HW1 - Network A Shows TRPs Lost 2 House MD 4 Network B...

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CSCI 570 – Analysis of Algorithms Homework 1 Due: June 6, 2008 Solutions 1. (5 points) problem 1 from chapter 1 Solution: False . E.g. n = 2. m 1 prefers w 1 and m 2 prefers w 2 . But w 1 prefers m 2 and w 2 prefers m 1 . There are two possible matchings, both stable. In one of them, no woman is happy. In the other, no man is happy. In particular, in neither matching is there a pair ( m,w ) such that m prefers w and w prefers m . 2. (5 points) problem 2 from chapter 1 Solution: True . Suppose not. Then we will argue that the matching S is not stable. This follows because both m and w prefer each other to their current partners, causing an instability. 3. (10 points) problem 3 from chapter 1 Solution: No, there isn’t always a stable pair of schedules. Here is an example showing why.
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Unformatted text preview: Network A Shows TRPs Lost 2 House MD 4 Network B Shows TRPs Heroes 1 Entourage 3 1 There are two possible matchings. Matching 1 : Lost v/s Heroes and House MD v/s Entourage. In this case, Network A wins both time slots. However, this matching is not stable. This is because, Network B can unilaterally change its own schedule, to go to matching 2, winning more time slots Matching 2 : Lost v/s Entourage and House MD v/s Heroes. Network A wins the second slot. Network B wins the first slot. This matching is not stable either, because Network A can unilaterally change its own schedule to go to matching 1, winning more time slots. 2...
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This note was uploaded on 09/01/2008 for the course CSCI 570 taught by Professor Shamsian during the Summer '06 term at USC.

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HW1 - Network A Shows TRPs Lost 2 House MD 4 Network B...

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