lec37 - Multidimensional Range Search Static collection of...

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Multidimensional Range Search Static collection of records. No inserts, deletes, changes. Only queries. Each record has k key fields. Multidimensional query. Given k ranges [ l i , u i ] , 1 <= i <= k . Report all records in collection such that l i <= k i <= u i , 1 <= i <= k .
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Multidimensional Range Search All employees whose age is between 30 and 40 and whose salary is between $40K and $70K . All cities with an annual rainfall between 40 and 60 inches, population between 100K and 200K , average temperature >= 70F , and number of horses between 1025 and 2500 .
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Data Structures For Range Search Unordered sequential list. Sorted tables. k tables. Table i is sorted by i ’th key. Cells. k -d trees. Range trees. k -fold trees. k -ranges.
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Performance Measures P(n,k) . Preprocessing time to construct search structure for n records, each has k key fields. For many applications, this time needs only to be reasonable. S(n,k) . Total space needed by the search structure. Q(n,k) . Time needed to answer a query.
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k-d Tree Binary tree. At each node of tree, pick a key field to partition records in that subtree into two approximately equal groups. Pick field i with max spread in values. Select median key value, m . Node stores i and m .
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