Friedrich Eisenbrand

135 papers A* 21A 9B 10C 1Journal 70Unranked 19

Year	Rank	Type	Title / Venue / Authors
2026	A*	`conf`	A parameterized linear formulation of the integer hull. SODA Friedrich Eisenbrand, Thomas Rothvoss
2026	A*	`conf`	Excluding a Line Minor via Design Matrices and Column Number Bounds for the Circuit Imbalance Measure. SODA Daniel Dadush, Friedrich Eisenbrand, Rom Pinchasi, Thomas Rothvoss, Neta Singer
2025	J	`jnl`	A parameterized linear formulation of the integer hull. CoRR Friedrich Eisenbrand, Thomas Rothvoss
2025	J	`jnl`	Excluding a Line Minor via Design Matrices and Column Number Bounds for the Circuit Imbalance Measure. CoRR Daniel Dadush, Friedrich Eisenbrand, Rom Pinchasi, Thomas Rothvoss, Neta Singer
2025	A*	`conf`	Forall-exist statements in pseudopolynomial time. SODA Eleonore Bach, Friedrich Eisenbrand, Thomas Rothvoss, Robert Weismantel
2025	J	`jnl`	From approximate to exact integer programming. Math. Program. Daniel Dadush, Friedrich Eisenbrand, Thomas Rothvoss
2025	J	`jnl`	Integer linear programming for unsupervised training set selection in molecular machine learning. Mach. Learn. Sci. Technol. Matthieu Haeberle, Puck van Gerwen, Rubén Laplaza, Ksenia R. Briling, Jan Weinreich, Friedrich Eisenbrand, Clémence Corminboeuf
2025	J	`jnl`	Integer points in the degree-sequence polytope. Discret. Optim. Eleonore Bach, Friedrich Eisenbrand, Rom Pinchasi
2025	J	`jnl`	Sparse Integer Programming Is Fixed-Parameter Tractable. Math. Oper. Res. Friedrich Eisenbrand, Christoph Hunkenschröder, Kim-Manuel Klein, Martin Koutecký, Asaf Levin, Shmuel Onn
2024	A*	`conf`	An Improved Bound on Sums of Square Roots via the Subspace Theorem. SoCG Friedrich Eisenbrand, Matthieu Haeberle, Neta Singer
2024	J	`jnl`	Integer linear programming for unsupervised training set selection in molecular machine learning. CoRR Matthieu Haeberle, Puck van Gerwen, Rubén Laplaza, Ksenia R. Briling, Jan Weinreich, Friedrich Eisenbrand, Clémence Corminboeuf
2024	A*	`conf`	Sensitivity, Proximity and FPT Algorithms for Exact Matroid Problems. FOCS Friedrich Eisenbrand, Lars Rohwedder, Karol Wegrzycki
2024	J	`jnl`	Sensitivity, Proximity and FPT Algorithms for Exact Matroid Problems. CoRR Friedrich Eisenbrand, Lars Rohwedder, Karol Wegrzycki
2023	J	`jnl`	An improved bound on sums of square roots via the subspace theorem. CoRR Friedrich Eisenbrand, Matthieu Haeberle, Neta Singer
2023	B	`conf`	From Approximate to Exact Integer Programming. IPCO Daniel Dadush, Friedrich Eisenbrand, Thomas Rothvoss
2023	J	`jnl`	Integer points in the degree-sequence polytope. CoRR Eleonore Bach, Friedrich Eisenbrand, Rom Pinchasi
2023	J	`jnl`	Reducibility bounds of objective functions over the integers. Oper. Res. Lett. Friedrich Eisenbrand, Christoph Hunkenschröder, Kim-Manuel Klein, Martin Koutecký, Asaf Levin, Shmuel Onn
2023	—	`conf`	Repetition-Structure Inference With Formal Prototypes. ISMIR Christoph Finkensiep, Matthieu Haeberle, Friedrich Eisenbrand, Markus Neuwirth, Martin Rohrmeier
2022	J	`jnl`	Approximate CVP J. Comput. Syst. Sci. Friedrich Eisenbrand, Moritz Venzin
2022	J	`jnl`	From approximate to exact integer programming. CoRR Daniel Dadush, Friedrich Eisenbrand, Thomas Rothvoss
