computer science publication server: No conditions. Results ordered -Date Deposited. 2021-04-22T23:48:43ZEPrintshttp://e-archive.informatik.uni-koeln.de/images/sitelogo.pnghttp://e-archive.informatik.uni-koeln.de/2014-06-30T12:41:52Z2014-06-30T12:41:52Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/741This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/7412014-06-30T12:41:52ZThe permutahedron of series-parallel posetsAnnelie von ArnimArnim, Annelie vonUlrich FaigleFaigle, UlrichRainer SchraderSchrader, Rainer2001-04-02T00:00:00Z2011-12-19T09:45:17Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/326This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/3262001-04-02T00:00:00ZSimple 0/1-PolytopesFor general polytopes, it has turned out that with respect to many questions it suffices to consider only the simple polytopes, i.e., d-dimensional polytopes where every vertex is contained in only d facets. In this paper, we show that the situation is very different within the class of 0/1-polytopes, since every simple 0/1-polytope is the (cartesian) product of some 0/1-simplices (which proves a conjecture of Ziegler), and thus, the restriction to simple 0/1-polytopes leaves only a very small class of objects with a rather trivial structure.Volker KaibelKaibel, VolkerMartin WolffWolff, Martin2001-04-02T00:00:00Z2011-10-21T13:42:56Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/74This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/742001-04-02T00:00:00ZLinear Programming Duality : An Introduction to Oriented MatroidsThis book presents an elementary introduction to the theory of oriented matroids. The way oriented matroids are introduced emphasizes that they are the most general - and hence simplest - structures for which linear Programming Duality results can be stated and proved. The main theme of the book is duality. Using Farkas' Lemma as the basis the authors start with results on polyhedra in R n and show how to restate the essence of the proofs in terms of sign patterns of oriented matroids. Most of the standard material in Linear Programming is presented in the setting of real space as well as in the more abstract theory of oriented matroids. This approach clarifies the theory behind Linear Programming and proofs become simpler. The last part of the book deals with the facial structure of polytopes respectively their oriented matroid counterparts. It is an introduction to more advanced topics in oriented matroid theory. Each chapter contains suggestions for further reading and the references provide an overview of the research in this field.Achim BachemBachem, AchimWalter KernKern, Walter2001-04-02T00:00:00Z2014-07-04T13:19:06Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/143This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/1432001-04-02T00:00:00ZThe Permutahedron of N-sparse PosetsThe permutahedron of a poset is the convex hull of all incidence vectors of linear extensions. For the case of N-sparse posets in which any five elements induce at most one N we give a characterization of the permutahedron in terms of linear inequalities. This yields an LP-solution for minimizing the weighted mean completion time for jobs with unit processing times and N-sparse precedence constraints. We close with an extension of our approach to arbitrary processing timesAnnelie von ArnimArnim, Annelie vonRainer SchraderSchrader, RainerYaoguang WangWang, Yaoguang2001-04-02T00:00:00Z2011-09-28T14:52:07Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/179This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/1792001-04-02T00:00:00ZFacets of the generalized permutahedron of a posetGiven a poset P as a precedence relation on a set of jobs with processing time vector p, the generalized permutahedron ext{perm}(P,p) of P is defined as the convex hull of all job completion time vectors corresponding to a linear extension of P. Thus, the generalized permutahedron allows for the single machine weighted flowtime scheduling problem to be formulated as a linear programming problem over ext{perm}(P,p). Queyranne and Wang (1991) as well as von Arnim and Schrader (1997) gave a collection of valid inequalities for this polytope. Here we present a description of its geometric structure that depends on the series decomposition of the poset P, prove a dimension formula for ext{perm}(P,p), and characterize the facet inducing inequalities under the known classes of valid inequalities.Annelie von ArnimArnim, Annelie vonAndreas S. SchulzSchulz, Andreas S.2001-04-02T00:00:00Z2012-01-16T13:41:46Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/327This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/3272001-04-02T00:00:00ZUpper Bounds on the Maximal Number of Facets of 0/1-PolytopesWe prove two new upper bounds on the number of facets that a d-dimensional 0/1-polytope can have. The first one is 2(d-1)!