Top | recent changes | Preferences

Example: min-weight fractional vertex cover

Minimize v c(v) x(v) subject to:
x(v) ≥ 0 for each vertex v ∈ V.
x(u)+x(v) ≥ 1 for each edge (u,v) ∈ E.

Dual: maximum edge packing:

Maximize e y(e) subject to
y(e) ≥ 0 for each edge ∈ E.
e ∋ w y(e) ≤ c(v) for each vertex w.

Using duality to bound OPT integer solution:

cost(OPT vertex cover) ≥ cost(any feasible solution to the dual)
(follows from weak duality.)

linear-time 2-approximation algorithm for min-cost vertex cover using dual

An edge packing y is maximal if there is no other feasible edge packing y' such that y ≤ y'. (In other words, no edge weight can be increased without violating some constraint in the dual.)


  1. find a maximal feasible edge packing y
  2. return all vertices v whose packing constraint is tight

prove: the algorithm is a 2-approximation algorithm


Top | recent changes | Preferences
This page is read-only | View other revisions
Last edited January 24, 2004 3:09 pm by NealYoung (diff)