2022	J	`jnl`	Metric learning for kernel ridge regression: assessment of molecular similarity. Mach. Learn. Sci. Technol. Raimon Fabregat, Puck van Gerwen, Matthieu Haeberle, Friedrich Eisenbrand, Clémence Corminboeuf
2021	J	`jnl`	A QPTAS for stabbing rectangles. CoRR Friedrich Eisenbrand, Martina Gallato, Ola Svensson, Moritz Venzin
2021	A*	`conf`	Block-Structured Integer and Linear Programming in Strongly Polynomial and Near Linear Time. SODA Jana Cslovjecsek, Friedrich Eisenbrand, Christoph Hunkenschröder, Lars Rohwedder, Robert Weismantel
2021	A	`conf`	Efficient Sequential and Parallel Algorithms for Multistage Stochastic Integer Programming Using Proximity. ESA Jana Cslovjecsek, Friedrich Eisenbrand, Michal Pilipczuk, Moritz Venzin, Robert Weismantel
2020	J	`jnl`	Approximate $\mathrm{CVP}_{\infty}$ in time $2^{0.802 \, n}$. CoRR Friedrich Eisenbrand, Moritz Venzin
2020	A	`conf`	Approximate CVP ESA Friedrich Eisenbrand, Moritz Venzin
2020	J	`jnl`	Efficient sequential and parallel algorithms for multistage stochastic integer programming using proximity. CoRR Jana Cslovjecsek, Friedrich Eisenbrand, Michal Pilipczuk, Moritz Venzin, Robert Weismantel
2020	J	`jnl`	N-fold integer programming via LP rounding. CoRR Jana Cslovjecsek, Friedrich Eisenbrand, Robert Weismantel
2020	J	`jnl`	Proximity Results and Faster Algorithms for Integer Programming Using the Steinitz Lemma. ACM Trans. Algorithms Friedrich Eisenbrand, Robert Weismantel
2019	J	`jnl`	An Algorithmic Theory of Integer Programming. CoRR Friedrich Eisenbrand, Christoph Hunkenschröder, Kim-Manuel Klein, Martin Koutecký, Asaf Levin, Shmuel Onn
2019	J	`jnl`	An Improved Analysis of Local Search for Max-Sum Diversification. Math. Oper. Res. Alfonso Cevallos, Friedrich Eisenbrand, Rico Zenklusen
2018	B	`conf`	Diversity Maximization in Doubling Metrics. ISAAC Alfonso Cevallos, Friedrich Eisenbrand, Sarah Morell
2018	J	`jnl`	Diversity maximization in doubling metrics. CoRR Alfonso Cevallos, Friedrich Eisenbrand, Sarah Morell
2018	A*	`conf`	Faster Algorithms for Integer Programs with Block Structure. ICALP Friedrich Eisenbrand, Christoph Hunkenschröder, Kim-Manuel Klein
2018	J	`jnl`	Faster Algorithms for Integer Programs with Block Structure. CoRR Friedrich Eisenbrand, Christoph Hunkenschröder, Kim-Manuel Klein
2018	A*	`conf`	Proximity results and faster algorithms for Integer Programming using the Steinitz Lemma. SODA Friedrich Eisenbrand, Robert Weismantel
2018	J	`jnl`	The Support of Integer Optimal Solutions. SIAM J. Optim. Iskander Aliev, Jesús A. De Loera, Friedrich Eisenbrand, Timm Oertel, Robert Weismantel
2017	J	`jnl`	Geometric random edge. Math. Program. Friedrich Eisenbrand, Santosh S. Vempala
2017	B	`ed.`	Integer Programming and Combinatorial Optimization - 19th International Conference, IPCO 2017, Waterloo, ON, Canada, June 26-28, 2017, Proceedings IPCO Friedrich Eisenbrand, Jochen Könemann
2017	A*	`conf`	Local Search for Max-Sum Diversification. SODA Alfonso Cevallos, Friedrich Eisenbrand, Rico Zenklusen
2017	J	`jnl`	Proximity results and faster algorithms for Integer Programming using the Steinitz Lemma. CoRR Friedrich Eisenbrand, Robert Weismantel
