Parallel and fast sequential algorithms for undirected edge connectivity augmentation

@article{Benczr1999ParallelAF,
  title={Parallel and fast sequential algorithms for undirected edge connectivity augmentation},
  author={Andr{\'a}s A. Bencz{\'u}r},
  journal={Mathematical Programming},
  year={1999},
  volume={84},
  pages={595-640}
}
  • A. Benczúr
  • Published 1 April 1999
  • Computer Science, Mathematics
  • Mathematical Programming
1,E2,..., such that ⋃i≤τEi optmially increases the connectivity by τ, for any integer τ. The main result of the paper is that this sequence of edge sets can be divided into O(n) groups such that within one group, all Ei are basically the same. Using this result, we improve on the running time of edge connectivity augmentation, as well as we give the first parallel (RNC) augmentation algorithm. We also present new efficient subroutines for finding the so-called extreme sets and the cactus… 
2 Citations

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References

SHOWING 1-10 OF 40 REFERENCES

Successive edge-connectivity augmentation problems

TLDR
The augmentation algorithm of A. Frank can be used to solve the corresponding Successive Edge-Augmentation Problem and implies (a stronger version of) the Successive Augmentation Property, even for some non-uniform demands.

Augmenting Graphs to Meet Edge-Connectivity Requirements

  • A. Frank
  • Mathematics
    SIAM J. Discret. Math.
  • 1992
TLDR
A min-max formula is derived for $\gamma$ and a polynomial time algorithm to compute it is described, and the directed counterpart of the problem is solved and is shown to be NP-complete.

A matroid approach to finding edge connectivity and packing arborescences

  • H. Gabow
  • Computer Science, Mathematics
    STOC '91
  • 1991
TLDR
An algorithm that finds k edge-disjoint arborescences on a directed graph in time O(kmn + k3n2)2 is presented, based on two theorems of Edmonds that link these two problems and show how they can be solved.

The minimum augmentation of any graph to a K-edge-connected graph

TLDR
A good characterization and good algorithm are obtained for augmenting G0 to a K-edge-connected graph and applications are suggested in designing a reliable network aiming at the most effective use of exising network.

Augmenting hypergraphs by edges of size two

TLDR
This work gives a good characterization for the minimum number of edges of size two whose addition to a given hypergraph H makes it k-edge-connected, and describes a strongly polynomial algorithm to find both a minimum cardinality augmentation, and a minimum cost augmentation.

A Fast Algorithm for Optimally Increasing the Edge Connectivity

TLDR
The solution is particularly simple, it runs in O(nm) time, and it is a natural generalization of the algorithm in [K. Eswaran and R. Tarjan, SIAM J. Comput., 5 (1976), pp. 653--665] for the case where $\lambda+\delta =2$.

A representation of cuts within 6/5 times the edge connectivity with applications

  • A. Benczúr
  • Computer Science
    Proceedings of IEEE 36th Annual Foundations of Computer Science
  • 1995
TLDR
This paper gives an O(n/sup 2/)-sized planar geometric representation for all edge cuts with capacity less than 6/5c, and shows that in algorithms based on edge splitting, computing this representation O(log n) times substitute for one, or sometimes even /spl Omega/(n), u-/spl nu/ mincut computations can lead to significant savings.

Representing and Enumerating Edge Connectivity Cuts in RNC

TLDR
This paper presents a fast parallel algorithm for obtaining a succinct and algorithmically useful representation for an undirected edge-weighted graph and observes that for a unary weighted graph, the problems of counting and enumerating the connectivity cuts are in RNC.

Global min-cuts in RNC, and other ramifications of a simple min-out algorithm

TLDR
This algorithm provides the first proof that the min-cut problem for weighted undirected graphs is in 7ZAfC, and does more than find a single mm-cut; it finds all of them.

Covering Symmetric Supermodular Functions by Graphs +

  • A. Bencz
  • Mathematics, Computer Science
  • 1998
TLDR
A generalization of the theorem of Bang-Jensen and Jackson where, instead of a hypergraph whose connectivity is to be incereased, a symmetric supermodular function is speciied to bècovered' by undirected edges is derived.