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Fast set operations using treaps

1998
*
Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures - SPAA '98
*

We present parallel algorithms for union, intersection and difference on ordered sets using random balanced binary trees (

doi:10.1145/277651.277660
dblp:conf/spaa/BlellochR98
fatcat:opextcwyjbeqlfjjmn2wit3lfe
*treaps*[26]). ... As with the sequential algorithms on*treaps*for insertion and deletion, the main advantage of our algorithms are their simplicity. ... Figure 1 shows the result of a split on a*treap*. The expected time to split two*treaps*into*treaps*of size n and m is O(lg n + lg m) [26] . ...##
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Faster and smaller inverted indices with treaps

2013
*
Proceedings of the 36th international ACM SIGIR conference on Research and development in information retrieval - SIGIR '13
*

To achieve compression we represent the

doi:10.1145/2484028.2484088
dblp:conf/sigir/KonowNCL13
fatcat:stb7bxvqkvffnlwx6qv3nwq7fe
*treap*topology using compact data structures. ... Further, the*treap*invariants allow us to elegantly encode differentially both document identifiers and frequencies. ... Our explicit*treap*spans all the documents, but we can simulate a*treap*on the range of documents [d1, d2]: the root of the simulated*treap*is document dr = RM Q(d1, d2). ...##
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Using Treaps for Optimization of Graph Storage

2012
*
International Journal of Computer Applications
*

A special data structure

doi:10.5120/5612-7888
fatcat:xjhbiqd2snhp3mkfdnzrkcm7he
*Treap*, a combination of binary search tree and heaps has been used as a replacement to a large adjacency matrix. ... position by*treap*rotations. ... 1: Insert a node in a*Treap*1. ...##
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PERFORMANCE APPRAISAL OF TREAP AND HEAP SORT ALGORITHMS

2020
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Journal of Natural Sciences, Engineering and Technology
*

It was discovered that

doi:10.51406/jnset.v18i1.2027
fatcat:n45nvmf4azhbfatb5rjxzpmyye
*treap*was faster than heap sort in sorting and searching for elements using systems with homogenous properties. ...*Treap*as a method uses key and priority for searching in databases. When the keys are drawn from a large totally ordered set, the choice of storing the items is usually some sort of search tree. ... Derives the union of*treaps*T 1 and T 2 to form a new*treap*T. ...##
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K 2-Treaps: Range Top-k Queries in Compact Space
[chapter]

2014
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Lecture Notes in Computer Science
*

We introduce a data structure, the K 2 -

doi:10.1007/978-3-319-11918-2_21
fatcat:itmt4ixtirfu5fwmrymuhc65gy
*treap*, that represents grids in compact form and supports efficient prioritized range queries. ... We compare the K 2 -*treap*with state-of-the-art solutions on synthetic and real-world datasets, showing that it uses 30% of the space of competing solutions while solving queries up to 10 times faster. ... Our new representation, called K 2 -*treap*, is inspired by two previous data structures: the K 2 -tree [5] and the*treap*[18] . ...##
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An Exploratory Study of Critical Factors Affecting the Efficiency of Sorting Techniques (Shell, Heap and Treap)
[article]

2012
*
arXiv
*
pre-print

The efficiency of Shell, Heap and

arXiv:1203.1250v1
fatcat:76lcstmwijfptghj6eue7hu5ma
*Treap*sorting techniques in terms of both running time and memory usage was studied, experiments conducted and results subjected to factor analysis by SPSS. ...##
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B-Treaps: A Uniquely Represented Alternative to B-Trees
[chapter]

2009
*
Lecture Notes in Computer Science
*

We present the first uniquely represented data structure for an external memory model of computation, a B-tree analogue called a B-

doi:10.1007/978-3-642-02927-1_41
fatcat:kcemddgvpzf3heuco7npa3cw6e
*treap*. ... Like the B-tree, the B-*treap*has depth O(log B n), uses linear space with high probability, where B is the block transfer size of the external memory, and supports efficient one-dimensional range queries ... We call the resulting data structure a B-*treap*, for "bushy-*treap*." ...##
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Fast Set Operations Using Treaps

2018

We present parallel algorithms for union, intersection and difference on ordered sets using random balanced binary trees (

doi:10.1184/r1/6605603.v1
fatcat:igkuqylj55bdzi2jct637a5lfy
*treaps*[26]). ... As with the sequential algorithms on*treaps*for insertion and deletion, the main advantage of our algorithms are their simplicity. ... Figure 1 shows the result of a split on a*treap*. The expected time to split two*treaps*into*treaps*of size n and m is O(lg n + lg m) [26] . ...##
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Fast Set Operations Using Treaps

