Papers by Matthias Müller-hannemann
Journal of Cheminformatics
An important task in cheminformatics is to test whether two molecules are equivalent with respect... more An important task in cheminformatics is to test whether two molecules are equivalent with respect to their 2D structure. Mathematically, this amounts to solving the graph isomorphism problem for labelled graphs. In this paper, we present an approach which exploits chemical properties and the local neighbourhood of atoms to define highly distinctive node labels. These characteristic labels are the key for clever partitioning molecules into molecule equivalence classes and an effective equivalence test. Based on extensive computational experiments, we show that our algorithm is significantly faster than existing implementations within , and . We provide our Java implementation as an easy-to-use, open-source package (via GitHub) which is compatible with . It fully supports the distinction of different isotopes and molecules with radicals.
Journal of Mass Spectrometry
Passenger-friendly train disposition is a challenging, highly complex online optimization problem... more Passenger-friendly train disposition is a challenging, highly complex online optimization problem with uncertain and incomplete information about future delays. In this paper we focus on the timing within the disposition process. We introduce three different classification schemes to predict as early as possible the status of a transfer: whether it will almost surely break, is so critically delayed that it requires manual disposition, or can be regarded as only slightly uncertain or as being safe. The three approaches use lower bounds on travel times, historical distributions of delay data, and fuzzy logic, respectively. In experiments with real delay data we achieve an excellent classification rate. Furthermore, using realistic passenger flows we observe that there is a significant potential to reduce the passenger delay if an early rerouting strategy is applied.
Page 1. Efficient On-Trip Timetable Information in the Presence of Delays Lennart Frede1, Matthia... more Page 1. Efficient On-Trip Timetable Information in the Presence of Delays Lennart Frede1, Matthias Müller–Hannemann2 and Mathias Schnee1 1Darmstadt University of Technology, Computer Science, Hochschulstraße 10, 64289 ...
ABSTRACT This final book chapter is meant as a brief reflection on the current status of Algorith... more ABSTRACT This final book chapter is meant as a brief reflection on the current status of Algorithm Engineering and its future development. It is devoted to the many challenges this discipline has to face. By challenges we mean things that are worthy to invest a significant research effort, and working on these problems promises a high potential impact.
Transportation networks give rise to very complex and large-scale network optimization problems r... more Transportation networks give rise to very complex and large-scale network optimization problems requiring innovative solution techniques and ideas from mathematical optimization, theoretical computer science, and operations research. Applicable tools and concepts include those from graph and network algorithms, combinatorial optimization, approximation and online algorithms, stochastic and robust optimization. Since 2000, the series of ATMOS workshops brings together researchers and practitioners who are interested in all aspects of algorithmic methods and models for transportation optimization and provides a forum for the exchange and dissemination of new ideas and techniques. The scope of ATMOS comprises all modes of transportation. The 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2011
Journal of Graph Algorithms and Applications, 2001
We present a new approach for the generation of hexahedral finite element meshes for solid bodies... more We present a new approach for the generation of hexahedral finite element meshes for solid bodies in computer-aided design. The key idea is to use a purely combinatorial method, namely a shelling process, to decompose a topological ball with a prescribed surface mesh into combinatorial cubes, so-called hexahedra. The shelling corresponds to a series of graph transformations on the surface mesh which is guided by the cycle structure of the combinatorial dual. Our method transforms the graph of the surface mesh iteratively by changing the dual cycle structure until we get the surface mesh of a single hexahedron. Starting with a single hexahedron and reversing the order of the graph transformations, each transformation step can be interpreted as adding one or more hexahedra to the so far created hex complex. Given an arbitrary solid body, we first decompose it into simpler subdomains equivalent to topological balls by adding virtual 2-manifolds. Second, we determine a compatible quadrilateral surface mesh for all created subdomains. Then, in the main part we can use the shelling of topological balls to build up a hex complex for each subdomain independently. Finally, the combinatorial mesh(es) are embedded into the given solids and smoothed to improve quality.