2016	J	`jnl`	A note on non-degenerate integer programs with small sub-determinants. Oper. Res. Lett. Stephan Artmann, Friedrich Eisenbrand, Christoph Glanzer, Timm Oertel, Santosh S. Vempala, Robert Weismantel
2016	J	`jnl`	Local Search for Max-Sum Diversification. CoRR Alfonso Cevallos, Friedrich Eisenbrand, Rico Zenklusen
2016	A*	`conf`	Max-Sum Diversity Via Convex Programming. SoCG Alfonso Cevallos, Friedrich Eisenbrand, Rico Zenklusen
2015	J	`jnl`	Max-sum diversity via convex programming. CoRR Alfonso Cevallos, Friedrich Eisenbrand, Rico Zenklusen
2015	A	`conf`	Node-Balancing by Edge-Increments. ESA Friedrich Eisenbrand, Shay Moran, Rom Pinchasi, Martin Skutella
2015	J	`jnl`	Node-balancing by edge-increments. CoRR Friedrich Eisenbrand, Shay Moran, Rom Pinchasi, Martin Skutella
2015	A*	`conf`	On largest volume simplices and sub-determinants. SODA Marco Di Summa, Friedrich Eisenbrand, Yuri Faenza, Carsten Moldenhauer
2014	J	`jnl`	Geometric Random Edge. CoRR Friedrich Eisenbrand, Santosh S. Vempala
2014	J	`jnl`	On Sub-determinants and the Diameter of Polyhedra. Discret. Comput. Geom. Nicolas Bonifas, Marco Di Summa, Friedrich Eisenbrand, Nicolai Hähnle, Martin Niemeier
2014	J	`jnl`	On largest volume simplices and sub-determinants. CoRR Marco Di Summa, Friedrich Eisenbrand, Yuri Faenza, Carsten Moldenhauer
2013	J	`jnl`	Bin Packing via Discrepancy of Permutations. ACM Trans. Algorithms Friedrich Eisenbrand, Dömötör Pálvölgyi, Thomas Rothvoß
2013	A*	`conf`	Minimizing the number of lattice points in a translated polygon. SODA Friedrich Eisenbrand, Nicolai Hähnle
2013	J	`jnl`	Testing additive integrality gaps. Math. Program. Friedrich Eisenbrand, Nicolai Hähnle, Dömötör Pálvölgyi, Gennady Shmonin
2012	J	`jnl`	Coloring fuzzy circular interval graphs. Eur. J. Comb. Friedrich Eisenbrand, Martin Niemeier
2012	J	`jnl`	Minimizing the number of lattice points in a translated polygon CoRR Friedrich Eisenbrand, Nicolai Hähnle
2012	—	`conf`	On sub-determinants and the diameter of polyhedra. SCG Nicolas Bonifas, Marco Di Summa, Friedrich Eisenbrand, Nicolai Hähnle, Martin Niemeier
2011	A*	`conf`	Bin Packing via Discrepancy of Permutations. SODA Friedrich Eisenbrand, Dömötör Pálvölgyi, Thomas Rothvoß
2011	—	`conf`	Covering cubes and the closest vector problem. SCG Friedrich Eisenbrand, Nicolai Hähnle, Martin Niemeier
2011	J	`jnl`	On sub-determinants and the diameter of polyhedra CoRR Nicolas Bonifas, Marco Di Summa, Friedrich Eisenbrand, Nicolai Hähnle, Martin Niemeier
2011	J	`jnl`	Real-time Avionics Optimization. it Inf. Technol. Friedrich Eisenbrand, Martin Niemeier, Martin Skutella, José Verschae, Andreas Wiese
2011	B	`conf`	Set Covering with Ordered Replacement: Additive and Multiplicative Gaps. IPCO Friedrich Eisenbrand, Naonori Kakimura, Thomas Rothvoß, Laura Sanità
2011	—	`ch.`	The Euclidean Algorithm. Algorithms Unplugged Friedrich Eisenbrand
2010	J	`jnl`	Bin Packing via Discrepancy of Permutations CoRR Friedrich Eisenbrand, Dömötör Pálvölgyi, Thomas Rothvoß
2010	J	`jnl`	Connected facility location via random facility sampling and core detouring. J. Comput. Syst. Sci. Friedrich Eisenbrand, Fabrizio Grandoni, Thomas Rothvoß, Guido Schäfer
2010	J	`jnl`	Covering Cubes and the Closest Vector Problem CoRR Friedrich Eisenbrand, Nicolai Hähnle, Martin Niemeier
