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ps4 - 6.851 Advanced Data Structures(Spring10 Prof Erik...

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6.851 Advanced Data Structures (Spring’10) Prof. Erik Demaine Dr. Andr´ e Schulz TA: Aleksandar Zlateski Problem 4 Due: Thursday, Mar. 4 Be sure to read the instructions on the assignments section of the class web page. Analysis partition trees. Prove that Matouˇ sek’s theorem on the crossing number of fine par- titions implies a O ( n 1 2 + ε ) query time for partition trees for 2d halfspace counting. Hint: Choose as size of the fine partition r = d 2( c 2) (1 ) e , where c r is the bound for the crossing number. Speed up with LCP array. Suppose we have a data structure RMQ, that stores an indexed sequence of integers { a 1 ,a 2 ,...,a n } . A query
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