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  • 1
    Digitale Medien
    Digitale Medien
    The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings (2000)
    Springer
    Journal of the European Mathematical Society 2 (2000), S. 179-198 
    Details
    ISSN: 1435-9863
    Schlagwort(e): Mathematics Subject Classification (1991): 52B11, 52B20, 14M25
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract. In 1994, Sturmfels gave a polyhedral version of the Cayley Trick of elimination theory: he established an order-preserving bijection between the posets of coherent mixed subdivisions of a Minkowski sum ?1+...+? r of point configurations and of coherent polyhedral subdivisions of the associated Cayley embedding ?(?1,...,? r ). In this paper we extend this correspondence in a natural way to cover also non-coherent subdivisions. As an application, we show that the Cayley Trick combined with results of Santos on subdivisions of Lawrence polytopes provides a new independent proof of the Bohne-Dress theorem on zonotopal tilings. This application uses a combinatorial characterization of lifting subdivisions, also originally proved by Santos.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s100970050003
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  • 2
    Buch
    Buch
    Polyhedral subdivisions and projections of polytopes. Berlin, Technische Universität, Diss. 1996 (1996)
    Aachen :Shaker,
    Details
    Titel: Polyhedral subdivisions and projections of polytopes. Berlin, Technische Universität, Diss. 1996
    Autor: Rambau, Jörg
    Verlag: Aachen :Shaker,
    Erscheinungsjahr: 1996
    Seiten: 123 S.
    Serie: Berichte aus der Mathematik
    Materialart: Buch
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  • 3
    Buch
    Buch
    Kombinatorische Methoden in Geometrie, Topologie und Optimierung / (2002)
    Details
    Titel: Kombinatorische Methoden in Geometrie, Topologie und Optimierung /
    Autor: Rambau, Jörg
    Erscheinungsjahr: 2002
    Seiten: versch. Zähl.
    Materialart: Buch
    Sprache: Deutsch
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  • 4
    Buch
    Buch
    Online optimization of large scale systems (2001)
    Berlin u.a. :Springer,
    Details
    Titel: Online optimization of large scale systems
    Beteiligte Person(en): Grötschel, Martin , Krumke, Sven O. , Rambau, Jörg
    Verlag: Berlin u.a. :Springer,
    Erscheinungsjahr: 2001
    Seiten: 801 S.
    Materialart: Buch
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  • 5
    Buch
    Buch
    Triangulations /; 25 (2010)
    Berlin [u.a.] :Springer,
    Details
    Titel: Triangulations /; 25
    Autor: De Loera, Jesús A.
    Beteiligte Person(en): Rambau, Jörg , Santos, Francisco
    Verlag: Berlin [u.a.] :Springer,
    Erscheinungsjahr: 2010
    Seiten: XIII, 535 S. : , Ill., graph. Darst. ; , 27 cm
    Serie: Algorithms and computation in mathematics 25
    ISBN: 3-642-12970-6 , 978-3-642-12970-4 , 978-3-642-12971-1
    Materialart: Buch
    Sprache: Englisch
    URL: http://d-nb.info/100142624X/04
    URL: http://deposit.d-nb.de/cgi-bin/dokserv?id=3452498&prov=M&dok_var=1&dok_ext=htm
    URL: http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1207.52002
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  • 6
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    The Generalized Baues Problem for Cyclic Polytopes I. (1998)
    Details
    Publikationsdatum: 2014-11-10
    Beschreibung: The Generalized Baues Problem asks whether for a given point configuration the order complex of all its proper polyhedral subdivisions, partially ordered by refinement, is homotopy equivalent to a sphere. In this paper, an affirmative answer is given for the vertex sets of cyclic polytopes in all dimensions. This yields the first non-trivial class of point configurations with neither a bound on the dimension, the codimension, nor the number of vertice for which this is known to be true. Moreover, it is shown that all triangulations of cyclic polytopes are lifting triangulations. This contrasts the fact that in general there are many non-regular triangulations of cyclic polytopes. Beyond this, we find triangulations of $C(11,5)$ with flip deficiency. This proves---among other things---that there are triangulations of cyclic polytopes that are non-regular for every choice of points on the moment curve.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 7
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    Wo bleibt der Aufzug? (1999)
    Details
    Publikationsdatum: 2020-11-13
    Beschreibung: Dieser Artikel gibt eine allgemeinverständliche Einführung in die spezielle Problematik kombinatorischer Online-Problem am Beispiel der Fahrstuhlsteuerung.
    Schlagwort(e): ddc:000
    Sprache: Deutsch
    Materialart: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 8
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    Combinatorial Online Optimization (1998)
    Details
    Publikationsdatum: 2020-11-13
    Beschreibung: In ``classical'' optimization, all data of a problem instance are considered given. The standard theory and the usual algorithmic techniques apply to such cases only. Online optimization is different. Many decisions have to be made before all data are available. In addition, decisions once made cannot be changed. How should one act ``best'' in such an environment? In this paper we survey online problems coming up in combinatorial optimization. We first outline theoretical concepts, such as competitiveness against various adversaries, to analyze online problems and algorithms. The focus, however, lies on real-world applications. We report, in particular, on theoretical investigations and our practical experience with problems arising in transportation and the automatic handling of material.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 9
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    The Online Transportation Problem: Competitive Scheduling of Elevators (1998)
    Details
    Publikationsdatum: 2020-11-13
    Beschreibung: In this paper we consider the following online transportation problem (\textsc{Oltp}): Objects are to be transported between the vertices of a given graph. Transportation requests arrive online, specifying the objects to be transported and the corresponding source and target vertex. These requests are to be handled by a server which commences its work at a designated origin vertex and which picks up and drops objects at their starts and destinations. After the end of its service the server returns to its start. The goal of \textsc{Oltp} is to come up with a transportation schedule for the server which finishes as early as possible. We first show a lower bound of~$5/3$ for the competitive ratio of any deterministic algorithm. We then analyze two simple and natural strategies which we call \textsf{REPLAN} and \textsf{IGNORE}. \textsf{REPLAN} completely discards its schedule and recomputes a new one when a new request arrives. \textsf{IGNORE} always runs a (locally optimal) schedule for a set of known requests and ignores all new requests until this schedule is completed. We show that both strategies, \textsf{REPLAN} and \textsf{IGNORE}, are $5/2$-competitive. We also present a somewhat less natural strategy \textsf{SLEEP}, which in contrast to the other two strategies may leave the server idle from time to time although unserved requests are known. We also establish a competitive ratio of~$5/2$ for the algorithm \textsf{SLEEP}. Our results are extended to the case of ``open schedules'' where the server is not required to return to its start position at the end of its service.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 10
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    Simulation Studies for the Online-Dial-a-Ride Problem (1999)
    Details
    Publikationsdatum: 2020-11-13
    Beschreibung: In a large distribution center of Herlitz AG, Berlin, we invesigated the elevator subsystem of the fully automated pallet transportation system. Each elevator may carry one pallet and has to serve eight levels. The goal is to minimize the average resp.\ the maximum flow time. The variants of this elevator control problem have been subject of recent theoretical research and are known as online-dial-a-ride problems. In this paper we investigate several online algorithms for several versions of online-dial-a-ride problems by means of a simulation program, developed on the basis of the simulation library AMSEL. We draw statistics from samples of randomly generated data providing for different load situations. Moreover, we provide preliminary studies with real production data for a system of five elevators connected by a conveyor circuit, as can be found at the Herlitz plant. We show which algorithms are best under certain load situations and which lead to break downs under particular circumstances.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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