2010	—	`conf`	Diameter of Polyhedra: Limits of Abstraction. Flexible Network Design Friedrich Eisenbrand, Nicolai Hähnle, Alexander A. Razborov, Thomas Rothvoß
2010	J	`jnl`	Diameter of Polyhedra: Limits of Abstraction. Math. Oper. Res. Friedrich Eisenbrand, Nicolai Hähnle, Alexander A. Razborov, Thomas Rothvoß
2010	A*	`conf`	EDF-schedulability of Synchronous Periodic Task Systems is coNP-hard. SODA Friedrich Eisenbrand, Thomas Rothvoß
2010	—	`ch.`	Integer Programming and Algorithmic Geometry of Numbers - A tutorial. 50 Years of Integer Programming Friedrich Eisenbrand
2010	B	`ed.`	Integer Programming and Combinatorial Optimization, 14th International Conference, IPCO 2010, Lausanne, Switzerland, June 9-11, 2010. Proceedings IPCO Friedrich Eisenbrand, F. Bruce Shepherd
2010	—	`conf`	Recent Hardness Results for Periodic Uni-processor Scheduling. Scheduling Friedrich Eisenbrand, Thomas Rothvoß
2010	—	`conf`	Scheduling Periodic Tasks in a Hard Real-Time Environment. ICALP (1) Friedrich Eisenbrand, Nicolai Hähnle, Martin Niemeier, Martin Skutella, José Verschae, Andreas Wiese
2010	—	`conf`	Scheduling periodic tasks in a hard real-time environment. Scheduling Friedrich Eisenbrand, Nicolai Hähnle, Martin Niemeier, Martin Skutella, José Verschae, Andreas Wiese
2010	J	`jnl`	Set Covering with Ordered Replacement -- Additive and Multiplicative Gaps CoRR Friedrich Eisenbrand, Naonori Kakimura, Thomas Rothvoß, Laura Sanità
2010	—	`conf`	Solving an Avionics Real-Time Scheduling Problem by Advanced IP-Methods. ESA (1) Friedrich Eisenbrand, Karthikeyan Kesavan, Raju S. Mattikalli, Martin Niemeier, Arnold W. Nordsieck, Martin Skutella, José Verschae, Andreas Wiese
2010	A*	`conf`	Testing Additive Integrality Gaps. SODA Friedrich Eisenbrand, Nicolai Hähnle, Dömötör Pálvölgyi, Gennady Shmonin
2010	—	`ch.`	The LLL Algorithm and Integer Programming. The LLL Algorithm Karen I. Aardal, Friedrich Eisenbrand
2009	J	`jnl`	Algorithms for longer OLED lifetime. ACM J. Exp. Algorithmics Friedrich Eisenbrand, Andreas Karrenbauer, Chihao Xu
2009	J	`jnl`	Coloring Fuzzy Circular Interval Graphs. Electron. Notes Discret. Math. Friedrich Eisenbrand, Martin Niemeier
2009	J	`jnl`	Constrained Minkowski Sums: A Geometric Framework for Solving Interval Problems in Computational Biology Efficiently. Discret. Comput. Geom. Thorsten Bernholt, Friedrich Eisenbrand, Thomas Hofmeister
2009	—	`conf`	Diameter of polyhedra: limits of abstraction. SCG Friedrich Eisenbrand, Nicolai Hähnle, Thomas Rothvoß
2009	J	`jnl`	Multiline Addressing by Network Flow. Algorithmica Friedrich Eisenbrand, Andreas Karrenbauer, Martin Skutella, Chihao Xu
2009	J	`jnl`	Network Formulations of Mixed-Integer Programs. Math. Oper. Res. Michele Conforti, Marco Di Summa, Friedrich Eisenbrand, Laurence A. Wolsey
2009	—	`conf`	New Hardness Results for Diophantine Approximation. APPROX-RANDOM Friedrich Eisenbrand, Thomas Rothvoß
2008	—	`conf`	A PTAS for Static Priority Real-Time Scheduling with Resource Augmentation. ICALP (1) Friedrich Eisenbrand, Thomas Rothvoß
2008	J	`jnl`	Algorithms for Integer Programming. Bull. EATCS Friedrich Eisenbrand
2008	A*	`conf`	Approximating connected facility location problems via random facility sampling and core detouring. SODA Friedrich Eisenbrand, Fabrizio Grandoni, Thomas Rothvoß, Guido Schäfer
