Filters








25 Hits in 2.3 sec

Metode Akra-Bazzi Sebagai Generalisasi Metode Master Dalam Menyelesaikan Relasi Rekurensi

Muchammad Abrori
2013 Jurnal Fourier  
This research aims to know the Akra-Bazzi Method as an extension Method of the Master.  ...  Note that Akra-Bazzi Method can solve a rekurensi devide-and-conquer with shorter calculation.  ...  The Master Method is fairly powerfull and result in a closed form solution for devide-and-conquer recurrences with a special (but commonly-occuring) form [1] .  ... 
doi:10.14421/fourier.2013.22.63-72 fatcat:emwxnfwdsjeszgihh2prg4qba4

Verifying Asymptotic Time Complexity of Imperative Programs in Isabelle [article]

Bohua Zhan, Maximilian P. L. Haslbeck
2018 arXiv   pre-print
In addition to the basic arguments, our framework is able to handle advanced techniques for time complexity analysis, such as the use of the Akra-Bazzi theorem and amortized analysis.  ...  Various automation is built and incorporated into the auto2 prover to reason about separation logic with time credits, and to derive asymptotic behavior of functions.  ...  We thank Manuel Eberl for his impressive formalization of the Akra-Bazzi method and the functional correctness of the selection algorihtm, and Simon Wimmer for the formalization of the DP solution for  ... 
arXiv:1802.01336v1 fatcat:sencjmmrdzcdhalbbyjk2qmudm

Cache-Adaptive Analysis

Michael A. Bender, Erik D. Demaine, Roozbeh Ebrahimi, Jeremy T. Fineman, Rob Johnson, Andrea Lincoln, Jayson Lynch, Samuel McCauley
2016 Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures - SPAA '16  
Our techniques enable us to analyze a wide variety of algorithms -Master-Method-style algorithms, Akra-Bazzi-style algorithms, collections of mutually recursive algorithms, and algorithms, such as FFT,  ...  , which is not covered by the above theorems.  ...  The same basic technique works for Akra-Bazzi-style algorithms and even for collections of mutually-recursive Akra-Bazzi-style algorithms (see Theorem 6.10).  ... 
doi:10.1145/2935764.2935798 dblp:conf/spaa/BenderDEFJLLM16 fatcat:z3vm6vlydbfktckpucxokknvde

A Real Elementary Approach to the Master Recurrence and Generalizations [chapter]

Chee Yap
2011 Lecture Notes in Computer Science  
The master theorem provides a solution to a well-known divide-and-conquer recurrence, called here the master recurrence. This paper proves two cook-book style generalizations of this master theorem.  ...  The power and simplicity of our approach comes from re-interpreting integer recurrences as real recurrences, with emphasis on elementary techniques and real induction.  ...  For instance, the summation rules for the various growth-types are easily taught in introductory algorithms. Indeed, our perspectives have developed out of classroom teaching.  ... 
doi:10.1007/978-3-642-20877-5_3 fatcat:ih4ujesexfajbb5l3imqwnnrke

A simple master Theorem for discrete divide and conquer recurrences [article]

Olivier Garet
2021 arXiv   pre-print
The aim of this note is to provide a Master Theorem for some discrete divide and conquer recurrences: $$X_{n}=a_n+\sum_{j=1}^m b_j X_{\lfloor p_j n \rfloor},$$ where the $p_i$'s belong to $(0,1)$.  ...  The main novelty of this work is there is no assumption of regularity or monotonicity for $(a_n)$.  ...  of n≥1 |an| n s 0 +1 and our Master Theorem still applies.  ... 
arXiv:1902.10600v2 fatcat:7z4srr43kjcmdptgyfgoylixwy

Fast and Stable Pascal Matrix Algorithms [article]

Samuel F. Potter, Ramani Duraiswami
2017 arXiv   pre-print
We conduct numerical experiments which establish the speed and stability of our algorithm, as well as the poor performance of the Toeplitz factorization algorithm.  ...  These algorithms use a recursive factorization of the triangular Pascal matrices and improve upon the cripplingly unstable $O(n log n)$ fast Fourier transform-based algorithms which involve a Toeplitz  ...  We apply the Akra-Bazzi theorem [3] to show that T n = Θ(kn log 2 n).  ... 
arXiv:1711.08453v1 fatcat:mgibthhjzvethagdd2gmhrmgz4

A Master Theorem for Discrete Divide and Conquer Recurrences

Michael Drmota, Wojciech Szpankowski
2013 Journal of the ACM  
The discrete nature of this recurrence (represented by the floor function) introduces certain oscillations not captured by the traditional Master Theorem, for example due to Akra and Bazzi who primary  ...  We apply powerful techniques such as Dirichlet series, Mellin-Perron formula, and (extended) Tauberian theorems of Wiener-Ikehara to provide a complete and precise solution to this basic computer science  ...  Then we recover the asymptotics of T (x) directly by an application of the Wiener-Ikehara theorem: T (x) ∼ Cx s0 with C = a(−s 0 ) + g(−s 0 ) j b j p s0 j log(1/p j ) , which is in accordance with Akra-Bazzi  ... 
doi:10.1145/2487241.2487242 fatcat:ounr7asah5ajxd2pimlib65xti

A Master Theorem for Discrete Divide and Conquer Recurrences [chapter]

