ED - Nemhauser, George ED - Weismantel, R. T1 - Computational Integer Programming and Cutting Planes T2 - Handbooks in Operations Research and Management Science, Vol. 12 Y1 - 2005 SP - 69 EP - 122 PB - North-Holland ER - TY - CHAP A1 - Fügenschuh, Armin A1 - Homfeld, Henning A1 - Huck, Andreas A1 - Martin, Alexander ED - Jacob, R. ED - Müller-Hannemann, Matthias T1 - Locomotive and Wagon Scheduling in Freight Transport T2 - Proceedings of the ATMOS06 Y1 - 2006 ER - TY - CHAP A1 - Fügenschuh, Armin A1 - Martin, Alexander A1 - Mehlert, Christian A1 - Stöveken, Peter ED - Günther, H.-O. ED - Mattfeld, D. ED - Suhl, L. T1 - Ein Planungstool zur Schulzeitstaffelung T2 - Supply Chain Management und Logistik Y1 - 2005 SP - 419 EP - 436 ER - TY - CHAP A1 - Fügenschuh, Armin A1 - Martin, Alexander A1 - Stöveken, Peter ED - Fleuren, Hein ED - den Hertog, Dick ED - Kort, Peter T1 - Integrated Optimization of School Starting Times and Public Bus Services T2 - Operations Research Proceedings Y1 - 2005 SP - 150 EP - 157 ER - TY - CHAP A1 - Fügenschuh, Armin A1 - Martin, Alexander T1 - Mixed-integer models for topology optimization in sheet metal design T2 - Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007 Y1 - 2007 SP - 2060049 EP - 2060050 ER - TY - CHAP A1 - Fügenschuh, Armin A1 - ler, Björn A1 - Martin, Alexander A1 - Morsi, Antonio ED - Barnhart, Cynthia ED - Clausen, Uwe ED - Lauther, Ulrich ED - Möhring, Rolf T1 - The Transport PDE and Mixed-Integer Linear Programming T2 - Dagstuhl Seminar Proceedings 09261, Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Deutschland Y1 - 2009 ER - TY - CHAP A1 - Fügenschuh, Armin A1 - Hess, Wolfgang A1 - Schewe, Lars A1 - Martin, Alexander A1 - Ulbrich, Stefan ED - Groche, P. T1 - Verfeinerte Modelle zur Topologie- und Geometrie-Optimierung von Blechprofilen mit Kammern T2 - Sonderforschungsbereich 666 Y1 - 2008 SP - 17 EP - 28 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Hoang, Nam-Dung A1 - Karbstein, Marika A1 - Koch, Thorsten A1 - Martin, Alexander ED - Jünger, Michael ED - Reinelt, Gerhard T1 - How many Steiner terminals can you connect in 20 years? T2 - Facets of Combinatorial Optimization; Festschrift for Martin Grötschel Y1 - 2013 U6 - https://doi.org/10.1007/978-3-642-38189-8_10 SP - 215 EP - 244 PB - Springer ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Ferreira, Carlos A1 - Martin, Alexander T1 - Decomposing Matrices into Blocks JF - SIAM J. Optim. Y1 - 1998 UR - http://opus.kobv.de/zib/volltexte/1997/285/ VL - 9 IS - 1 SP - 236 EP - 269 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Hoang, Nam-Dung A1 - Karbstein, Marika A1 - Koch, Thorsten A1 - Martin, Alexander T1 - How Many Steiner Terminals Can You Connect in 20 Years? N2 - Steiner trees are constructed to connect a set of terminal nodes in a graph. This basic version of the Steiner tree problem is idealized, but it can effectively guide the search for successful approaches to many relevant variants, from both a theoretical and a computational point of view. This article illustrates the theoretical and algorithmic progress on Steiner tree type problems on two examples, the Steiner connectivity and the Steiner tree packing problem. T3 - ZIB-Report - 13-57 KW - Steiner tree KW - Steiner connectivity KW - Steiner tree packing Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42524 SN - 1438-0064 ER - TY - JOUR A1 - Dür, Mirjam A1 - Fügenschuh, Armin A1 - Martin, Alexander A1 - Schabel, Samuel A1 - Schönberger, Christine A1 - Villforth, Klaus T1 - Steuerung einer Sortieranlage, z.B. für Altpapier JF - Europäische Patentanmeldung Y1 - 2010 VL - EP 09 718 564.9 ER - TY - JOUR A1 - Fügenschuh, Armin A1 - Herty, Michael A1 - Klar, Axel A1 - Martin, Alexander T1 - Combinatorial and Continuous Models and Optimization for Traffic Flow on Networks JF - SIAM Journal on Optimization Y1 - 2006 VL - 16 IS - 4 SP - 1155 EP - 1176 ER - TY - JOUR A1 - Fügenschuh, Armin A1 - Martin, Alexander T1 - Welche Gemeinsamkeiten haben Jugendliche und Groß banken? JF - mathematiklehren Y1 - 2006 VL - 129 SP - 50 EP - 54 ER - TY - JOUR A1 - Dür, Mirjam A1 - Fügenschuh, Armin A1 - Martin, Alexander A1 - Schabel, Samuel A1 - Schönberger, Christine A1 - Villforth, Klaus T1 - Verfahren zum Einstellen und/oder Optimieren einer einen Gutstoff von einem Schlechtstoff trennenden Sortieranlage und Sortieranlage JF - Deutsches Patent Y1 - 2008 VL - DE 10 2008 013 034 ER - TY - JOUR A1 - Fügenschuh, Armin A1 - Martin, Alexander T1 - Verfahren und Vorrichtung zur automatischen Optimierung von Schulanfangszeiten und des öffentlichen Personenverkehrs und entsprechendes Computerprogramm JF - Deutsche Patentanmeldung Y1 - 2004 VL - DE 10 2004 020 786.0 ER - TY - JOUR A1 - Dür, Mirjam A1 - Fügenschuh, Armin A1 - Martin, Alexander A1 - Ulbrich, Stefan T1 - Verfahren und Vorrichtung zum Auswuchten von wellenelastischen Rotoren JF - Deutsche Patentanmeldung Y1 - 2006 VL - DE 10 2006 060 583.7 ER - TY - JOUR A1 - Fügenschuh, Armin A1 - Göttlich, Simone A1 - Kirchner, Claus A1 - Herty, Michael A1 - Martin, Alexander T1 - Efficient Reformulation and Solution of a Nonlinear PDE-Controlled Flow Network Model JF - Computing Y1 - 2009 VL - 85 IS - 3 SP - 245 EP - 265 ER - TY - JOUR A1 - Fügenschuh, Armin A1 - Homfeld, Henning A1 - Huck, Andreas A1 - Martin, Alexander A1 - Yuan, Zhi T1 - Scheduling Locomotives and Car Transfers in Freight Transport JF - Transportation Science Y1 - 2008 VL - 42 IS - 4 SP - 1 EP - 14 ER - TY - JOUR A1 - Fügenschuh, Armin A1 - Martin, Alexander T1 - A Multicriterial Approach for Optimizing Bus Schedules and School Starting Times JF - Annals of Operations Research Y1 - 2006 VL - 147 IS - 1 SP - 199 EP - 216 ER - TY - JOUR A1 - Eisenblätter, Andreas A1 - Fügenschuh, Armin A1 - Fledderus, E. A1 - Geerdes, Hans-Florian A1 - Heideck, B. A1 - Junglas, Daniel A1 - Koch, Thorsten A1 - Kürner, T. A1 - Martin, Alexander ED - Martin, Alexander T1 - Mathematical Methods for Automatic Optimization of UMTS Radio Networks Y1 - 2003 UR - http://momentum.zib.de/paper/momentum-d43.pdf IS - D4.3 PB - IST-2000-28088 MOMENTUM ER - TY - JOUR A1 - Eisenblätter, Andreas A1 - Geerdes, Hans-Florian A1 - Junglas, Daniel A1 - Koch, Thorsten A1 - Kürner, T. A1 - Martin, Alexander T1 - Final Report on Automatic Planning and Optimisation Y1 - 2003 UR - http://momentum.zib.de/paper/momentum-d47.pdf IS - D4.7 PB - IST-2000-28088 MOMENTUM ER - TY - GEN A1 - Dittel, Agnes A1 - Fügenschuh, Armin A1 - Martin, Alexander T1 - Polyhedral Aspects of Self-Avoiding Walks N2 - In this paper, we study self-avoiding walks of a given length on a graph. We consider a formulation of this problem as a binary linear program. We analyze the polyhedral structure of the underlying polytope and describe valid inequalities. Proofs for their facial properties for certain special cases are given. In a variation of this problem one is interested in optimal configurations, where an energy function measures the benefit if certain path elements are placed on adjacent vertices of the graph. The most prominent application of this problem is the protein folding problem in biochemistry. On a set of selected instances, we demonstrate the computational merits of our approach. T3 - ZIB-Report - 11-11 KW - Polyhedral Combinatorics KW - Integer Programming KW - Self-Avoiding Path KW - Protein Folding Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12576 ER - TY - THES A1 - Martin, Alexander T1 - Integer Programs with Block Structure N2 - In this thesis we study and solve integer programs with block structure, i.\,e., problems that after the removal of certain rows (or columns) of the constraint matrix decompose into independent subproblems. The matrices associated with each subproblem are called blocks and the rows (columns) to be removed linking constraints (columns). Integer programs with block structure come up in a natural way in many real-world applications. The methods that are widely used to tackle integer programs with block structure are decomposition methods. The idea is to decouple the linking constraints (variables) from the problem and treat them at a superordinate level, often called master problem. The resulting residual subordinate problem then decomposes into independent subproblems that often can be solved more efficiently. Decomposition methods now work alternately on the master and subordinate problem and iteratively exchange information to solve the original problem to optimality. In Part I we follow a different approach. We treat the integer programming problem as a whole and keep the linking constraints in the formulation. We consider the associated polyhedra and investigate the polyhedral consequences of the involved linking constraints. The variety and complexity of the new inequalities that come into play is illustrated on three different types of real-world problems. The applications arise in the design of electronic circuits, in telecommunication and production planning. We develop a branch-and-cut algorithm for each of these problems, and our computational results show the benefits and limits of the polyhedral approach to solve these real-world models with block structure. Part II of the thesis deals with general mixed integer programming problems, that is integer programs with no apparent structure in the constraint matrix. We will discuss in Chapter 5 the main ingredients of an LP based branch-and-bound algorithm for the solution of general integer programs. Chapter 6 then asks the question whether general integer programs decompose into certain block structures and investigate whether it is possible to recognize such a structure. The remaining two chapters exploit information about the block structure of an integer program. In Chapter 7 we parallelize parts of the dual simplex algorithm, the method that is commonly used for the solution of the underlying linear programs within a branch-and-cut algorithm. In Chapter 8 we try to detect small blocks in the constraint matrix and to derive new cutting planes that strengthen the integer programming formulation. These inequalities may be associated with the intersection of