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Fast set operations using treaps

Guy E. Blelloch, Margaret Reid-Miller
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 (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] .  ... 
doi:10.1145/277651.277660 dblp:conf/spaa/BlellochR98 fatcat:opextcwyjbeqlfjjmn2wit3lfe

Faster and smaller inverted indices with treaps

Roberto Konow, Gonzalo Navarro, Charles L.A. Clarke, Alejandro López-Ortíz
2013 Proceedings of the 36th international ACM SIGIR conference on Research and development in information retrieval - SIGIR '13  
To achieve compression we represent the 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).  ... 
doi:10.1145/2484028.2484088 dblp:conf/sigir/KonowNCL13 fatcat:stb7bxvqkvffnlwx6qv3nwq7fe

Using Treaps for Optimization of Graph Storage

Dharya Arora, Shalini Batra
2012 International Journal of Computer Applications  
A special data structure 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.  ... 
doi:10.5120/5612-7888 fatcat:xjhbiqd2snhp3mkfdnzrkcm7he

PERFORMANCE APPRAISAL OF TREAP AND HEAP SORT ALGORITHMS

A. D. GBADEBO, A. T. AKINWALE, S. AKINLEYE
2020 Journal of Natural Sciences, Engineering and Technology  
It was discovered that 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.  ... 
doi:10.51406/jnset.v18i1.2027 fatcat:n45nvmf4azhbfatb5rjxzpmyye

K 2-Treaps: Range Top-k Queries in Compact Space [chapter]

Nieves R. Brisaboa, Guillermo de Bernardo, Roberto Konow, Gonzalo Navarro
2014 Lecture Notes in Computer Science  
We introduce a data structure, the K 2 -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] .  ... 
doi:10.1007/978-3-319-11918-2_21 fatcat:itmt4ixtirfu5fwmrymuhc65gy

An Exploratory Study of Critical Factors Affecting the Efficiency of Sorting Techniques (Shell, Heap and Treap) [article]

Olusegun Folorunso, Olufunke R. Vincent, Oluwatimilehin Salako
2012 arXiv   pre-print
The efficiency of Shell, Heap and Treap sorting techniques in terms of both running time and memory usage was studied, experiments conducted and results subjected to factor analysis by SPSS.  ... 
arXiv:1203.1250v1 fatcat:76lcstmwijfptghj6eue7hu5ma

B-Treaps: A Uniquely Represented Alternative to B-Trees [chapter]

Daniel Golovin
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-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."  ... 
doi:10.1007/978-3-642-02927-1_41 fatcat:kcemddgvpzf3heuco7npa3cw6e

Fast Set Operations Using Treaps

Margaret Reid-Miller
2018
We present parallel algorithms for union, intersection and difference on ordered sets using random balanced binary trees (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] .  ... 
doi:10.1184/r1/6605603.v1 fatcat:igkuqylj55bdzi2jct637a5lfy

Fast Set Operations Using Treaps

Guy E. Blelloch, Margaret Reid-Miller
2018
We present parallel algorithms for union, intersection and difference on ordered sets using random balanced binary trees (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] .  ... 
doi:10.1184/r1/6605606 fatcat:c6m4oxm43rac3dsjzvmncjtwdu

Balloon: A Forward-Secure Append-Only Persistent Authenticated Data Structure [chapter]

Tobias Pulls, Roel Peeters
2015 Lecture Notes in Computer Science  
Since the hash 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.  ... 
doi:10.1007/978-3-319-24177-7_31 fatcat:buw6qm66yvhvrppbts4vvkieti

Efficient Representation of Multidimensional Data over Hierarchical Domains [chapter]

Nieves R. Brisaboa, Ana Cerdeira-Pena, Narciso López-López, Gonzalo Navarro, Miguel R. Penabad, Fernando Silva-Coira
2016 Lecture Notes in Computer Science  
This approach can be implemented compactly by generalizing to more dimensions the k^2-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.  ... 
doi:10.1007/978-3-319-46049-9_19 fatcat:djijmdp2q5bx5aveaizglabibi

Pipelining with Futures

G. E. Blelloch
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 (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.  ... 
doi:10.1007/s002240000117 fatcat:yajvmjt27zfcjbmenwrje6lbku

Efficient Management of Short-Lived Data [article]

Albrecht Schmidt, Christian S. Jensen
2005 arXiv   pre-print
The algorithms are based on fully functional, persistent 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 .  ... 
arXiv:cs/0505038v1 fatcat:lf2spozujneevdljxy2xopcf5a

Efficient Maintenance of Ephemeral Data [chapter]

Albrecht Schmidt, Christian S. Jensen
2006 Lecture Notes in Computer Science  
The algorithms are based on fully functional 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.  ... 
doi:10.1007/11733836_12 fatcat:3pru2lonyvgvrcyrjmj6a4i4zu

Collision Resolution in Hash Tables for Vocabulary Accumulation During Parallel Indexing

Matt Crane, Andrew Trotman
2015 Proceedings of the 20th Australasian Document Computing Symposium on ZZZ - ADCS '15  
Document Frequency 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.  ... 
doi:10.1145/2838931.2838942 dblp:conf/adcs/CraneT15 fatcat:3qy2hx77erdm3dfgio7vqclsuy
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