2008	J	`jnl`	Convexly Independent Subsets of the Minkowski Sum of Planar Point Sets. Electron. J. Comb. Friedrich Eisenbrand, János Pach, Thomas Rothvoß, Nir B. Sopher
2008	—	`ch.`	Der Euklidische Algorithmus. Taschenbuch der Algorithmen Friedrich Eisenbrand
2008	J	`jnl`	Energy-Aware Stage Illumination. Int. J. Comput. Geom. Appl. Friedrich Eisenbrand, Stefan Funke, Andreas Karrenbauer, Domagoj Matijevic
2008	J	`jnl`	Flow Faster: Efficient Decision Algorithms for Probabilistic Simulations CoRR Lijun Zhang, Holger Hermanns, Friedrich Eisenbrand, David N. Jansen
2008	J	`jnl`	Flow Faster: Efficient Decision Algorithms for Probabilistic Simulations. Log. Methods Comput. Sci. Lijun Zhang, Holger Hermanns, Friedrich Eisenbrand, David N. Jansen
2008	J	`jnl`	Parametric Integer Programming in Fixed Dimension. Math. Oper. Res. Friedrich Eisenbrand, Gennady Shmonin
2008	A	`conf`	Static-Priority Real-Time Scheduling: Response Time Computation Is NP-Hard. RTSS Friedrich Eisenbrand, Thomas Rothvoß
2008	J	`jnl`	The stable set polytope of quasi-line graphs. Comb. Friedrich Eisenbrand, Gianpaolo Oriolo, Gautier Stauffer, Paolo Ventura
2007	A	`conf`	0/1 Vertex and Facet Enumeration with BDDs. ALENEX Markus Behle, Friedrich Eisenbrand
2007	—	`conf`	A geometric framework for solving subsequence problems in computational biology efficiently. SCG Thorsten Bernholt, Friedrich Eisenbrand, Thomas Hofmeister
2007	—	`conf`	Algorithms for Longer OLED Lifetime. WEA Friedrich Eisenbrand, Andreas Karrenbauer, Chihao Xu
2007	A	`conf`	Flow Faster: Efficient Decision Algorithms for Probabilistic Simulations. TACAS Lijun Zhang, Holger Hermanns, Friedrich Eisenbrand, David N. Jansen
2007	J	`jnl`	New Approaches for Virtual Private Network Design. SIAM J. Comput. Friedrich Eisenbrand, Fabrizio Grandoni, Gianpaolo Oriolo, Martin Skutella
2007	J	`jnl`	Packing a Truck - Now with a Twist! Int. J. Comput. Geom. Appl. Friedrich Eisenbrand, Stefan Funke, Andreas Karrenbauer, Joachim Reichel, Elmar Schömer
2006	J	`jnl`	Carathéodory bounds for integer cones. Oper. Res. Lett. Friedrich Eisenbrand, Gennady Shmonin
2006	B	`conf`	Mapping Task-Graphs on Distributed ECU Networks: Efficient Algorithms for Feasibility and Optimality. RTCSA Werner Damm, Alexander Metzner, Friedrich Eisenbrand, Gennady Shmonin, Reinhard Wilhelm, Sebastian Winkel
2006	A	`conf`	Multiline Addressing by Network Flow. ESA Friedrich Eisenbrand, Andreas Karrenbauer, Martin Skutella, Chihao Xu
2006	C	`conf`	Provisioning a Virtual Private Network Under the Presence of Non-communicating Groups. CIAC Friedrich Eisenbrand, Edda Happ
2005	J	`jnl`	A linear algorithm for integer programming in the plane. Math. Program. Friedrich Eisenbrand, Sören Laue
2005	A*	`conf`	An improved approximation algorithm for virtual private network design. SODA Friedrich Eisenbrand, Fabrizio Grandoni
2005	—	`conf`	BDDs in a Branch and Cut Framework. WEA Bernd Becker, Markus Behle, Friedrich Eisenbrand, Ralf Wimmer
2005	B	`conf`	Circular Ones Matrices and the Stable Set Polytope of Quasi-Line Graphs. IPCO Friedrich Eisenbrand, Gianpaolo Oriolo, Gautier Stauffer, Paolo Ventura
