lecture16 - CS 473: Algorithms Chandra Chekuri...

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CS 473: Algorithms Chandra Chekuri chekuri@cs.illinois.edu 3228 Siebel Center University of Illinois, Urbana-Champaign Fall 2009 Chekuri CS473ug
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Part I Baseball Pennant Race Chekuri CS473ug
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Pennant Race Chekuri CS473ug
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Pennant Race: Example Example Team Won Left New York 92 2 Baltimore 91 3 Toronto 91 3 Boston 89 2 Can Boston win the pennant? Chekuri CS473ug
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Pennant Race: Example Example Team Won Left New York 92 2 Baltimore 91 3 Toronto 91 3 Boston 89 2 Can Boston win the pennant? No, because Boston can win at most 91 games. Chekuri CS473ug
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Another Example Example Team Won Left New York 92 2 Baltimore 91 3 Toronto 91 3 Boston 90 2 Can Boston win the pennant? Chekuri CS473ug
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Another Example Example Team Won Left New York 92 2 Baltimore 91 3 Toronto 91 3 Boston 90 2 Can Boston win the pennant? Not clear unless we know what the remaining games are! Chekuri CS473ug
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Refining the Example Example Team Won Left NY Bal Tor Bos New York 92 2 - 1 1 0 Baltimore 91 3 1 - 1 1 Toronto 91 3 1 1 - 1 Boston 90 2 0 1 1 - Can Boston win the pennant? Chekuri CS473ug
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Refining the Example Example Team Won Left NY Bal Tor Bos New York 92 2 - 1 1 0 Baltimore 91 3 1 - 1 1 Toronto 91 3 1 1 - 1 Boston 90 2 0 1 1 - Can Boston win the pennant? Suppose Boston does Chekuri CS473ug
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Refining the Example Example Team Won Left NY Bal Tor Bos New York 92 2 - 1 1 0 Baltimore 91 3 1 - 1 1 Toronto 91 3 1 1 - 1 Boston 90 2 0 1 1 - Can Boston win the pennant? Suppose Boston does Boston wins both its games to get 92 wins Chekuri CS473ug
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Refining the Example Example Team Won Left NY Bal Tor Bos New York 92 2 - 1 1 0 Baltimore 91 3 1 - 1 1 Toronto 91 3 1 1 - 1 Boston 90 2 0 1 1 - Can Boston win the pennant? Suppose Boston does Boston wins both its games to get 92 wins New York must lose both games Chekuri CS473ug
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Refining the Example Example Team Won Left NY Bal Tor Bos New York 92 2 - 1 1 0 Baltimore 91 3 1 - 1 1 Toronto 91 3 1 1 - 1 Boston 90 2 0 1 1 - Can Boston win the pennant? Suppose Boston does Boston wins both its games to get 92 wins New York must lose both games; now both Baltimore and Toronto have at least 92 Chekuri CS473ug
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Refining the Example Example Team Won Left NY Bal Tor Bos New York 92 2 - 1 1 0 Baltimore 91 3 1 - 1 1 Toronto 91 3 1 1 - 1 Boston 90 2 0 1 1 - Can Boston win the pennant? Suppose Boston does Boston wins both its games to get 92 wins New York must lose both games; now both Baltimore and Toronto have at least 92 Winner of Baltimore-Toronto game has 93 wins! Chekuri CS473ug
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Abstracting the Problem Given A set of teams S For each x S , the current number of wins w x For any x , y S , the number of remaining games g xy between x and y A team z Can z win the pennant? Chekuri CS473ug
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Towards a Reduction z can win the pennant if z wins at least m games no other team wins more than m games Chekuri CS473ug
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Towards a Reduction z can win the pennant if z wins at least m games to maximize z ’s chances we make z win all its remaining games and hence m = w z + x S g xz no other team wins more than m games Chekuri CS473ug
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Towards a Reduction z can win the pennant if z wins at least m games to maximize z ’s chances we make z
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This note was uploaded on 01/22/2012 for the course CS 573 taught by Professor Chekuri,c during the Fall '08 term at University of Illinois, Urbana Champaign.

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lecture16 - CS 473: Algorithms Chandra Chekuri...

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