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Four Results on Randomized Incremental Constructions
 Comput. Geom. Theory Appl
, 1993
"... We prove four results on randomized incremental constructions (RICs): ffl an analysis of the expected behavior under insertion and deletions, ffl a fully dynamic data structure for convex hull maintenance in arbitrary dimensions, ffl a tail estimate for the space complexity of RICs, ffl a lower ..."
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Cited by 92 (17 self)
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We prove four results on randomized incremental constructions (RICs): ffl an analysis of the expected behavior under insertion and deletions, ffl a fully dynamic data structure for convex hull maintenance in arbitrary dimensions, ffl a tail estimate for the space complexity of RICs, ffl a lower bound on the complexity of a game related to RICs. 1
New data structures for orthogonal range searching
 In Proc. 41st IEEE Symposium on Foundations of Computer Science
, 2000
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Tight(er) Worstcase Bounds on Dynamic Searching and Priority Queues
 In STOC’2000
, 2000
"... We introduce a novel technique for converting static polynomial space search structures for ordered sets into fullydynamic linear space data structures. Based on this we present optimal bounds for dynamic integer searching, including finger search, and exponentially improved bounds for priority queu ..."
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Cited by 43 (2 self)
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We introduce a novel technique for converting static polynomial space search structures for ordered sets into fullydynamic linear space data structures. Based on this we present optimal bounds for dynamic integer searching, including finger search, and exponentially improved bounds for priority queues.
Dynamic Ordered Sets with Exponential Search Trees
 Combination of results presented in FOCS 1996, STOC 2000 and SODA
, 2001
"... We introduce exponential search trees as a novel technique for converting static polynomial space search structures for ordered sets into fullydynamic linear space data structures. This leads to an optimal bound of O ( √ log n/log log n) for searching and updating a dynamic set of n integer keys i ..."
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Cited by 26 (1 self)
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We introduce exponential search trees as a novel technique for converting static polynomial space search structures for ordered sets into fullydynamic linear space data structures. This leads to an optimal bound of O ( √ log n/log log n) for searching and updating a dynamic set of n integer keys in linear space. Here searching an integer y means finding the maximum key in the set which is smaller than or equal to y. This problem is equivalent to the standard text book problem of maintaining an ordered set (see, e.g., Cormen, Leiserson, Rivest, and Stein: Introduction to Algorithms, 2nd ed., MIT Press, 2001). The best previous deterministic linear space bound was O(log n/log log n) due Fredman and Willard from STOC 1990. No better deterministic search bound was known using polynomial space.
Strongly historyindependent hashing with applications
 In Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
, 2007
"... We present a strongly history independent (SHI) hash table that supports search in O(1) worstcase time, and insert and delete in O(1) expected time using O(n) data space. This matches the bounds for dynamic perfect hashing, and improves on the best previous results by Naor and Teague on history ind ..."
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Cited by 12 (4 self)
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We present a strongly history independent (SHI) hash table that supports search in O(1) worstcase time, and insert and delete in O(1) expected time using O(n) data space. This matches the bounds for dynamic perfect hashing, and improves on the best previous results by Naor and Teague on history independent hashing, which were either weakly history independent, or only supported insertion and search (no delete) each in O(1) expected time. The results can be used to construct many other SHI data structures. We show straightforward constructions for SHI ordered dictionaries: for n keys from {1,..., n k} searches take O(log log n) worstcase time and updates (insertions and deletions) O(log log n) expected time, and for keys in the comparison model searches take O(log n) worstcase time and updates O(log n) expected time. We also describe a SHI data structure for the ordermaintenance problem. It supports comparisons in O(1) worstcase time, and updates in O(1) expected time. All structures use O(n) data space. 1
Time and space efficient multimethod dispatching
 IN SWAT: SCANDINAVIAN WORKSHOP ON ALGORITHM THEORY
, 2002
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On the Longest Upsequence Problem for Permutations
, 1999
"... Given a permutation of n numbers, its longest upsequence can be found in time O#n log log n#. Finding the longest upsequence #resp. longest downsequence# of a permutation solves the maximum independent set problem #resp. the clique problem # for the corresponding permutation graph. Moreover, we ..."
