منابع مشابه
Matroid matching with Dilworth truncation
Let H = (V, E) be a hypergraph and let k ≥ 1 and l ≥ 0 be fixed integers. LetM be the matroid with ground-set E s.t. a set F ⊆ E is independent if and only if each X ⊆ V with k|X| − l ≥ 0 spans at most k|X| − l hyperedges of F . We prove that if H is dense enough, thenM satisfies the double circuit property, thus the min-max formula of Dress and Lovász on the maximum matroid matching holds forM...
متن کاملMatching Problems with Delta-Matroid Constraints
Given an undirected graph G = (V,E) and a directed graph D = (V,A), the master/slave matching problem is to find a matching of maximum cardinality in G such that for each arc (u, v) ∈ A with u being matched, v is also matched. This problem is known to be NP-hard in general, but polynomially solvable in a special case where the maximum size of a connected component of D is at most two. This pape...
متن کاملOptimal truncation in matching markets
Since no stable matching mechanism can induce truth-telling as a dominant strategy for all participants, there is often room in matching markets for strategic misrepresentation (Roth [25]). In this paper we study a natural form of strategic misrepresentation: reporting a truncation of one’s true preference list. Roth and Rothblum [28] prove an important but abstract result: in certain symmetric...
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The matroid parity (MP) problem is a natural extension of the matching problem to the matroid setting. It can be formulated as a 0− 1 linear program using the so-called rank and line constraints. We call the associated family of polytopes MP polytopes. We then prove the following: (i) when the matroid is a gammoid, each MP polytope is a projection of a perfect matching polytope into a suitable ...
متن کاملAn algorithm for weighted fractional matroid matching
LetM be a matroid on ground set E. A subset l ⊆ E is called a line when r(l) ∈ {1, 2}. Given a set of lines L = {l1, . . . , lk} in M , a vector x ∈ RL+ is called a fractional matching when ∑ l∈L xla(F )l ≤ r(F ) for every flat F ofM . Here a(F )l is equal to 0 when l∩F = ∅, equal to 2 when l ⊆ F and equal to 1 otherwise. We refer to ∑ l∈L xl as the size of x. It was shown by Chang et al. that ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.07.076