1	Searching with Structured Keys Objectives To look at search structures for variable length and multidimensional keys. To understand several basic radix search techniques, their advantages and disadvantages To look at range queries and partial match searches in multidimensional structures.
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3	Radix Sorting Technique
4	Radix Searching Techniques
5	Digital Search Trees
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7	Digital Search Tree Updates
8	Digital Search Tree Updates
9	Digital Search Trees - Costs The number of nodes inspected in a search is, at most, the number of leading bits needed to distinguish it from other keys For “randomly distributed” keys this should be Θ(log n), but if keys agree on lead bits problems arise But, visiting each node involves a key comparison, this may be the bulk of the cost
10	Radix Search Tries “trie” as in “retrieval” is pronounced “try”
11	Radix Search Trie Updates If you “fall out”, hang a new node on there If you come to a leaf continue the path in the tree with the two elements until the bits differ
12	"Only n nodes of storage" Only n nodes of storage Just one full key compare No “useless” tests
13	Patricia: Step 1 Leave out 1 way branch nodes Add to each node the position of the bit to be tested (we will still move left to right)
14	"Patricia:" Patricia: Step 2 Add the “dummy value” 00000 (which is either not stored or stored in the header). Store keys in internal nodes that are ancestors of their leaf positions in the tree
15	Patricia Insertions Insertions can be made in the natural way. Follow the search path of new leaf. Determine the highest number bit where new key and leaf key differ. Retrace search path to the point where a test on this bit could occur. Insert new node there with the node on the path to leaf node as one child and a new leaf containing the new key
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20	Radix Techniques Insensitive to order of insertions Sensitive to particular value Very useful for long or variable length keys