Assignment 16

Due Friday, 5/10/96.

Chapter 12: 12, 13, 16, 17, 20

A. The vertex cover porblem is to find a vertex cover of minimum size in a given undirected graph (called the optimal vertex cover).

Show the following algorithm produces a vertex cover, C , such that |C | <= 2 |Coptimal |.

Let G = (V,E):

C <- empty set
E' <- E
while E' /= 0 do
   let (u,v) in E'
   C <- C U {u,v}
   remove from E' every edge including either u or v
end
return C
Hint: Consider set A = {(u,v) in E' | (u,v) picked in the while loop}. Don't forget to prove the algorithm really does select a node cover.