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# lecture18 - CS 473 Algorithms Chandra Chekuri...

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CS 473: Algorithms Chandra Chekuri [email protected] 3228 Siebel Center University of Illinois, Urbana-Champaign Fall 2009 Chekuri CS473ug

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Overview Definitions Part I Introduction to Reductions Chekuri CS473ug
Overview Definitions Reductions A reduction from Problem X to Problem Y means (informally) that if we have an algorithm for Problem Y , we can use it to find an algorithm for Problem X . Chekuri CS473ug

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Overview Definitions Reductions A reduction from Problem X to Problem Y means (informally) that if we have an algorithm for Problem Y , we can use it to find an algorithm for Problem X . Using Reductions We use reductions to find algorithms to solve problems. Chekuri CS473ug
Overview Definitions Reductions A reduction from Problem X to Problem Y means (informally) that if we have an algorithm for Problem Y , we can use it to find an algorithm for Problem X . Using Reductions We use reductions to find algorithms to solve problems. We also use reductions to show that we can’t find algorithms for some problems. (We say that these problems are hard .) Chekuri CS473ug

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Overview Definitions Reductions A reduction from Problem X to Problem Y means (informally) that if we have an algorithm for Problem Y , we can use it to find an algorithm for Problem X . Using Reductions We use reductions to find algorithms to solve problems. We also use reductions to show that we can’t find algorithms for some problems. (We say that these problems are hard .) Also, the right reductions might win you a million dollars! Chekuri CS473ug
Overview Definitions Example 1: Bipartite Matching and Flows How do we solve the Bipartite Matching Problem? Given a bipartite graph G = ( U V , E ) and number k , does G have a matching of size k ?

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Overview Definitions Example 1: Bipartite Matching and Flows How do we solve the Bipartite Matching Problem? Given a bipartite graph G = ( U V , E ) and number k , does G have a matching of size k ?
Overview Definitions Example 1: Bipartite Matching and Flows How do we solve the Bipartite Matching Problem? Given a bipartite graph G = ( U V , E ) and number k , does G have a matching of size k ? s t Solution Reduce it to Max-Flow . G has a matching of size k iff there is a flow from s to t of value k .

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Overview Definitions Example 1: Bipartite Matching and Flows How do we solve the Bipartite Matching Problem? Given a bipartite graph G = ( U V , E ) and number k , does G have a matching of size k ? s t Solution Reduce it to Max-Flow . G has a matching of size k iff there is a flow from s to t of value k .
Overview Definitions Example 1: Bipartite Matching and Flows How do we solve the Bipartite Matching Problem? Given a bipartite graph G = ( U V , E ) and number k , does G have a matching of size k ? s t Solution Reduce it to Max-Flow . G has a matching of size k iff there is a flow from s to t of value k .

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