+2(d-1) (which is the best one currently known for small dimensions), while the second one of O((d-2)!) is the best known bound for large dimensions.Tamas FleinerFleiner, TamasVolker KaibelKaibel, VolkerGünter RoteRote, Günter2001-04-02T00:00:00Z2011-11-16T11:11:23Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/153This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/1532001-04-02T00:00:00ZThe Circuit Polytope: FacetsGiven an undirected graph G=(V,E) and a costs c(e) attached to the edges of G, the weighted girth problem is to find a circuit in G having minimum total cost. This problem is in general NP-hard since the traveling salesman problem can be reduced to it. A promising approach to hard combinatorial optimization problems is given by the so-called cutting plane methods. These involve linear programming techniques based on a partial description of the convex hull of the incidence vectors of possible solutions. We consider the weighted girth problem in the case where G is the complete graph and study the facial structure of the circuit polytope and some related polyhedra. In the appendix we give complete characterizations of some small circuit polytopes.Petra BauerBauer, Petra2001-04-02T00:00:00Z2012-01-09T10:38:49Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/182This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/1822001-04-02T00:00:00ZInteger polyhedra from supermodular functions on series-parallel posetsWe define a class of integer polyhedra induced by supermodular functions on series-parallel posets. We show that permutahedra and generalized polymatroids are special instances of our approach.Rainer SchraderSchrader, RainerGeorg WambachWambach, Georg2001-04-02T00:00:00Z2012-01-09T10:37:51Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/181This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/1812001-04-02T00:00:00ZThe Setup Polyhedron of Series-Parallel PosetsTo every linear extension L of a poset P=(P,<) we associate a {0,1}-vector x = x(L) with xe = 1 if and only if e is preceded by a jump in L or e is the first element in L. Let Q = conv{ x(L) | L in L(P) } be the convex hull of all incidence vectors of linear extensions of P. For the case of series-parallel posets we give a linear description of Q.Rainer SchraderSchrader, RainerGeorg WambachWambach, Georg2001-04-02T00:00:00Z2012-01-16T15:42:04Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/318This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/3182001-04-02T00:00:00ZAbstract Objective Function Graphs on the 3-cube: A Classification by RealizabilityWe call an orientation of the graph of a simple polytope P an abstract objective function (AOF) graph if it satisfies two conditions that make the simplex algorithm (e.g. with the Random-Facet pivot rule of Kalai and Matousek, Sharir, and Welzl) work: it has to be acyclic and it has to induce a unique sink in every subgraph that corresponds to a face of the polytope. For the graph of the 3-dimensional cube we investigate the question which among all possible AOF graphs are realizable in the sense that they are induced by some linear program (with a polytope of feasible solutions that is combinatorially a 3-dimensional cube). It turns out that (up to isomorphism) precisely two AOF graphs are not realizable.Bernd GärtnerGärtner, BerndVolker KaibelKaibel, Volker2001-04-02T00:00:00Z2012-01-16T14:59:53Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/248This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/2482001-04-02T00:00:00ZThe setup polytope of N-sparse posetsThe setup problem is the following single-machine scheduling problem: There are n jobs with individual processing times, arbitrary precedence relations and sequence-dependent setup costs (or changeover times). The setup cost sef arises in a schedule if job f is processed immediately after job e, e.g., the machine must be cleaned of e and prepared for f. The goal is to find a schedule minimizing the total setup costs (and thus, for changeover times, the makespan). We consider the case of ''precedence-induced'' setup costs where a nonzero term sef occurs only if e and f are unrelated with respect to the precedence relations. Moreover, we assume that the setup costs depend only on f, i.e., sef = sf for all e which are unrelated to f.
Two special cases of the setup problem with precedence-induced setup costs are the jump numberproblem and the bump number problem. We suggest a new polyhedral model for the precedence-induced setup problem. To every linear extension L = e1 e2 en ... of a poset P = (P1 <) with n elements, we associate a 0, 1-vector x L in R P with xe L = 1 if and only if e starts a chain in L (e = e1 or e = ei+1 | ei ). The setup polytope S is the convex hull of the incidence vectors of all linear extensions of P. For N-sparse posets P, i.e., posets whose comparability graph is P4-sparse, we give a complete linear description of S. The integrality part of the proof employs the concept of box total dual integrality.Rainer SchraderSchrader, RainerGeorg WambachWambach, Georg