International Journal of Computational Geometry & Applications, 2000
We investigate a purely combinatorial approach to the following mesh refinement problem: Given a ... more We investigate a purely combinatorial approach to the following mesh refinement problem: Given a coarse mesh of polygons in three-dimensional space, find a decomposition into well-shaped quadrilaterals such that the resulting mesh is conforming and satisfies prescribed local density constraints. We present a new approach based on network flow techniques. In particular, we show that this problem can efficiently be solved by a reduction to a minimum cost bidirected flow problem, if the mesh does not contain branching edges, that is, edges incident to more than two polygons. This approach handles optimization criteria such as density, angles and regularity. In our model we get rid of restrictions on the set of feasible solutions imposed by templates. On the other hand, we still use advantages of general templates with respect to mesh quality for the individual refinement of the mesh polygons. For meshes with branchings, the problem is feasible if and only if a certain system of linear ...
International Journal for Numerical Methods in Engineering, 1999
ABSTRACT We present a new approach to quadrilateral mesh refinement, which reduces the problem to... more ABSTRACT We present a new approach to quadrilateral mesh refinement, which reduces the problem to its structural core. The resulting problem formulation belongs to a class of discrete problems, network-flow problems, which has been thoroughly investigated and is well understood. The network-flow model is flexible enough to allow the simultaneous incorporation of various aspects such as the control of angles and aspect ratios, local density control, and templates (meshing primitives) for the internal refinement of mesh elements. We show that many different variants of the general quadrilateral mesh-refinement problem are covered. In particular, we present a novel strategy, which provably finds a conformal refinement unless there is none. Copyright © 1999 John Wiley & Sons, Ltd.
Computational Geometry, 2002
Several promising approaches for hexahedral mesh generation work as follows: Given a prescribed q... more Several promising approaches for hexahedral mesh generation work as follows: Given a prescribed quadrilateral surface mesh they first build the combinatorial dual of the hexahedral mesh. This dual mesh is converted into the primal hexahedral mesh, and finally embedded and smoothed into the given domain. Two such approaches, the modified whisker weaving algorithm by Folwell and Mitchell, as well as a method proposed by the author, rely on an iterative elimination of certain dual cycles in the surface mesh. An intuitive interpretation of the latter method is that cycle eliminations correspond to complete sheets of hexahedra in the volume mesh. Although these methods can be shown to work in principle, the quality of the generated meshes heavily relies on the dual cycle structure of the given surface mesh. In particular, it seems that difficulties in the hexahedral meshing process and poor mesh qualities are often due to self-intersecting dual cycles. Unfortunately, all previous work on quadrilateral surface mesh generation has focused on quality issues of the surface mesh alone but has disregarded its suitability for a high-quality extension to a three-dimensional mesh. In this paper, we develop a new method to generate quadrilateral surface meshes without self-intersecting dual cycles. This method reuses previous b-matching problem formulations of the quadrilateral mesh refinement problem. The key insight is that the b-matching solution can be decomposed into a collection of simple cycles and paths of multiplicity two, and that these cycles and paths can be consistently embedded into the dual surface mesh. A second tool uses recursive splitting of components into simpler subcomponents by insertion of internal twomanifolds. We show that such a two-manifold can be meshed with quadrilaterals such that the induced dual cycle structure of each subcomponent is free of self-intersections if the original component satisfies this property. Experiments show that we can achieve hexahedral meshes with a good quality.
