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Analysis of a Block Arithmetic Coding: Discrete divide and conquer recurrences

Michael Drmota, Wojciech Szpankowski
2011 2011 IEEE International Symposium on Information Theory Proceedings  
This tree, in its suboptimal heuristic version, is constructed by a simple divide and conquer algorithm, whose analysis is the subject of this paper.  ...  In 1993 Boncelet introduced a block arithmetic scheme for entropy coding that combines advantages of stream arithmetic coding with algorithmic simplicity.  ...  ACKNOWLEDGMENT This work was supported in part by the Austrian Science Foundation FWF Grant No.  ... 
doi:10.1109/isit.2011.6033751 dblp:conf/isit/DrmotaS11 fatcat:6ffgiop6uzcshc4dotxv3ztnxq

The Solution of Linear Probabilistic Recurrence Relations

Bazzi, Mitter
2003 Algorithmica  
Then, following [2], we argue that the solution holds under a broad class of perturbations including floors and ceilings that usually accompany the recurrences that arise when analyzing randomized divide-and-conquer  ...  Linear probabilistic divide-and-conquer recurrence relations arise when analyzing the running time of divide-and-conquer randomized algorithms.  ...  We thank the anonymous referees for valuable suggestions, and David Karger for helpful discussions.  ... 
doi:10.1007/s00453-002-1003-4 fatcat:os57sbs6wrf3djwcqgzlwemxum

A Master Theorem for Discrete Divide and Conquer Recurrences

Michael Drmota, Wojciech Szpankowski
2013 Journal of the ACM  
Divide-and-conquer recurrences are one of the most studied equations in computer science.  ...  To the best of our knowledge, discrete divide and conquer recurrences were not studied in this generality and such detail; in particular, this allows us to compare the redundancy of Boncelet's algorithm  ...  Our goal is to present such an analysis for discrete divide and conquer recurrences. The complexity of a divide and conquer algorithm is well described by its divide and conquer recurrence.  ... 
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  
Divide-and-conquer recurrences are one of the most studied equations in computer science.  ...  To the best of our knowledge, discrete divide and conquer recurrences were not studied in this generality and such detail; in particular, this allows us to compare the redundancy of Boncelet's algorithm  ...  Our goal is to present such an analysis for discrete divide and conquer recurrences. The complexity of a divide and conquer algorithm is well described by its divide and conquer recurrence.  ... 
doi:10.1137/1.9781611973082.28 dblp:conf/soda/DrmotaS11 fatcat:yuw4skgo5vcq3oi3c3pdahrfp4

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  ...  Both theoretical and experimental results show that our algorithm offers an excellent compromise in terms of space and time requirements, compared to the known best alternatives.  ...  Both divide and conquer and dichopile are linear in q and almost linear in n, with an advantage for divide and conquer.  ... 
doi:10.1016/j.tcs.2012.07.025 fatcat:xuwakjtgp5b3vbxvx7sf5ushma

Fast FAST [chapter]

Noga Alon, Daniel Lokshtanov, Saket Saurabh
2009 Lecture Notes in Computer Science  
We present a randomized subexponential time, polynomial space parameterized algorithm for the k-Weighted Feedback Arc Set in Tournaments (k-FAST) problem.  ...  For integers m, k and r, a family F of functions from [m] to [r] is called a universal (m, k, r)-coloring family if for any graph G on the set of vertices [m] with at most k edges, there exists an f ∈  ...  For simplicity we omit all floor and ceiling signs whenever these are not crucial. We make no attempt to optimize the absolute constants in theÕ( √ k) or in the O( √ k) notation.  ... 
doi:10.1007/978-3-642-02927-1_6 fatcat:e3b2ta4ztzb4nkppmsskeipzii

General Techniques for Analyzing Recursive Algorithms with Applications

Rakesh M. Verma
1997 SIAM journal on computing (Print)  
The complexity of divide-and-conquer algorithms is often described by recurrences of various forms.  ...  In the process of solving such recurrences, we establish interesting connections between some elegant mathematics and analysis of recurrences.  ...  Reingold which analyzes a different (min-max) recurrence. Thanks also go to both of them.  ... 
doi:10.1137/s0097539792240583 fatcat:vgxhgck6vzb3bjiph4q2qlqrsy

