# Problem 7 4 graduate student party gsc organizes a

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rectangles. Problem 7-4. Graduate student party GSC organizes a party. Since this is a graduate student party, GSC must ensure that none of the students in the party has too much fun. In particular, it must ensure that no participating student is too sociable . We say that a student s is sociable, if there are 5 or more other people within a two-meter radius from s . To solve this issue, GSC decides to attach a GPS transmitter to every entering student. The ( x, y )-coordinates of all students are measured every few seconds. Assuming there are n students, their coordinates are represented by a sequence ( x 1 , y 1 ) . . . ( x n , y n ). GSC now just needs a fast algorithm that, given the student coordinates, determines if there is any sociable student in the party (if so, the party is declared a failure and closed immediately). Give an efficient algorithm for checking if any of the students is sociable (the algorithm does not have to find such student if one exists). Your algorithm can be randomized and should run in expected O ( n ) time.
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• Spring '03
• PiotrIndyk
• Algorithms, Big O notation, Analysis of algorithms

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