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Unformatted text preview: CSE450/598 Design And Analysis of Algorithms HW01 Grading Keys 1. (10 pts) Design a polynomial time algorithm to decide whether an instance for the stable matching problem has a unique stable matching. You need to describe your algorithm and prove its correctness. Solutions: (5pts) Run the man-proposing GS algorithm and the woman-proposing GS al- gorithm for the same instance. If both runs produce the same matching, the instance has a unique stable matching. Otherwise, the instance has two or more stable matchings. (5pts) The first run produces a stable matching in which each man is matched with his best- partner. The second run produces a stable matching in which each man is matched with his worst-partner. The instance has a unique stable matchine if and only if for each man, his best-partner is also his worst-partner. 2. (10 pts) Let f ( n ) = 0 . 001 n 3 and g ( n ) = 1000 × n × log 2 n . Find the smallest integer N ≥ such that f ( N ) ≤ g ( N ) but f ( N +1) > g ( N +1). Show the values of+1)....
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This note was uploaded on 05/05/2008 for the course CSE 450 taught by Professor Guoliangxue during the Spring '08 term at ASU.
- Spring '08