B. A. Sheil, `Median split trees: a fast lookup technique for frequency occurring keys', Commun. ACM, 20, (11), 841--850 (1977).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....This is due to the easily proven fact that, if there are two or more non zero probabilities (access probabilities or failure probabilities) in any optimal subtree X, then at least one non zero probability must be in each of the two subtrees of X. Binary split trees were introduced by Sheil [5], who conjectured that the arbitrary removal of nodes with high access probabilities from the lexicographic ordering (for placement in roots of higher subtrees) made the normal dynamic programming techniques inapplicable. However, Huang and Wong [1] noted that the keys missing from any given range ....

B. A. Sheil, Median split trees: A fast lookup technique for frequently occurring keys, Comm. ACM 21 (1978) 947--958.

....is predetermined but the split value for the root may be chosen to divide the remaining n Gamma 1 records between the left and right subtrees in any of n possible ways. If failed searches are considered, the split value may be any of n 2 possibilities. Binary split trees were introduced by Sheil [6], who conjectured that the arbitrary removal of nodes with high access probabilities from the lexicographic ordering (for placement in roots of higher subtrees) made the normal dynamic programming techniques inapplicable. However, Huang and Wong [2] and Perl [5] noted that the keys missing from ....

....of records by eliminating any values which would result in too great a cost being contributed to the tree. In this section we present the basic modifications in simple form and an analysis of the time gained, and then in the next section we discuss some refinements along the same lines. Sheil [6] defined a median split tree where, by always choosing a split value such that the number of records in the left and right subtrees are equal (or nearly so) an almost complete tree results. Since this is a valid split tree and has a worst case cost of lg(n) probes, therefore lg(n) is an upper ....

B. A. Sheil, Median split trees: A fast lookup technique for frequently occurring keys, Comm. ACM 21 (1978) 947--958.

....2. When comparing two addresses, compare the fifth octet first. If the addresses are not equal, the very first comparison will fail more often than when using other octets. 3. Use the fifth octet as the branching function at the root of a tree database. If the addresses are stored in a tree [28] or trie structure [25] and the address bits are used to decide the branch to be taken, using bits from this octet would provide maximum discrimination. Compare this to using the bits from the first three octets. Most of the bits in the first three octets are the same in all addresses and we would ....

B. A. Sheil, "Median Split Trees: A Fast Lookup Technique for Frequently Occurring Keys," Comm. of ACM, Vol. 21, No. 11, November 1978, pp. 947-958.

....tree is nearly 4 times slower than a binary search of a sorted list. However, insertion is much faster, requiring just two bit operations. Another approach is to use a tree structure, such as a binary tree (Knuth, 1973) trie (Knuth, 1973; Fredkin, 1960; Sedgewick, 1988) or median split tree (Sheil, 1978). However, while very efficient at sorting and searching for particular keys, these approaches do not support anagram and regular expression searching except by scanning the whole tree. Operations such as regular expression searching and approximate matching (where the pattern being matched ....

Sheil, B.A. (1978) Median split trees : a fast lookup technique for frequently occuring keys. Comm. Association for Computing Machinery 21(11): 947--958, November.

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B. A. Sheil, `Median split trees: a fast lookup technique for frequency occurring keys', Commun. ACM, 20, (11), 841--850 (1977).

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