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An Extended Note on the Comparison-optimal Dual Pivot Quickselect [article]

Daniel Krenn
2016 arXiv   pre-print
It turns out that the main terms of these asymptotic expansions coincide with the main terms of the corresponding analysis of the classical quickselect, but still---as this was shown for Yaroslavskiy quickselect  ...  In this note the precise minimum number of key comparisons any dual-pivot quickselect algorithm (without sampling) needs on average is determined.  ...  It was analyzed in [2] , where an exact formula and a precise asymptotic expansion was stated.  ... 
arXiv:1607.05008v2 fatcat:dxs5rgbp6zfl7mrnyen6ajoyim

An Extended Note on the Comparison-optimal Dual-Pivot Quickselect

Daniel Krenn
2017 2017 Proceedings of the Fourteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)  
It turns out that the main terms of these asymptotic expansions coincide with the main terms of the corresponding analysis of the classical quickselect, but still-as this was shown for Yaroslavskiy quickselect-more  ...  In this note the precise minimum number of key comparisons any dual-pivot quickselect algorithm (without sampling) needs on average is determined.  ...  It was analyzed in [2] , where an exact formula and a precise asymptotic expansion was stated.  ... 
doi:10.1137/1.9781611974775.11 dblp:conf/analco/Krenn17 fatcat:rn4r75kmdrdrjcyvk3d3w2uq3q

Performance Optimisation of Smoothed Particle Hydrodynamics Algorithms for Multi/Many-Core Architectures

Fabio Baruffa, Luigi Iapichino, Nicolay J. Hammer, Vasileios Karakasis
2017 2017 International Conference on High Performance Computing & Simulation (HPCS)  
For our purpose, we have used the QUICKSELECT algorithm [13] , which is based on QUICKSORT.  ...  Our initial experiments comparing the two algorithms (our straightforward QUICKSELECT implementation vs.  ... 
doi:10.1109/hpcs.2017.64 dblp:conf/ieeehpcs/BaruffaIHK17 fatcat:v4kxjqbxnnhw3ccufz4i7r6pfe

Using trend clusters for spatiotemporal interpolation of missing data in a sensor network

Annalisa Appice, Anna Ciampi, Donato Malerba, Pietro Guccione
2013 Journal of Spatial Information Science  
(Forward selection based construction of a polynomial).  ...  The expansion process is described in Algorithm 2. The expansion of [c k ,ẑ k ] is driven by a seed node p and is recursively defined.  ... 
doi:10.5311/josis.2013.6.102 fatcat:kbahf67kyva33nhoivfochz67a

Analysis of Pivot Sampling in Dual-Pivot Quicksort: A Holistic Analysis of Yaroslavskiy's Partitioning Scheme

Markus E. Nebel, Sebastian Wild, Conrado Martínez
2015 Algorithmica  
Finding a given order statistic of a list of elements is known as the selection problem and can be solved by specialized algorithms like Quickselect.  ...  For example in our recurrence (6), rather elementary means sufficed to determine the leading term of an asymptotic expansion of the solution; obtaining more terms of the expansion is much harder, though  ...  In particular, if we have an asymptotic expansion for t n , we get an asymptotic expansion for F n ; the latter might however get truncated in precision when we end up in case 3 of Theorem D.1.  ... 
doi:10.1007/s00453-015-0041-7 fatcat:drpb6zoljzhxnl2svy4jcb6w4i

A Practical Index Structure Supporting Fréchet Proximity Queries Among Trajectories [article]

Joachim Gudmundsson, Michael Horton, John Pfeifer, Martin P. Seybold
2020 arXiv   pre-print
Based on clustering for metric indexes, we obtain a dynamic tree structure whose size is linear in the number of trajectories, regardless of the trajectory's individual sizes or the spatial dimension,  ...  Techniques, such as heuristic-guided pivot selection, may further reduce the number of \delta calls.  ...  Results based on the second query generation method indicate that in the respective gure.  ... 
arXiv:2005.13773v1 fatcat:iaeevus3g5hc3ctcwqgjqyjp3u

Partial Policy Iteration for L1-Robust Markov Decision Processes [article]

Chin Pang Ho and Marek Petrik and Wolfram Wiesemann
2020 arXiv   pre-print
This, however, contradicts the way in which bases are selected by the algorithm. Proof of Theorem 2.  ...  The optimal policies in RMDPs are history-dependent, stochastic and NP-hard to compute even when restricted to be stationary (Iyengar, 2005; Wiesemann et al., 2013) .  ... 
arXiv:2006.09484v1 fatcat:lwcty6bhdvdmbfc36bfwtybq7a

FPGA Implementation of Computer Vision Algorithms: Application on Linear Time Selection Algorithm [article]

Georgios N. Tzimpragos, National Technological University Of Athens, National Technological University Of Athens, Δημήτριος Σούντρης
2012
Additionally, we have to highlight that based on our exploration results we achieve significant increased performance compared to the software implementation (C++).  ...  Sorting network based architectures first range the samples and then select the sample of corresponding rank.  ...  Thus, we compare the performance of the method we chose to implement with another common method(quickselect which is also another popular solution is based on the quicksort algorithm, so we can also conclude  ... 
doi:10.26240/heal.ntua.11716 fatcat:hfrc4lmpzfhc3mkfxivorqtmgq

Reinforcement Learning on Resource Bounded Systems

Jaden Travnik
2018
In this setting, after applying quickselect to find the closest c prototypes, the value of the closest prototypes' features would be based on the prototypes' proximity to the state relative to the other  ...  The closer the value of λ decay is to 1, the longer the history will be, with the length of the history in timesteps given by the formula timesteps = 1 1−λ decay as seen in Figure 2 .6.  ... 
doi:10.7939/r39g5gv5s fatcat:vfep7jfwvbenxewdoe76kuw6ri

Designing efficient attention mechanisms for deep neural networks [article]

Giannis Daras, National Technological University Of Athens
2020
Note that the name Expanders originates from the "expansion" property which is described in the last bullet.  ...  Introduction Introduction to Deep Learning History of Artificial Intelligence People have always dreamed of machines that can think.  ...  Reformer takes the greedy approach of splitting to clusters based on a top-k approach. Similarly, Routing Transformers [138] follow a greedy approach to form balanced clusters based on K-means.  ... 
doi:10.26240/heal.ntua.19572 fatcat:bk2mh47hjfhbfmtlulxpwigwui