greedy on-line is (1/2)-competitive |
greedy on-line is 2-competitive |
primal:
dual:
the cost of any feasible dual solution is an upper bound on opt.
Note: the integrality gap is 0, since this is a special case of maximum-weight matching.
greedy:
1. At each time step t: 2. Assign to time slot t the maximum-weight job j not yet assigned. 3. For the analysis, set yj = zj = wj.
thm: The above algorithm is 2-competitive
Proof: