Packing and partitioning orbitopes
نویسندگان
چکیده
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 ...
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In this paper, we consider symmetric binary programs that contain set packing, partitioning, or covering (ppc) inequalities. To handle symmetries as well as ppc-constraints simultaneously, we introduce constrained symresacks which are the convex hull of all binary points that are lexicographically not smaller than their image w.r.t. a coordinate permutation and which fulfill some ppc-constraint...
متن کاملSet Covering, Packing and Partitioning Problems
where A is a mxn matrix of zeroes and ones, e = (1,...,1) is a vector of m ones and c is a vector of n (arbitrary) rational components. This pure 0-1 linear programming problem is called the set covering problem. When the inequalities are replaced by equations the problem is called the set partitioning problem, and when all of the ≥ constraints are replaced by ≤ constraints, the problem is call...
متن کاملOn Partitioning and Packing Products with Rectangles
In [1] we introduced and studied for product hypergraphs Hn = Qni=1Hi , where Hi = (Vi; Ei) , the minimal size (Hn) of a partition of Vn =Qni=1 Vi into sets that are elements of En = Qni=1 Ei . The main result was that (Hn) = n Y i=1 (Hi); (1) if the Hi's are graphs with all loops included. A key step in the proof concerns the special case of complete graphs. Here we show that (1) also holds wh...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2007
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-006-0081-5