Combinatorial auction problem is a problem of auction theory where participants are allowed to bid on packages of items. This algorithm computes the optimal combinatorial auction clearing using the Integer Linear Programming (ILP) formulation.

Input:

Please give your input as a list of Bids, where a Bid has a String identifier, a Set<String> of identifiers for the items being bid on, and an int representing a value the bidder is willing to pay.

Output:

A List<String> of the optimal Bid identifiers to be selected by the auctioneer.