The Eco- Efficiency of Using Smart Masonry in the Rehabilitation Projects of the Heritage buildings (Dept.A)

gehan elsayed, Hassan Randa
2020 MEJ. Mansoura Engineering Journal  
Masonry units are considered to be traditional and environmental materials used in constructing valuable buildings in historic and Heritage sites all over the world.  ...  directed to the persons concerned the heritage sites development), and then collecting and analyzing data to test those hypotheses(by measuring the efficiency of using the new technical masonry in the  ...  The post-tensioning ligaments were intended to initiate pressure in the dividers (walls) to conquer the strain made by out-of-plane flexural loads.  ... 
doi:10.21608/bfemu.2020.124779 fatcat:qvfznehp3ndezkkrkjwjkykjj4

Algorithms and analyses for maximal vector computation

Parke Godfrey, Ryan Shipley, Jarek Gryz
2006 The VLDB journal  
Early algorithms based on divide-and-conquer established seemingly good average and worst-case asymptotic runtimes. In fact, the problem can be solved in O(n) average-case (holding k as fixed).  ...  This arises in many contexts and, as such, has been well studied.  ...  Divide-and-conquer is quite elegant and efficient in other contexts.  ... 
doi:10.1007/s00778-006-0029-7 fatcat:5pw4an5oardhxlxpbmc7fvgdvy

Concentration-Bound Analysis for Probabilistic Programs and Probabilistic Recurrence Relations [article]

Jinyi Wang, Yican Sun, Hongfei Fu, Mingzhang Huang, Amir Kafshdar Goharshady, Krishnendu Chatterjee
2020 arXiv   pre-print
In this work, we propose a novel approach for deriving concentration bounds for probabilistic programs and probabilistic recurrence relations through the synthesis of exponential supermartingales.  ...  Analyzing probabilistic programs and randomized algorithms are classical problems in computer science.  ...  Joseph Tassarotti for pointing out a miscalculation in Remark 6.  ... 
arXiv:2008.00425v3 fatcat:zsnelpclkncr5j6yie2uaoayf4

Two Queens in Westminster

Henry Morford
1872 The Aldine  
In the Chapel of Henry the Seventh, Where the sculptured ceilings rare Show the conquered stone-work hanging Like cobweb films in air, There are held two shrines in keeping, Whose memories closely press  ...  They dine with a popping of muskets outside, and a recurrence of sulphurous smells.  ... 
doi:10.2307/20636324 fatcat:is567ka52rhehcov7bvvat4aze

Patriotism and Powder

1872 The Aldine  
In the Chapel of Henry the Seventh, Where the sculptured ceilings rare Show the conquered stone-work hanging Like cobweb films in air, There are held two shrines in keeping, Whose memories closely press  ...  They dine with a popping of muskets outside, and a recurrence of sulphurous smells.  ... 
fatcat:cuera43l45aoxo3736zbgl25wu

An improved master theorem for divide-and-conquer recurrences [chapter]

Salvador Roura
1997 Lecture Notes in Computer Science  
This paper presents new theorems to analyze divide-and-conquer recurrences, which improve other similar ones in several aspects.  ...  In particular, these theorems provide more information, free us almost completely from technicalities like floors and ceilings, and cover a wider set of toll functions and weight distributions, stochastic  ...  I thank my advisor Conrado Martínez for his support while working on this problem, and several referees for their helpful comments.  ... 
doi:10.1007/3-540-63165-8_201 fatcat:kzhindaikjem5piq3leyi4eb3m

Improved master theorems for divide-and-conquer recurrences

Salvador Roura
2001 Journal of the ACM  
This paper presents new theorems to analyze divide-and-conquer recurrences, which improve other similar ones in several aspects.  ...  In particular, these theorems provide more information, free us almost completely from technicalities like floors and ceilings, and cover a wider set of toll functions and weight distributions, stochastic  ...  I thank my advisor Conrado Martínez for his support while working on this problem, and several referees for their helpful comments.  ... 
doi:10.1145/375827.375837 fatcat:qiizocf5fnfznarmihrw72pqye

Page 36 of Friend; A Religious and Literary Journal Vol. 4, Issue 5 [page]

1830 Friend; A Religious and Literary Journal  
have never been on the earth since they first descended; and twenty hours, the workmen here, as in} most other mines, are divided into three bands, each of which works only eight hours, and their houses  ...  You are landed below, at a depth of three hundred feet, in the first floor, near St. Anthony's chapel, an early | production of the miners.  ... 
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