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Unformatted text preview: 1 CS 345 Data Mining Online algorithms Search advertising Online algorithms Âˇ Classic model of algorithms Â˘ You get to see the entire input, then compute some function of it Â˘ In this context, â€śoffline algorithmâ€ť Âˇ Online algorithm Â˘ You get to see the input one piece at a time, and need to make irrevocable decisions along the way Âˇ Similar to data stream models Example: Bipartite matching 1 2 3 4 a b c d Girls Boys Example: Bipartite matching 1 2 3 4 a b c d M = {(1,a),(2,b),(3,d)} is a matching Cardinality of matching = M = 3 Girls Boys Example: Bipartite matching 1 2 3 4 a b c d Girls Boys M = {(1,c),(2,b),(3,d),(4,a)} is a perfect matching Matching Algorithm Âˇ Problem: Find a maximumcardinality matching for a given bipartite graph Â˘ A perfect one if it exists Âˇ There is a polynomialtime offline algorithm (Hopcroft and Karp 1973) Âˇ But what if we donâ€™t have the entire graph upfront? 2 Online problem Âˇ Initially, we are given the set Boys Âˇ In each round, one girlâ€™s choices are revealed Âˇ At that time, we have to decide to either: Â˘ Pair the girl with a boy Â˘ Donâ€™t pair the girl with any boy Âˇ Example of application: assigning tasks to servers Online problem 1 2 3 4 a b c d (1,a) (2,b) (3,d) Greedy algorithm Âˇ Pair the new girl with any eligible boy Â˘ If there is none, donâ€™t pair girl Âˇ How good is the algorithm? Competitive Ratio Âˇ For input I, suppose greedy produces matching M greedy while an optimal matching is M opt Competitive ratio = min all possible inputs I (M greedy /M opt ) Analyzing the greedy algorithm Âˇ Consider the set G of girls matched in M opt but not in M greedy Âˇ Then it must be the case that every boy adjacent to girls in G is already matched in M greedy...
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 Fall '09
 Advertising, Algorithms, Data Mining, Web banner, Online algorithm, Online algorithms, advertiser

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