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Cited by 2 (0 self)
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Given a permutation of n numbers, its longest upsequence can be found in time O#n log log n#. Finding the longest upsequence #resp. longest downsequence# of a permutation solves the maximum independent set problem #resp. the clique problem # for the corresponding permutation graph. Moreover, we discuss the problem of e#eciently constructing the Young tableau for a given permutation. Keywords: Algorithms; Permutation; Upsequence; Strati#ed tree; Young tableau. 1 Introduction Consider a sequence of values #v 1 ;:::;v n #. If one deletes i #not necessarily adjacent# values from the sequence, one has a subsequence of length n , i. This subsequence is called an upsequence #resp. downsequence# if its values are in nondecreasing #resp. nonincreasing# order. Gries #6, p. 262# gives a simple algorithm for #nding the length of the longest upsequence in a given sequence with n values in time O#n log n#. This algorithm scans the sequence from left to right and maintains the minimum value...
Melding Priority Queues
 In Proc. of 9th SWAT
, 2004
"... We show that any priority queue data structure that supports insert, delete, and findmin operations in pq(n) time, when n is an upper bound on the number of elements in the priority queue, can be converted into a priority queue data structure that also supports fast meld operations with essentially ..."
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Cited by 2 (0 self)
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We show that any priority queue data structure that supports insert, delete, and findmin operations in pq(n) time, when n is an upper bound on the number of elements in the priority queue, can be converted into a priority queue data structure that also supports fast meld operations with essentially no increase in the amortized cost of the other operations. More specifically, the new data structure supports insert, meld and findmin operations in O(1) amortized time, and delete operations in O(pq(n) + α(n, n)) amortized time, where α(m, n) is a functional inverse of the Ackermann function. The construction is very simple, essentially just placing a nonmeldable priority queue at each node of a unionfind data structure. We also show that when all keys are integers in the range [1, N], we can replace n in the bound stated above by min{n, N}. Applying this result to nonmeldable priority queue data structures obtained recently by Thorup, and by Han and Thorup, we obtain meldable RAM priority queues with O(log log n) amortized cost per operation, or O ( √ log log n) expected amortized cost per operation, respectively. As a byproduct, we obtain improved algorithms for the minimum directed spanning tree problem in graphs with integer edge weights: A deterministic O(m log log n) time algorithm and a randomized O(m √ log log n) time algorithm. These bounds improve, for sparse enough graphs, on the O(m + n log n) running time of an algorithm by Gabow, Galil, Spencer and Tarjan that works for arbitrary edge weights.
Engineering a Sorted List Data Structure for 32 Bit Keys
"... Search tree data structures like van Emde Boas (vEB) trees are a theoretically attractive alternative to comparison based search trees because they have better asymptotic performance for small integer keys and large inputs. This paper studies their practicability using 32 bit keys as an example. Whi ..."
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Cited by 1 (0 self)
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Search tree data structures like van Emde Boas (vEB) trees are a theoretically attractive alternative to comparison based search trees because they have better asymptotic performance for small integer keys and large inputs. This paper studies their practicability using 32 bit keys as an example. While direct implementations of vEBtrees cannot compete with good implementations of comparison based data structures, our tuned data structure significantly outperforms comparison based implementations for searching and shows at least comparable performance for insertion and deletion.
Improved Time and Space Complexities for Transposition Invariant String Matching
"... Given strings A = a1a2...am and B = b1b2...bn over a finite alphabet Σ ⊂ Z of size O(σ), and a distance d() defined among strings, the transposition invariant version of d() is d t (A,B) = mint∈Z d(A+t,B), where A+t = (a1+t)(a2+t)...(am+t). Distances d() of most interest are Levenshtein distance an ..."
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Given strings A = a1a2...am and B = b1b2...bn over a finite alphabet Σ ⊂ Z of size O(σ), and a distance d() defined among strings, the transposition invariant version of d() is d t (A,B) = mint∈Z d(A+t,B), where A+t = (a1+t)(a2+t)...(am+t). Distances d() of most interest are Levenshtein distance and indel distance (the dual of the Longest Common Subsequence), which can be computed in O(mn) time. Recent algorithms compute d t (A,B) in O(mn log log min(m,n)) time for those distances. In this paper we show how those complexities can be reduced to O(mn log log σ). Furthermore, we reduce the space requirements from O(mn) to O(σ 2 + min(m,n)). Key words: longest common subsequence, edit distance, music sequence comparison, transposition invariance, sparse dynamic programming 1