Show that the family of bridge sets, BW (R), is the set of bases of a matroid for any tree (T, W) and any R ⊆ T . (Goemans et al. [2012]) Find a combinatorial 2-factor approximation algorithm for the...



Show that the family of bridge sets, BW (R), is the set of bases of a matroid


for any tree (T, W) and any R ⊆ T .


(Goemans et al. [2012])


Find a combinatorial 2-factor approximation algorithm for the SURVIVABLE


NETWORK DESIGN PROBLEM with rij = k for all i, j (i.e. the MINIMUM


WEIGHT k-EDGE-CONNECTED SUBGRAPH PROBLEM).


Hint: Replace each edge by a pair of oppositely directed edges (with the same


weight) and apply either Exercise 26 of Chapter 13 or Theorem 6.18 directly.


(Khuller and Vishkin [1994])


Note: For more results for similar problems, see Khuller and Raghavachari


[1996], Gabow [2005], Jothi, Raghavachari and Varadarajan [2003], and Gabow


et al. [2009].



Dec 06, 2021
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