Branchings and Partitions
نویسندگان
چکیده
منابع مشابه
Approximate maximum weight branchings
We consider a special subgraph of a weighted directed graph: one comprising only the k heaviest edges incoming to each vertex. We show that the maximum weight branching in this subgraph closely approximates the maximum weight branching in the original graph. Specifically, it is within a factor of k k+1 . Our interest in finding branchings in this subgraph is motivated by a data compression appl...
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Chu and Liu, Ecbnonds, and Bock have independently devised an ef f ic ient aZgorYithm to f i n d an optimum branching i n a d i rected haph. runs i n O(m2ogn) time i f the problem graph has n vertices and m edges. A modification for dense graphs gives a running time 2 of O(n 1. We also show that the unmodified algorithm runs i n 2 O(n(Zog n) + m) time on an average graph, asswning a uniform pro...
متن کاملSmall degree out-branchings
Using a suitable orientation, we give a short proof of a result of Czumaj and Strothmann [3]: Every 2-edge-connected graph G contains a spanning tree T with the property that dT (v) ≤ dG(v)+3 2 for every vertex v. Trying to find an analogue of this result in the directed case, we prove that every 2-arc-strong digraph D has an out-branching B such that d+B(x) ≤ d+D(x) 2 + 1. As a corollary, ever...
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Let D be a finite directed acyclic multigraph and t be a vertex of D such that for each other vertex x of D, there are n pairwise openly disjoint paths in D from x to t. It is proved that there exist n spanning trees BI , , B,, in D directed toward t such that for each vertex x # t of D, the N paths from x to t in B1, ,B,, are pairwise openly disjoint. @ 1999 Elsevier Science B.V. All rights re...
متن کاملOut-branchings with Extremal Number of Leaves
An out-tree T in a digraph D is subgraph of D which is an orientation of a tree that has only one vertex of in-degree 0 (root). A vertex of T is a leaf if it has out-degree 0. A spanning out-tree is called an out-branching. We’ll overview some recent algorithmic and theoretical results on out-branchings with minimum and maximum number of leaves.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1975
ISSN: 0002-9939
DOI: 10.2307/2040408