k - SNAP - Stanford University

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So after the first N(1-1/e) rounds, we cannot allocate a query to any advertiser Revenue = B∙N (1-1/e) Competitive ratio = 1-1/e 3/7/2011 Jure Leskovec, <strong>Stanford</strong> C246: Mining Massive Datasets 32
Arbitrary bids, budgets Consider query q, advertiser i Bid = x i Budget = b i BALANCE can be terrible Consider two advertisers A 1 and A 2 A 1: x 1 = 1, b 1 = 110 A 2: x 2 = 10, b 2 = 100 3/7/2011 Jure Leskovec, <strong>Stanford</strong> C246: Mining Massive Datasets 33
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 and 22: The environment: There is one ad s
Page 23 and 24: BALANCE by Mehta, Saberi, Vazirani,
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: Fact: H n = ∑ i=1..n1/i = approx.

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