We show by a counterexample that the dual-ascent procedure proposed by Herrmann, Ioannou, Minis and Proth in a 1996 issue of the European Journal of Operational Research is incorrect in the sense that it does not generate a valid lower bound to the optimal value of fixed-charge capacitated network design problems. We provide a Cheap Kids Uggs Uk
correct dual-ascent procedure based on the same ideas and we give an interpretation of it in terms of a simple Lagrangean relaxation. Although correct, this procedure is not effective, as in general, it provides a less tighter bound than the linear programming relaxation.
It is known that a quantum computer can search an unordered Ugg Shops Uk
list of N items using <img height="19" border="0" style="vertical-align:bottom" width="50" alt="" title="" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0020019099000691-si1.gif"> look-ups, which is quadratically faster than any classical algorithm. We examine the case where the list is ordered, and show that no quantum computer can do with fewer than <img height="19" border="0" style="vertical-align:bottom" width="153" alt="" title="" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0020019099000691-si2.gif"> look-ups.