2018

We present parallel algorithms for union, intersection and difference on ordered sets using random balanced binary trees (

doi:10.1184/r1/6605606
fatcat:c6m4oxm43rac3dsjzvmncjtwdu
*treaps*[26]). ... As with the sequential algorithms on*treaps*for insertion and deletion, the main advantage of our algorithms are their simplicity. ... Figure 1 shows the result of a split on a*treap*. The expected time to split two*treaps*into*treaps*of size n and m is O(lg n + lg m) [26] . ...##
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Balloon: A Forward-Secure Append-Only Persistent Authenticated Data Structure
[chapter]

2015
*
Lecture Notes in Computer Science
*

Since the hash

doi:10.1007/978-3-319-24177-7_31
fatcat:buw6qm66yvhvrppbts4vvkieti
*treap*is a Merkle tree, its root fixes the entire hash*treap*. ... to structure the*treap*. ... Remove the event identifier of ei from the hash*treap*and insert a random key. Do any rebalancing of the*treap*if needed. 2. Insert a new event with a random key and value using B.Insert. 3. ...##
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Efficient Representation of Multidimensional Data over Hierarchical Domains
[chapter]

2016
*
Lecture Notes in Computer Science
*

This approach can be implemented compactly by generalizing to more dimensions the k^2-

doi:10.1007/978-3-319-46049-9_19
fatcat:djijmdp2q5bx5aveaizglabibi
*treap*, a compact representation of two-dimensional points that allows for efficient summarization queries along generic ... Dataset kn-*treap*CMHD kn-*treap*CMHD kn-*treap*CMHD kn-*treap*CMHD kn-*treap*CMHD kn-*treap*CMHD 0% Zeroes 25% Zeroes 50% Zeroes Binary Irregular Binary Irregular Binary Irregular 4D 16 3 10 20 ... of the k n -*treap*. ...##
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Pipelining with Futures

1999
*
Theory of Computing Systems
*

We describe and analyze four algorithms for which this is the case: a parallel merging algorithm on trees, parallel algorithms for finding the union and difference of two randomized balanced trees (

doi:10.1007/s002240000117
fatcat:yajvmjt27zfcjbmenwrje6lbku
*treaps*...*Treap*Difference The inverse operation to taking the union of two*treaps*is taking their difference; remove any keys from the first*treap*that appear in the second*treap*. ... When the splitter is in the*treap*, splitm excludes it from the resulting*treaps*and returns it along with the two split*treaps*. Otherwise, it simply returns the two resulting*treaps*. ...##
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Efficient Management of Short-Lived Data
[article]

2005
*
arXiv
*
pre-print

The algorithms are based on fully functional, persistent

arXiv:cs/0505038v1
fatcat:lf2spozujneevdljxy2xopcf5a
*treaps*, which are a combination of binary search trees with respect to a primary attribute and heaps with respect to a secondary attribute. ... Comparing*Treaps*to Competitors To estimate the performance and resource consumption of the*treap*index relative to other data structures, we compared the behaviour of*treaps*to a number of competing approaches ... The structure of a*treap*node is shown in Figure 1 . ...##
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Efficient Maintenance of Ephemeral Data
[chapter]

2006
*
Lecture Notes in Computer Science
*

The algorithms are based on fully functional

doi:10.1007/11733836_12
fatcat:3pru2lonyvgvrcyrjmj6a4i4zu
*treaps*, which are a combination of binary search trees with respect to a primary attribute and heaps with respect to a secondary attribute. ... Operations on*Treaps*This section introduces the most important operations on*treaps*. ...*Treaps*being also heaps implies that nodes with minimal expiration times cluster at the*treap*root. ...##
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Collision Resolution in Hash Tables for Vocabulary Accumulation During Parallel Indexing

2015
*
Proceedings of the 20th Australasian Document Computing Symposium on ZZZ - ADCS '15
*

Document Frequency

doi:10.1145/2838931.2838942
dblp:conf/adcs/CraneT15
fatcat:3qy2hx77erdm3dfgio7vqclsuy
*Treap*A*treap*is a data structure that provides two orderings on the data. The first is the same as the BST described above. ... size, with*treaps*being consistently the worse of the two. ...
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