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Two advertisers A and B A bids on query x, B bids on x and y Both have budgets of $4 Query stream: xxxxyyyy Worst case greedy choice: BBBB____ Optimal: AAAABBBB Competitive ratio = ½ This is the worst case 3/7/2011 Jure Leskovec, <strong>Stanford</strong> C246: Mining Massive Datasets 22
BALANCE by Mehta, Saberi, Vazirani, and Vazirani For each query, pick the advertiser with the largest unspent budget Break ties arbitrarily 3/7/2011 Jure Leskovec, <strong>Stanford</strong> C246: Mining Massive Datasets 23
Page 1 and 2: CS246: Mining Massive Datasets Jure
Page 3 and 4: 1 2 3 Girls 4 d Boys 3/7/2011 Jure
Page 5 and 6: 1 2 3 Girls 4 d Boys M = {(1,c),(2,
Page 7 and 8: Initially, we are given the set Boy
Page 9 and 10: Greedy algorithm for online graph m
Page 11 and 12: Consider the set G of girls matched
Page 13 and 14: Banner ads (1995-2001) Initial for
Page 15 and 16: 3/7/2011 Jure Leskovec, Stanford C2
Page 17 and 18: A stream of queries arrives at the
Page 19 and 20: Advertiser Bid CTR Bid * CTR A B C
Page 21: The environment: There is one ad s
Page 25 and 26: Consider simple case: Two advertis
Page 27 and 28: In the general case, worst competit
Page 29 and 30: … A 1 A 2 A 3 A N-1 A N B/(N-2) B
Page 31 and 32: Fact: H n = ∑ i=1..n1/i = approx.
Page 33 and 34: Arbitrary bids, budgets Consider q

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