2005	—	`conf`	Energy-aware stage illumination. SCG Friedrich Eisenbrand, Stefan Funke, Andreas Karrenbauer, Domagoj Matijevic
2005	A*	`conf`	New Approaches for Virtual Private Network Design. ICALP Friedrich Eisenbrand, Fabrizio Grandoni, Gianpaolo Oriolo, Martin Skutella
2005	—	`conf`	Packing a trunk: now with a twist! Symposium on Solid and Physical Modeling Friedrich Eisenbrand, Stefan Funke, Andreas Karrenbauer, Joachim Reichel, Elmar Schömer
2004	—	`conf`	Bounded Model Checking and Inductive Verification of Hybrid Discrete-continuous Systems. MBMV Bernd Becker, Markus Behle, Friedrich Eisenbrand, Martin Fränzle, Marc Herbstritt, Christian Herde, Jörg Hoffmann, Daniel Kröning, Bernhard Nebel, Ilia Polian, Ralf Wimmer
2004	J	`jnl`	On the complexity of fixed parameter clique and dominating set. Theor. Comput. Sci. Friedrich Eisenbrand, Fabrizio Grandoni
2004	A*	`conf`	Point containment in the integer hull of a polyhedron. SODA Ernst Althaus, Friedrich Eisenbrand, Stefan Funke, Kurt Mehlhorn
2003	B	`conf`	A Faster Algorithm for Two-Variable Integer Programming. ISAAC Friedrich Eisenbrand, Sören Laue
2003	A*	`conf`	A combinatorial algorithm for computing a maximum independent set in a t-perfect graph. SODA Friedrich Eisenbrand, Stefan Funke, Naveen Garg, Jochen Könemann
2003	J	`jnl`	A compact linear program for testing optimality of perfect matchings. Oper. Res. Lett. Paolo Ventura, Friedrich Eisenbrand
2003	J	`jnl`	Bounds on the Chvátal Rank of Polytopes in the 0/1-Cube. Comb. Friedrich Eisenbrand, Andreas S. Schulz
2003	J	`jnl`	Detecting directed 4-cycles still faster. Inf. Process. Lett. Friedrich Eisenbrand, Fabrizio Grandoni
2003	A	`conf`	Fast Integer Programming in Fixed Dimension. ESA Friedrich Eisenbrand
2003	A	`conf`	Packing a Trunk. ESA Friedrich Eisenbrand, Stefan Funke, Joachim Reichel, Elmar Schömer
2003	J	`jnl`	Primal separation for 0/1 polytopes. Math. Program. Friedrich Eisenbrand, Giovanni Rinaldi, Paolo Ventura
2002	A*	`conf`	0/1 optimization and 0/1 primal separation are equivalent. SODA Friedrich Eisenbrand, Giovanni Rinaldi, Paolo Ventura
2001	J	`jnl`	Cutting Planes and the Elementary Closure in Fixed Dimension. Math. Oper. Res. Alexander Bockmayr, Friedrich Eisenbrand
2001	B	`conf`	Fast 2-Variable Integer Programming. IPCO Friedrich Eisenbrand, Günter Rote
2001	—	`conf`	Fast Reduction of Ternary Quadratic Forms. CaLC Friedrich Eisenbrand, Günter Rote
2001	J	`jnl`	Short vectors of planar lattices via continued fractions. Inf. Process. Lett. Friedrich Eisenbrand
2000	—	`conf`	Combining Logic and Optimization in Cutting Plane Theory. FroCoS Alexander Bockmayr, Friedrich Eisenbrand
2000	—	`—`	Gomory-Chvátal cutting planes and the elementary closure of polyhedra. Friedrich Eisenbrand
1999	B	`conf`	Bounds on the Chvátal Rank of Polytopes in the 0/1-Cube. IPCO Friedrich Eisenbrand, Andreas S. Schulz
1999	J	`jnl`	On factor refinement in number fields. Math. Comput. Johannes Buchmann, Friedrich Eisenbrand
1999	J	`jnl`	On the Chvátal Rank of Polytopes in the 0/1 Cube. Discret. Appl. Math. Alexander Bockmayr, Friedrich Eisenbrand, Mark E. Hartmann, Andreas S. Schulz
1999	J	`jnl`	On the Membership Problem for the Elementary Closure of a Polyhedron. Comb. Friedrich Eisenbrand