Packing of arborescences with matroid constraints via matroid intersection
نویسندگان
چکیده
منابع مشابه
Matroid-Based Packing of Arborescences
We provide the directed counterpart of a slight extension of Katoh and Tanigawa’s result [8] on rooted-tree decompositions with matroid constraints. Our result characterizes digraphs having a packing of arborescences with matroid constraints. It is a proper extension of Edmonds’ result [1] on packing of spanning arborescences and implies – using a general orientation result of Frank [4] – the a...
متن کاملOn packing spanning arborescences with matroid constraint
Let D = (V + s,A) be a digraph with a designated root vertex s. Edmonds’ seminal result [4] implies that D has a packing of k spanning s-arborescences if and only if D has a packing of k (s, t)-paths for all t ∈ V , where a packing means arc-disjoint subgraphs. Let M be a matroid on the set of arcs leaving s. A packing of (s, t)-paths is called M-based if their arcs leaving s form a base of M w...
متن کاملReachability-based matroid-restricted packing of arborescences
The fundamental result of Edmonds [5] started the area of packing arborescences and the great number of recent results shows increasing interest of this subject. Two types of matroid constraints were added to the problem in [2, 3, 9], here we show that both contraints can be added simultaneously. This way we provide a solution to a common generalization of the reachability-based packing of arbo...
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In this paper, we consider the following variant of the matroid intersection problem. We are given two matroids M1,M2 on the same ground set E and a subset A of E. Our goal is to find a common independent set I of M1,M2 such that |I ∩A| is maximum among all common independent sets of M1,M2 and such that (secondly) |I| is maximum among all common independent sets of M1,M2 satisfying the first co...
متن کاملMatroid Intersection
Last lecture we covered matroid intersection, and defined matroid union. In this lecture we review the definitions of matroid intersection, and then show that the matroid intersection polytope is TDI. This is Chapter 41 in Schrijver’s book. Next we review matroid union, and show that unlike matroid intersection, the union of two matroids is again a matroid. This material is largely contained in...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2019
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-019-01377-0