k - SNAP - Stanford University

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Problem: Find a maximum-cardinality matching for a given bipartite graph A perfect one if it exists There is a polynomial-time offline algorithm (Hopcroft and Karp 1973) But what if we do not know the entire graph upfront? 3/7/2011 Jure Leskovec, <strong>Stanford</strong> C246: Mining Massive Datasets 6
Initially, we are given the set Boys In each round, one girl’s choices are revealed At that time, we have to decide to either: Pair the girl with a boy Do not pair the girl with any boy Example of application: Assigning tasks to servers 3/7/2011 Jure Leskovec, <strong>Stanford</strong> C246: Mining Massive Datasets 7
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: 1 2 3 Girls 4 d Boys M = {(1,c),(2,
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 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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