Parameterized Approximation Scheme for the Multiple Knapsack Problem by Klaus Jansen (SODA’09). Speaker: Yue Wang 04/14/2009. Outline. Introduction Definition of problem Relative Works Approximation Scheme for MKP Instances with similar capacities General instances.
Parameterized Approximation Scheme for the Multiple Knapsack Problemby Klaus Jansen (SODA’09)
Speaker: Yue Wang
MKP has no FPTAS!
PTAS: approximation algorithm running in
MKP has (Chekuri and Khanna)
EPTAS: a PTAS with running time of the form
(this paper)FPTAS, PTAS and EPTAS
as the pieces of item assigned to group .
M machines: parts. N jobs: n items.
. All other items are now selected completely.
By using the property and the strip packing algorithm of Kenyon and Remila.
, is the number of bins in
, the number of place is again at most . In total they have to consider at most choices and replacements.
The times complexity of this approximation algorithm
Any questions, comments and concerns?