linear programming - Covering Polygon with Circles of different radius -

i have closed polygon , cover set of k circles of different radius such area covered circles outside polygon minimal. seems ideal candidate linear programming. know standard formulation / algorithm problem?

you have @ smallest-circle problem equivalent problem k = 1.

in above wiki page said linear algorithm exists. algorithm described in loc. cit. paper of nimrod megiddo complicated.

so feeling that, might able state problem linear programming, finding best algorithm far obvious.