MIT6_851S10_assn04 - algorithm for computing the sux array...

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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 Fne par- titions implies a O ( n 2 1 + ε ) query time for partition trees for 2d halfspace counting. Hint: Choose as size of the Fne partition r = 2( c 2) (1 ) ± , 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 rmq ( i , j ) returns the index of the smallest element of the subsequence { a i ,...,a j } in O (1) time. RMQ can be build in O ( n ) time. 1. Show how to compute the LCP array using an RMQ data structure along the DC3
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Unformatted text preview: algorithm for computing the sux array in linear time. In particular, show how to compute an entry of the LCP in O (1) time if we have the knowledge of the LCP array of the dierence cover T . 2. Use the RMQ data structure and the LCP array to speed up the search in a sux array from O ( | P | log | T | ) to O ( | P | + log | T | ). 1 MIT OpenCourseWare 6.851 Advanced Data Structures Spring 2010 For information about citing these materials or our Terms of Use, visit: ....
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This note was uploaded on 03/31/2011 for the course EECS 6.851 taught by Professor Erikdemaine during the Spring '10 term at MIT.

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MIT6_851S10_assn04 - algorithm for computing the sux array...

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