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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  
We introduce a new representation of the inverted index that performs faster ranked unions and intersections while using less space.  ...  To achieve compression we represent the treap topology using compact data structures.  ...  CONCLUSIONS AND FUTURE WORK We have introduced a new inverted index representation based on the treap data structure.  ... 
doi:10.1145/2484028.2484088 dblp:conf/sigir/KonowNCL13 fatcat:stb7bxvqkvffnlwx6qv3nwq7fe

Improved Single-Term Top-k Document Retrieval [chapter]

Simon Gog, Gonzalo Navarro
2014 2015 Proceedings of the Seventeenth Workshop on Algorithm Engineering and Experiments (ALENEX)  
On natural language text collections, finding the k documents most relevant to a query is generally solved with inverted indexes.  ...  In the latter case, it uses about the same space of the tokenized text (and replaces it), while answering phrase queries an order of magnitude faster than a positional inverted index.  ...  We showed on those collections that our index is faster than typical positional inverted outperforms positional inverted indexes on phrase queries.  ... 
doi:10.1137/1.9781611973754.3 dblp:conf/alenex/GogN15 fatcat:wlzdqcerdfgbjd322254lhsdpa

Top-k Query Processing with Conditional Skips

Edward Bortnikov, David Carmel, Guy Golan-Gueta
2017 Proceedings of the 26th International Conference on World Wide Web Companion - WWW '17 Companion  
[11] used a Wavelet tree data structure [15] to represent a posting-list using the Dual-Sorted inverted list.  ...  [6] took advantage of a two-tiered index, in which the first tier is a small index, containing only higher impact entries of each inverted list.  ... 
doi:10.1145/3041021.3054191 dblp:conf/www/BortnikovCG17 fatcat:5iny65e4rjhodnwyfiuxkx2wuq

Randomized search trees

R. Seidel, C. R. Aragon
1996 Algorithmica  
Deletion of an item x from T can beachieved by \inverting" the insertion operation: First locate x, then rotate it down until it becomes a leaf (where the decision to rotate left or right is dictated by  ...  By the in-order property the left subtree of the root will be a treap for X 1 and the right subtree will be a treap for X 2 .  ... 
doi:10.1007/bf01940876 fatcat:blbh5y4hifaedg36dt6skcyvmy

Randomized search trees

C.R. Aragon, R.G. Seidel
1989 30th Annual Symposium on Foundations of Computer Science  
Deletion of an item x from T can beachieved by \inverting" the insertion operation: First locate x, then rotate it down until it becomes a leaf (where the decision to rotate left or right is dictated by  ...  By the in-order property the left subtree of the root will be a treap for X 1 and the right subtree will be a treap for X 2 .  ... 
doi:10.1109/sfcs.1989.63531 dblp:conf/focs/AragonS89 fatcat:5txipnxj7rcadkyep2wf42hy54

Randomized Search Trees

R. Seidel, C.R. Aragon
1996 Algorithmica  
Deletion of an item x from T can beachieved by \inverting" the insertion operation: First locate x, then rotate it down until it becomes a leaf (where the decision to rotate left or right is dictated by  ...  By the in-order property the left subtree of the root will be a treap for X 1 and the right subtree will be a treap for X 2 .  ... 
doi:10.1007/s004539900061 fatcat:fqjquz27njcklkl2qjf77jakta

Using bistellar flips for rotations in point location structures

Benoît Hudson, Gary L. Miller
2004 Canadian Conference on Computational Geometry  
In particular, we have investigated implementing a treap analogue. A treap is a binary search tree with the added property that every point inserted into the tree gets a random priority.  ...  Because a search tree built in random order has 1 32 H8 EA G4 76 depth, so does the treap.  ... 
dblp:conf/cccg/HudsonM04 fatcat:5nlga5jlwrbadagtmpavt76eay

Smooth heaps and a dual view of self-adjusting data structures [article]

László Kozma, Thatchaphol Saranurak
2018 arXiv   pre-print
Observe that the permutation input of A bst is inverted and reversed.  ...  Treap view. We associate each item x i in X with a pair of values (i, x i ), and we transform the list into a treap over the pairs (using an arbitrary method for treap-building).  ... 
arXiv:1802.05471v2 fatcat:f7bwxo4pobeepcjrjydhdbjfau

