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Faster Deterministic Sorting and Searching in Linear Space
, 1995
"... We present a significant improvement on linear space deterministic sorting and searching. On a unitcost RAM with word size w, an ordered set of n wbit keys (viewed as binary strings or integers) can be maintained in O ` min ` p log n; log n log w + log log n; log w log log n " time p ..."
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We present a significant improvement on linear space deterministic sorting and searching. On a unitcost RAM with word size w, an ordered set of n wbit keys (viewed as binary strings or integers) can be maintained in O ` min ` p log n; log n log w + log log n; log w log log n " time per operation, including insert, delete, member search, and neighbour search. The cost for searching is worstcase while the cost for updates is amortized. For range queries, there is an additional cost of reporting the found keys. As an application, n keys can be sorted in linear space at a worstcase cost of O \Gamma n p log n \Delta . The best previous method for deterministic sorting and searching in linear space has been the fusion trees which supports queries in O(logn= log log n) amortized time and sorting in O(n log n= log log n) worstcase time. We also make two minor observations on adapting our data structure to the input distribution and on the complexity of perfect hashing. 1 I...
Efficient IP table lookup via adaptive stratified trees with selective reconstructions
 12TH EUROPEAN SYMP ON ALGORITHMS
, 2004
"... IP address lookup is a critical operation for high bandwidth routers in packet switching networks such as Internet. The lookup is a nontrivial operation since it requires searching for the longest prefix, among those stored in a (large) given table, matching the IP address. Ever increasing routing ..."
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IP address lookup is a critical operation for high bandwidth routers in packet switching networks such as Internet. The lookup is a nontrivial operation since it requires searching for the longest prefix, among those stored in a (large) given table, matching the IP address. Ever increasing routing tables size, traffic volume and links speed demand new and more efficient algorithms. Moreover, the imminent move to IPv6 128bit addresses will soon require a rethinking of previous technical choices. This article describes a the new data structure for solving the IP table look up problem christened the Adaptive Stratified Tree (AST). The proposed solution is based on casting the problem in geometric terms and on repeated application of efficient local geometric optimization routines. Experiments with this approach have shown that in terms of storage, query time and update time the AST is at a par with state of the art algorithms based on data compression or string manipulations (and often it is better on some of the measured quantities).
6.897: Advanced Data Structures Spring 2005
, 2005
"... In the last lecture we used round elimination to prove lower bounds for the static predecessor problem in the cell probe model. We showed a lower bound of Ω(min{lga w, lgb n}) on the number of probes required to solve the problem, where a = O(lg space(n)), the number of bits to index the data struct ..."
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In the last lecture we used round elimination to prove lower bounds for the static predecessor problem in the cell probe model. We showed a lower bound of Ω(min{lga w, lgb n}) on the number of probes required to solve the problem, where a = O(lg space(n)), the number of bits to index the data structure, and b = w, the number of bits returned by a single cell probe. For a polynomial size data structure, this implies that when lg n lg lg n = lg 2 w, some problem instances require Ω( lg w lg lg w) = Ω( lg n lg lg n) probes. The bound lgw n is matched by fusion trees, but van Emde Boas achieves lg w per query, which does not match lga w. In this lecture we show upper and lower bounds of Θ(min{lgw n, 2 An O( lg w lg a