Michael Drmota, Wojciech Szpankowski
2011 Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms  
The discrete nature of this recurrence (represented by the floor function) introduces certain oscillations not captured by the traditional Master Theorem, for example due to Akra and Bazzi who primary  ...  We apply powerful techniques such as Dirichlet series, Mellin-Perron formula, and (extended) Tauberian theorems of Wiener-Ikehara to provide a complete and precise solution to this basic computer science  ...  Then we recover the asymptotics of T (x) directly by an application of the Wiener-Ikehara theorem: T (x) ∼ Cx s0 with C = a(−s 0 ) + g(−s 0 ) j b j p s0 j log(1/p j ) , which is in accordance with Akra-Bazzi  ... 
doi:10.1137/1.9781611973082.28 dblp:conf/soda/DrmotaS11 fatcat:yuw4skgo5vcq3oi3c3pdahrfp4

On the Solution of Linear Recurrence Equations

Mohamad Akra, Louay Bazzi
1998 Computational optimization and applications  
In this article, we present a general solution for linear divide-and-conquer recurrences of the form Our approach handles more cases than the Master method does[1].  ...  This transform helps in mapping the sequence under consideration to the two dimensional plane where the solution becomes easier to obtain.  ...  of the Order transform to solve Equation 2 in the plane. • In Theorem 4 we show that our results agree with the Master method when the latter is applicable. • In Corollary 1 we summarize the results as  ... 
doi:10.1023/a:1018373005182 fatcat:jxf5vbo4pzecdglmuwe76ol66m

Verified Tail Bounds for Randomized Programs [chapter]

Joseph Tassarotti, Robert Harper
2018 Lecture Notes in Computer Science  
We mechanize a theorem by Karp, along with several extensions, that provide an easy to use "cookbook" method for verifying tail bounds, much like the traditional "Master Theorem" gives bounds for deterministic  ...  The development of type systems and static analyses that automatically bound the complexity of programs is an active area of research.  ...  Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of these organizations.  ... 
doi:10.1007/978-3-319-94821-8_33 fatcat:b3effzpfd5ck5bwd7haukjcyaa

Hierarchical Algorithm for Hidden Markov Model

SANAA CHAFIK, DAOUI CHERKI
2013 International Journal of Advanced Computer Science and Applications  
The objective of this work is to reduce the task of solving the Forward algorithm, by offering faster improved algorithm which is based on divide and conquer technique.  ...  The Forward algorithm is an inference algorithm for hidden Markov models, which often leads to a very large hidden state space.  ...  Whereas, the complexity of improved Forward algorithm can be calculated by using Akra Bazzi theorem [16] (A generalization to the well known Master Theorem [17] ) which allows calculating the complexity  ... 
doi:10.14569/specialissue.2013.030203 fatcat:rrlxbtginzfxnbc5a77hhfay2a

A new dichotomic algorithm for the uniform random generation of words in regular languages

Johan Oudinet, Alain Denise, Marie-Claude Gaudel
2013 Theoretical Computer Science  
When using floating point arithmetics, its bit-complexity is O(q log 2 n) in space and O(qn log 2 n) in time, where n stands for the length of the word, and q stands for the number of states of a finite  ...  We implemented the algorithm and compared its behavior to the state-of-the-art algorithms, on a set of large automata from the VLTS benchmark suite.  ...  Akra and Bazzi, 1998) .  ... 
doi:10.1016/j.tcs.2012.07.025 fatcat:xuwakjtgp5b3vbxvx7sf5ushma

Synthesis with Asymptotic Resource Bounds [article]

Qinheping Hu, John Cyphert, Loris D'Antoni, Thomas Reps
2021 arXiv   pre-print
These typing rules are justified by theorems used in analysis of algorithms, such as the Master Theorem and the Akra-Bazzi method.  ...  Prior methods for synthesis with a resource metric require the user to specify a concrete expression exactly describing resource usage, whereas our method uses big-O notation to specify the asymptotic  ...  Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors, and do not necessarily reflect the views of the sponsoring entities.  ... 
arXiv:2103.04188v2 fatcat:q32grfvsl5egxmitaj5okaldl4

Continuous amortization and extensions: With applications to bisection-based root isolation

Michael A. Burr
2016 Journal of symbolic computation  
Figure 1 : The intervals J 1 , J 3 , and J 5 all contribute to the local size bound at x because they contain the point x and the stopping criterion is False on them.  ...  Here, w(J) denotes the length of the interval J. 2 In previous work (Burr et al. (2009), Sharma and Yap (2012), and Burr and Krahmer (2012) ), a local size bound was called a stopping function.  ...  algorithms, the master theorem (Cormen et al., 2001) and the Akra-Bazzi theorem (Akra and Bazzi, 1998) provide formulae for computing the complexity of such algorithms.  ... 
doi:10.1016/j.jsc.2016.01.007 fatcat:bee6vuww4zfx7bt3y2gonumqhm

Optimal construction of a layer-ordered heap [article]

Jake Pennington, Patrick Kreitzberg, Kyle Lucke, Oliver Serang
2020 arXiv   pre-print
The layer-ordered heap (LOH) is a simple, recently proposed data structure used in optimal selection on $X+Y$, thealgorithm with the best known runtime for selection on $X_1+X_2+\cdots+X_m$, and the fastest  ...  Here, we introduce a few algorithms for constructing LOHs, analyze their complexity, and demonstrate that one algorithm is optimal for building a LOH of any rank $\alpha$.  ...  for this algorithm is solved by neither the master theorem [3] nor the more general Akra-Bazzi method [1] .  ... 
arXiv:2007.13356v2 fatcat:kmz3a5f4yzdiro2r3tavsqsldu
« Previous Showing results 1 — 15 out of 25 results