منابع مشابه
Packing and Partitioning Orbitopes
We introduce orbitopes as the convex hulls of 0/1-matrices that are lexicographically maximal subject to a group acting on the columns. Special cases are packing and partitioning orbitopes, which arise from restrictions to matrices with at most or exactly one 1-entry in each row, respectively. The goal of investigating these polytopes is to gain insight into ways of breaking certain symmetries ...
متن کاملExtended Formulations for Packing and Partitioning Orbitopes
We give compact extended formulations for the packing and partitioning orbitopes (with respect to the full symmetric group) described and analyzed in [6]. These polytopes are the convex hulls of all 0/1-matrices with lexicographically sorted columns and at most, resp. exactly, one 1-entry per row. They are important objects for symmetry reduction in certain integer programs. Using the extended ...
متن کاملExtended Formulations for Column Constrained Orbitopes
In the literature, packing and partitioning orbitopes were discussed to handle symmetries that act on variable matrices in certain binary programs. In this paper, we extend this concept by restrictions on the number of 1-entries in each column. We develop extended formulations of the resulting polytopes and present numerical results that show their effect on the LP relaxation of a graph partiti...
متن کاملThe maximum k-colorable subgraph problem and orbitopes
Given an undirected node-weighted graph and a positiveinteger k, the maximum k-colorable subgraph problem is to select ak-colorable induced subgraph of largest weight. The natural integerprogramming formulation for this problem exhibits a high degree ofsymmetry which arises by permuting the color classes. It is well knownthat such symmetry has negative effects on the perform...
متن کاملOn the polar derivative of a polynomial
For a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, Dewan et al [K. K. Dewan, N. Singh and A. Mir, Extension of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). In this paper we improve and extend the above inequality. Our result generalizes certai...
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ژورنال
عنوان ژورنال: Communications in Analysis and Geometry
سال: 2013
ISSN: 1019-8385,1944-9992
DOI: 10.4310/cag.2013.v21.n3.a5