a b

5.10 In some applications one is interested only in the number of points that lie in a range rather than in reporting all of them. Such queries are often referred to as range counting queries. In this case one would like to avoid having an additive term of O(k) in the query time. Describe how a 1-dimensional range tree can be adapted such that a range counting query can be performed in O(logn) time. Prove the a. query time bound b. Using the solution to the 1-dimensional problem, describe how d- dimensional range counting queries can be answered in O(log" n) time. Prove the query time. 5.10 In some applications one is interested only in the number of points that lie in a range rather than in reporting all of them. Such queries are often referred to as range counting queries. In this case one would like to avoid having an additive term of O(k) in the query time. Describe how a 1-dimensional range tree can be adapted such that a range counting query can be performed in O(logn) time. Prove the a. query time bound b. Using the solution to the 1-dimensional problem, describe how d- dimensional range counting queries can be answered in O(log" n) time. Prove the query time