several knapsack problems. We will see that they significantly improve the quality of the general integer programming solver introduced in Chapter 5. T3 - ZIB-Report - SC-99-03 KW - integer programming KW - cutting planes KW - block structure Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3911 ER - TY - GEN A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Koch, Thorsten A1 - Miltenberger, Matthias A1 - Kniasew, Dimitri A1 - Schlögel, Dominik A1 - Martin, Alexander A1 - Weninger, Dieter T1 - Tackling Industrial-Scale Supply Chain Problems by Mixed-Integer Programming N2 - SAP's decision support systems for optimized supply network planning rely on mixed-integer programming as the core engine to compute optimal or near-optimal solutions. The modeling flexibility and the optimality guarantees provided by mixed-integer programming greatly aid the design of a robust and future-proof decision support system for a large and diverse customer base. In this paper we describe our coordinated efforts to ensure that the performance of the underlying solution algorithms matches the complexity of the large supply chain problems and tight time limits encountered in practice. T3 - ZIB-Report - 16-45 KW - supply chain management, supply network optimization, mixed-integer linear programming, primal heuristics, numerical stability, large-scale optimization Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61107 SN - 1438-0064 ER - TY - CHAP A1 - Schewe, Lars A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Pfetsch, Marc T1 - Mathematical optimization for evaluating gas network capacities T2 - Evaluating Gas Network Capacities Y1 - 2015 SN - 9781611973686 SP - 87 EP - 102 PB - Society for Industrial and Applied Mathematics ER - TY - CHAP A1 - Fügenschuh, Armin A1 - Homfeld, Henning A1 - Martin, Alexander T1 - Leitwegeplanung T2 - Mathematik für Innovationen in Industrie und Dienstleistungen Y1 - 2007 ER - TY - GEN A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Pfetsch, Marc ED - Jünger, Michael ED - Reinelt, Gerhard T1 - Progress in Academic Computational Integer Programming T2 - Facets of Combinatorial Optimization Y1 - 2013 U6 - https://doi.org/10.1007/978-3-642-38189-8_19 SP - 483 EP - 506 PB - Springer ER - TY - JOUR A1 - Gamrath, Gerald A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Miltenberger, Matthias A1 - Weninger, Dieter T1 - Progress in presolving for mixed integer programming JF - Mathematical Programming Computation N2 - This paper describes three presolving techniques for solving mixed integer programming problems (MIPs) that were implemented in the academic MIP solver SCIP. The task of presolving is to reduce the problem size and strengthen the formulation, mainly by eliminating redundant information and exploiting problem structures. The first method fixes continuous singleton columns and extends results known from duality fixing. The second analyzes and exploits pairwise dominance relations between variables, whereas the third detects isolated subproblems and solves them independently. The performance of the presented techniques is demonstrated on two MIP test sets. One contains all benchmark instances from the last three MIPLIB versions, while the other consists of real-world supply chain management problems. The computational results show that the combination of all three presolving techniques almost halves the solving time for the considered supply chain management problems. For the MIPLIB instances we obtain a speedup of 20 % on affected instances while not degrading the performance on the remaining problems. Y1 - 2015 U6 - https://doi.org/10.1007/s12532-015-0083-5 VL - 7 IS - 4 SP - 367 EP - 398 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Ferreira, Carlos E. A1 - Martin, Alexander T1 - Decomposing Matrices into Blocks N2 - In this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so-called {\em bordered block diagonal form}. More precisely, given some matrix $A$, we try to assign as many rows as possible to some number of blocks of limited size such that no two rows assigned to different blocks intersect in a common column. Bordered block diagonal form is desirable because it can guide and speed up the solution process for linear and integer programming problems. We show that various matrices from the LP- and MIP-libraries NETLIB and MITLIB can indeed be decomposed into this form by computing optimal decompositions or decompositions with proven quality. These computations are done with a branch-and-cut algorithm based on polyhedral investigations of the matrix decomposition problem. In practice, however, one would use heuristics to find a good decomposition. We present several heuristic ideas and test their performance. Finally, we investigate the usefulness of optimal matrix decompositions into bordered block diagonal form for integer programming by using such decompositions to guide the branching process in a branch-and-cut code for general mixed integer programs. T3 - ZIB-Report - SC-97-15 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2849 ER -