Randomized Ternary Search Tries [article]

Nicolai Diethelm
2017 arXiv   pre-print
This paper presents a new kind of self-balancing ternary search trie that uses a randomized balancing strategy adapted from Aragon and Seidel's randomized binary search trees ("treaps").  ...  The deletion of a string s from an r-trie can be achieved by "inverting" the insertion operation: Set the strPrio field of the terminal node of s to 0.  ...  This paper now presents a new kind of self-balancing ternary search trie that uses a randomized balancing strategy adapted from Aragon and Seidel's randomized binary search trees ("treaps") [5] .  ... 
arXiv:1606.04042v20 fatcat:atuab7p625gl3gxerbdtyiv54m

An introduction to randomized algorithms

Richard M. Karp
1991 Discrete Applied Mathematics  
A one-way function is, roughly speaking, a function that is easy to compute but hard to invert.  ...  A snapshot of the treap structure at any one time is independent of any items that were inserted and later deleted and is uniquely determined by the two fields of the items currently present in the treap  ... 
doi:10.1016/0166-218x(91)90086-c fatcat:d3pgh36rvvhphcxov4p5yhvvhu

Information Retrieval of Sequential Data in Heterogeneous XML Databases [chapter]

Eugen Popovici, Pierre-François Marteau, Gildas Ménier
2006 Lecture Notes in Computer Science  
The inverted list resulting from the indexing process is encoded using binary randomized search trees, namely TREAPS as defined in [11] , associated to hashtable structures.  ...  TREAP structures can balance the search tree according to the asked frequency of items. This provides an access speed-up over the use of regular hashtables [12] .  ... 
doi:10.1007/11670834_19 fatcat:kktag6u3xjgt5lvbmoh77pndgm

Self-Adjusting of Ternary Search Tries Using Conditional Rotations and Randomized Heuristics

G. H. Badr
2005 Computer journal  
Let T be the treap of n items, and let 1 ≤ i, j ≤ n.  ...  It is easy to see that for any set X such a treap exists.  ... 
doi:10.1093/comjnl/bxh073 fatcat:pbkshuxuqvgo3bovrzwbgghop4

The Geometry of Binary Search Trees [chapter]

Erik D. Demaine, Dion Harmon, John Iacono, Daniel Kane, Mihai Pâtraşcu
2009 Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms  
, constructed based on these next values. (4) The tree Ti−1. (5) The treap formed by the next access time of the nodes of τi at time i + 1; τ is an arbitrary binaryification of this general treap. (6)  ...  The construction that we are led to can be seen as inverting the proof of Lemma 2.2, because split trees are stored in heap order by the previous access (instead of the next access).  ... 
doi:10.1137/1.9781611973068.55 fatcat:ezjgiqarxfhnrgnzshpvaammmy

Compact Representations of Ordered Sets

Daniel K. Blandford, Guy E. Blelloch
2018
The time bound for our operations contains a factor of 1/α.We present experimental results for the STL (C++ Standard Template Library) implementation of Red-Black trees, and for an implementation of Treaps  ...  Each entry (or posting list) in an inverted file index is a list of the document numbers of documents containing a specific term.  ...  Most of the space used by a search engine is in the representation of an inverted file index, a data structure that maps search terms to lists of documents containing those terms.  ... 
doi:10.1184/r1/6604220.v1 fatcat:3vwbjmcimfavrjcirt7ewvyq7y

Document Prioritization for Scalable Query Processing

Hao Wu, Hui Fang
2014 Proceedings of the 23rd ACM International Conference on Conference on Information and Knowledge Management - CIKM '14  
[20] proposed to construct index based on the treap data structure.  ...  We use the inverted indexes whose postings in an inverted list are sorted based on document IDs. The indexes are compressed using a state of the art method, i.e,. New-PFD compression method [36] .  ... 
doi:10.1145/2661829.2661914 dblp:conf/cikm/WuF14 fatcat:57kurikpobaxpfxz5aspavvowu
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