algorithm - Is this a special case of the NP-complete set packing? -

algorithm - Is this a special case of the NP-complete set packing? -

i'm problem equivalent set packing, , thus, np-complete, verify. have next situation: there set of pens (i.e. universe). store sells bundles of these pens, subsets of universe. know guy has pens (also subset of universe) store, have no thought bundles bought. might have lost pens , gotten others other bundles friends gave him. want map bundles sold store subset of pens friend has cover highest amount of pens , chosen bundles must not contain pen friend doesn't have. example:

possible pens: {0, 1, 2, 3, 4, 5} bundles sold store: {0, 1} | {0, 1, 2} | {2, 3} | {3} | {3, 4, 5} | {4, 5} friend has: {0, 1, 2, 3} here, there perfect matches: {{0, 1, 2}, {3}} , {{0, 1}, {2, 3}}. these equivalent friend 2 has: {0, 2, 3} in case, there no perfect match. possible matches {{3}} , {{2, 3}}. best match {{2, 3}}.

i problem np-complete given number m of pens, number n of bundles , number l of friend's pens ?

algorithm np