k - SNAP - Stanford University

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y A 1 A 2 B x Opt revenue = 2B B Balance revenue = 2B-x = B+y A 1 A 2 Not used x Queries allocated to A 1 in optimal solution Queries allocated to A 2 in optimal solution We have y ≥ x Balance revenue is minimum for x=y=B/2 Minimum Balance revenue = 3B/2 Competitive Ratio = 3/4 3/7/2011 Jure Leskovec, <strong>Stanford</strong> C246: Mining Massive Datasets 26
In the general case, worst competitive ratio of BALANCE is 1–1/e = approx. 0.63 Interestingly, no online algorithm has a better competitive ratio! We do not through the details here, but let’s see the worst case that gives this ratio 3/7/2011 Jure Leskovec, <strong>Stanford</strong> C246: Mining Massive Datasets 27
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: Consider simple case: Two advertis
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

k - SNAP - Stanford University

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