Transportation networks give rise to very complex and large-scale network optimization problems r... more Transportation networks give rise to very complex and large-scale network optimization problems requiring innovative solution techniques and ideas from mathematical optimization, theoretical computer science, and operations research. Applicable tools and concepts include those from graph and network algorithms, combinatorial optimization, approximation and online algorithms, stochastic and robust optimization. Since 2000, the series of ATMOS workshops brings together researchers and practitioners who are interested in all aspects of algorithmic methods and models for transportation optimization and provides a forum for the exchange and dissemination of new ideas and techniques. The scope of ATMOS comprises all modes of transportation. The 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2011
Background: Mass spectrometry has become the analytical method of choice in metabolomics research... more Background: Mass spectrometry has become the analytical method of choice in metabolomics research. The identification of unknown compounds is the main bottleneck. In addition to the precursor mass, tandem MS spectra carry informative fragment peaks, but the coverage of spectral libraries of measured reference compounds are far from covering the complete chemical space. Compound libraries such as PubChem or KEGG describe a larger number of compounds, which can be used to compare their in silico fragmentation with spectra of unknown metabolites. Results: We created the MetFrag suite to obtain a candidate list from compound libraries based on the precursor mass, subsequently ranked by the agreement between measured and in silico fragments. In the evaluation MetFrag was able to rank most of the correct compounds within the top 3 candidates returned by an exact mass query in KEGG. Compared to a previously published study, MetFrag obtained better results than the commercial MassFrontier software. Especially for large compound libraries, the candidates with a good score show a high structural similarity or just different stereochemistry, a subsequent clustering based on chemical distances reduces this redundancy. The in silico fragmentation requires less than a second to process a molecule, and MetFrag performs a search in KEGG or PubChem on average within 30 to 300 seconds, respectively, on an average desktop PC.
Algorithmica, 2000
. We investigate the following mesh refinement problem: Given a mesh of polygons in three-dime... more . We investigate the following mesh refinement problem: Given a mesh of polygons in three-dimensional space, find a decomposition into strictly convex quadrilaterals such that the resulting mesh is conforming and satisfies prescribed local density constraints. The conformal mesh refinement problem is shown to be feasible if and only if a certain system of linear equations over GF(2) has
... Zürich and Darmstadt, August 2006 Riko Jacob and Matthias Müller-Hannemann PC co-chairs of AT... more ... Zürich and Darmstadt, August 2006 Riko Jacob and Matthias Müller-Hannemann PC co-chairs of ATMOS 2006 Page 6. ... Martin Aronsson, Per Kreuger (Swedish Institute of Computer Science, Kista, Sweden), and Jonata Gjerdrum (Green Cargo AB, Sweden) ...
Journal of Experimental Algorithmics, 2012
ABSTRACT Natural language is a rich source of constraint satisfaction problems (CSPs), with a uni... more ABSTRACT Natural language is a rich source of constraint satisfaction problems (CSPs), with a uniquely structured solution domain. We describe a number of approaches to satisfying the particular case of unordered letter-level constraints, including anagrams, ...
A combinatorial approach for the generation of hexahedral meshes by means of successive dual cycl... more A combinatorial approach for the generation of hexahedral meshes by means of successive dual cycle elimination has been proposed by the second author in previous work.
Given a point set K of terminals in the plane, the octilinear Steiner tree problem is to find a s... more Given a point set K of terminals in the plane, the octilinear Steiner tree problem is to find a shortest tree that interconnects all terminals and edges run either in horizontal, vertical, or ±45 • diagonal direction. This problem is fundamental for the novel octilinear routing paradigm in VLSI design, the socalled X-architecture. As the related rectilinear and the Euclidian Steiner tree problem are well-known to be NP-hard, the same was widely believed for the octilinear Steiner tree problem but left open for quite some time. In this paper, we prove the NPcompleteness of the decision version of the octilinear Steiner tree problem. We also show how to reduce the octilinear Steiner tree problem to the Steiner tree problem in graphs of polynomial size with the following approximation guarantee. We construct a graph of size O( n 2 ε 2 ) which contains a (1+ε)-approximation of a minimum octilinear Steiner tree for every ε > 0 and n = |K|. Hence, we can apply any α-approximation algorithm for the Steiner tree problem in graphs (the currently best known bound is α ≈ 1.55) and achieve an (α + ε)-approximation bound for the octilinear Steiner tree problem. This approximation guarantee also holds for the more difficult case where the Steiner tree has to avoid blockages (obstacles bounded by octilinear polygons).
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Papers by Matthias Müller-hannemann