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advertising-1 - 1 CS 345 Data Mining Online algorithms...

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Unformatted text preview: 1 CS 345 Data Mining Online algorithms Search advertising Online algorithms ¡ Classic model of algorithms ¢ You get to see the entire input, then compute some function of it ¢ In this context, “offline algorithm” ¡ Online algorithm ¢ You get to see the input one piece at a time, and need to make irrevocable decisions along the way ¡ 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 ¡ 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 don’t have the entire graph upfront? 2 Online problem ¡ 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 ¢ Don’t pair the girl with any boy ¡ 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 ¡ Pair the new girl with any eligible boy ¢ If there is none, don’t pair girl ¡ How good is the algorithm? Competitive Ratio ¡ 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 ¡ Consider the set G of girls matched in M opt but not in M greedy ¡ Then it must be the case that every boy adjacent to girls in G is already matched in M greedy...
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advertising-1 - 1 CS 345 Data Mining Online algorithms...

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