The Cross-Entropy Method for the Winner Determination Problem in Combinatorial Auctions

Table 1

Data of Test Case 1.

Serial number	Bids	Bidding	Serial number	Bids	Bidding
1	2, 4, 8	2401	16	8	903
2	2, 4, 6	2042	17	3	270
3	4	840	18	1, 4, 5	1658
4	4, 6, 8	2305	19	4, 5	1516
5	2, 4, 6	1996	20	1, 2	677
6	6	533	21	1, 7	569
7	4, 6, 8	2228	22	1	109
8	4, 6	1411	23	5, 6	1145
9	6, 8	1472	24	4, 8	1793
10	4	826	25	2, 6	1300
11	2, 4, 5	2135	26	6, 7	1032
12	5	629	27	2, 4	1479
13	4, 7, 8	2095	28	1, 4	937
14	7	421	27	3, 4	1075
15	3, 5, 8	1881	30	2	608