Results 1  10
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40
Cacheoblivious Btrees
, 2000
"... Abstract. This paper presents two dynamic search trees attaining nearoptimal performance on any hierarchical memory. The data structures are independent of the parameters of the memory hierarchy, e.g., the number of memory levels, the blocktransfer size at each level, and the relative speeds of me ..."
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Cited by 145 (23 self)
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Abstract. This paper presents two dynamic search trees attaining nearoptimal performance on any hierarchical memory. The data structures are independent of the parameters of the memory hierarchy, e.g., the number of memory levels, the blocktransfer size at each level, and the relative speeds of memory levels. The performance is analyzed in terms of the number of memory transfers between two memory levels with an arbitrary blocktransfer size of B; this analysis can then be applied to every adjacent pair of levels in a multilevel memory hierarchy. Both search trees match the optimal search bound of Θ(1+logB+1 N) memory transfers. This bound is also achieved by the classic Btree data structure on a twolevel memory hierarchy with a known blocktransfer size B. The first search tree supports insertions and deletions in Θ(1 + logB+1 N) amortized memory transfers, which matches the Btree’s worstcase bounds. The second search tree supports scanning S consecutive elements optimally in Θ(1 + S/B) memory transfers and supports insertions and deletions in Θ(1 + logB+1 N + log2 N) amortized memory transfers, matching the performance of the Btree for B = B Ω(log N log log N).
Tight(er) worstcase bounds on dynamic searching and priority queues
 In Proc. of the 32nd Annual ACM Symposium on Theory of Computing (STOC ’00
, 2000
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Cell probe complexity  a survey
 In 19th Conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS), 1999. Advances in Data Structures Workshop
"... The cell probe model is a general, combinatorial model of data structures. We give a survey of known results about the cell probe complexity of static and dynamic data structure problems, with an emphasis on techniques for proving lower bounds. 1 ..."
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Cited by 28 (0 self)
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The cell probe model is a general, combinatorial model of data structures. We give a survey of known results about the cell probe complexity of static and dynamic data structure problems, with an emphasis on techniques for proving lower bounds. 1
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 27 (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.
Integer Priority Queues with Decrease Key in . . .
 STOC'03
, 2003
"... We consider Fibonacci heap style integer priority queues supporting insert and decrease key operations in constant time. We present a deterministic linear space solution that with n integer keys support delete in O(log log n) time. If the integers are in the range [0,N), we can also support delete i ..."
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Cited by 27 (2 self)
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We consider Fibonacci heap style integer priority queues supporting insert and decrease key operations in constant time. We present a deterministic linear space solution that with n integer keys support delete in O(log log n) time. If the integers are in the range [0,N), we can also support delete in O(log log N) time. Even for the special case of monotone priority queues, where the minimum has to be nondecreasing, the best previous bounds on delete were O((log n) 1/(3−ε) ) and O((log N) 1/(4−ε)). These previous bounds used both randomization and amortization. Our new bounds a deterministic, worstcase, with no restriction to monotonicity, and exponentially faster. As a classical application, for a directed graph with n nodes and m edges with nonnegative integer weights, we get single source shortest paths in O(m + n log log n) time, or O(m + n log log C) ifC is the maximal edge weight. The later solves an open problem of Ahuja, Mehlhorn, Orlin, and
Static Dictionaries on AC^0 RAMs: Query time Θ(,/log n / log log n) is necessary and sufficient
, 1996
"... In this paper we consider solutions to the static dictionary problem ���� � on RAMs, i.e. random access machines where the only restriction on the finite instruction set is that all computational instructions are ���� � in. Our main result is a tight upper and lower bound ���� � ���©���������������� ..."
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Cited by 20 (6 self)
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In this paper we consider solutions to the static dictionary problem ���� � on RAMs, i.e. random access machines where the only restriction on the finite instruction set is that all computational instructions are ���� � in. Our main result is a tight upper and lower bound ���� � ���©��������������������� of on the time for answering membership queries in a set of � size when reasonable space is used for the data structure storing the set; the upper bound can be obtained using space ������ � �� � ���� �. Several variations of this result are also obtained. Among others, we show a tradeoff between time and circuit depth under the unitcost assumption: any RAM instruction set which permits a linear space, constant query time solution to the static dictionary problem must have an instruction of depth �������©���������������©���� � , where � is the word size of the machine (and ���© � the size of the universe). This matches the depth of multiplication and integer division, used in the perfect hashing scheme by Fredman, Komlós and Szemerédi.
Exponential structures for efficient cacheoblivious algorithms
 In Proceedings of the 29th International Colloquium on Automata, Languages and Programming
, 2002
"... Abstract. We present cacheoblivious data structures based upon exponential structures. These data structures perform well on a hierarchical memory but do not depend on any parameters of the hierarchy, including the block sizes and number of blocks at each level. The problems we consider are searchi ..."
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Cited by 20 (3 self)
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Abstract. We present cacheoblivious data structures based upon exponential structures. These data structures perform well on a hierarchical memory but do not depend on any parameters of the hierarchy, including the block sizes and number of blocks at each level. The problems we consider are searching, partial persistence and planar point location. On a hierarchical memory where data is transferred in blocks of size B, some of the results we achieve are: – We give a linearspace data structure for dynamic searching that supports searches and updates in optimal O(log B N) worstcase I/Os, eliminating amortization from the result of Bender, Demaine, and FarachColton (FOCS ’00). We also consider finger searches and updates and batched searches. – We support partiallypersistent operations on an ordered set, namely, we allow searches in any previous version of the set and updates to the latest version of the set (an update creates a new version of the set). All operations take an optimal O(log B (m + N)) amortized I/Os, where N is the size of the version being searched/updated, and m is the number of versions. – We solve the planar point location problem in linear space, taking optimal O(log B N) I/Os for point location queries, where N is the number of line segments specifying the partition of the plane. The preprocessing requires O((N/B) log M/B N) I/Os, where M is the size of the ‘inner ’ memory. 1