Valuations for Matroid Polytope Subdivisions
نویسندگان
چکیده
منابع مشابه
Valuations for matroid polytope subdivisions
We prove that the ranks of the subsets and the activities of the bases of a matroid define valuations for the subdivisions of a matroid polytope into smaller matroid polytopes.
متن کاملFenchel-type duality for matroid valuations
The weighted matroid intersection problem has recently been extended to the valuated matroid intersection problem: Given a pair of valuated matroids Mi = (V,Bi, ωi) (i = 1, 2) defined on a common ground set V , find a common base B ∈ B1∩B2 that maximizes ω1(B)+ω2(B). This paper develops a Fenchel-type duality theory related to this problem with a view to establishing a convexity framework for n...
متن کاملOn the cardinality constrained matroid polytope
Given a combinatorial optimization problem Π and an increasing finite sequence c of natural numbers, we obtain a cardinality constrained version Πc of Π by permitting only those feasible solutions of Π whose cardinalities are members of c. We are interested in polyhedra associated with those problems, in particular in inequalities that cut off solutions of forbidden cardinality. Maurras [11] an...
متن کاملTrioid: A generalization of matroid and the associated polytope
Abstract. We consider a generalization of the well known greedy algorithm, called mstep greedy algorithm, where m elements are examined in each iteration. When m = 1 or 2, the algorithm reduces to the standard greedy algorithm. For m = 3 we provide a complete characterization of the independence system, called trioid, where the m-step greedy algorithm guarantees an optimal solution for all weig...
متن کاملThe Lattice of Flats and its Underlying Flag Matroid Polytope
Let M be a matroid and F the collection of all linear orderings of bases ofM. orflags of M. We define the flag matroid polytope A(F)We determine when two vertices of A(F) are adjacent, and provide a bijection between maximal chains in the lattice of flats of M and certain maximal faces of A(F).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2010
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2010-064-9