Packing algorithms for arborescences (and spanning trees) in capacitated graphs

  • Harold N. Gabow
  • K. S. Manu
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 920)

Abstract

In a digraph with real-valued edge capacities, we pack the greatest number of arborescences in time O(n3m log (n2/m)); the packing uses at most m distinct arborescences. Here n and m denote the number of vertices and edges respectively. Similar results hold for integral packing: we pack the greatest number of arborescences in time O(minn, log (nN)n2m log (n2/m)), using at most m+n−2 distinct arborescences; here N denotes the largest capacity. These results improve all previous strong- and weak-polynomial bounds for capacitated digraphs. The algorithm extends to related problems, including packing spanning trees in an undirected capacitated graph, and covering such graphs by forests. The algorithm provides a new proof of Edmonds' theorem for arborescence packing, for both integral and real capacities. The algorithm works by maintaining a certain laminar family of sets.

Keywords

Span Tree Greedy Algorithm Fractional Packing Packing Algorithm Integral Packing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Harold N. Gabow
    • 1
  • K. S. Manu
    • 1
  1. 1.Department of Computer ScienceUniversity of Colorado at BoulderBoulderUSA

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