منابع مشابه
Finding optimum branchings
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 کاملA note on finding optimum branchings
The subject of t h i s note i s Tarjan's aZgorithm for finding an optimum branching in a directed graph. ed out, namely (i) an incorrect cZaim invoZving branching uniqueness, and (ii) an imprecise way of updating edge vaZues i n each i terat ion. val idi ty of the algorithm. I t is s h m here that they may be f ixed v i a a simpZe modification, which Zeaves unchanged the overall time and space ...
متن کاملApproximating optimum branchings in linear time
We prove that maximum weight branchings in directed graphs can be approximated in time O(m) up to a factor of 1− ǫ, where ǫ > 0 is an arbitrary constant.
متن کاملApproximate 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...
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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ژورنال
عنوان ژورنال: Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics
سال: 1967
ISSN: 0022-4340
DOI: 10.6028/jres.071b.032