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Average case complexity of linear multivariate problems I. Theory

H Woźniakowski
1992 Journal of Complexity  
We use relations between average case and worst case settings. These relations reduce the study of the average case to the worst case for a different class of functions.  ...  In this way we show how optimal sample points from the worst case setting can be used in the average case.  ...  setting by utilizing relations between average case and worst case settings.  ... 
doi:10.1016/0885-064x(92)90001-r fatcat:cap4dlcbfngktnrgo6hut5vd5i

Special Issue On Worst-case Versus Average-case Complexity Editors' Foreword

Oded Goldreich, Salil Vadhan
2007 Computational Complexity  
An even more ambitious goal is to understand the relationship between average-case complexity and worst-case complexity, e.g., whether NP = P implies that NP has problems that are hard on average.  ...  These two motivations are actually supported by a variety of different notions of average-case complexity (surveyed in [17, 13, 6] ) and relating these notions is an important direction for research in  ...  Salil Vadhan's work on this issue was supported by NSF grants CCF-0133096 and CNS-0430336.  ... 
doi:10.1007/s00037-007-0232-y fatcat:ngds2ex4njfyfaza2xcqqqbx3y

Generalized Leapfrogging Samplesort: A Class of O(n ^2 n) Worst-Case Complexity and O(n n) Average-Case Complexity Sorting Algorithms [article]

Eliezer A. Albacea
2018 arXiv   pre-print
We present a practical implementation of this class of algorithms and we show that the worst-case complexity is O(n ^2 n) and the average-case complexity is O(n n).  ...  The original Leapfrogging Samplesort operates on a sorted sample of size s and an unsorted part of size s+1.  ...  It was shown that the worst-case complexity is O(n log 2 n) and the average-case complexity is O(n log n).  ... 
arXiv:1801.09431v1 fatcat:qhxh4b44vfd5pk2jcaiu35r2tu

Average case complexity\\ of linear multivariate problems

H. Wo\'zniakowski
1993 Bulletin of the American Mathematical Society  
We also address the optimal design problem for an LMP by using a relation to the worst case setting.  ...  The first Astd consists of function values and the second A*11 of all continuous linear functionals. Tractability of LMP means that the average case complexity is 0((l/e)p) with p independent of d.  ...  Optimal design for APP is analyzed by exhibiting a relation between average case and worst case errors of linear algorithms for APP.  ... 
doi:10.1090/s0273-0979-1993-00400-2 fatcat:2sdrieb54vbirmbplutbnyyb3e

Monotonic Robust Policy Optimization with Model Discrepancy

Yuankun Jiang, Chenglin Li, Wenrui Dai, Junni Zou, Hongkai Xiong
2021 International Conference on Machine Learning  
We theoretically derive a lower bound for the worst-case performance of a given policy by relating it to the expected performance.  ...  Experimental evaluations in several robot control tasks demonstrate that MRPO can generally improve both the average and worst-case performance in the source environments for training, and facilitate in  ...  distance between the worst and average case environments.  ... 
dblp:conf/icml/JiangLDZX21 fatcat:upveei6fjfacdhvfvyliovd2hy

Average complexity for linear operators over bounded domains

H Woźlniakowski
1987 Journal of Complexity  
Suppose one wants to compare worst case and average complexities for approximation of a linear operator.  ...  This and existing results enable us to compare the worst case and average complexities for balls of finite radius. We also analyze the average complexity for the normalized and relative errors.  ...  Wasilkowski and A. G. Werschulz.  ... 
doi:10.1016/0885-064x(87)90005-7 fatcat:o23vvmsi6vfptgndxl4zrcjsam

Toward Real-Time, Many-Task Applications on Large Distributed Systems [chapter]

Sangho Yi, Derrick Kondo, David P. Anderson
2010 Lecture Notes in Computer Science  
Using micro and macro-benchmarks executed in emulation experiments, we show that RT-BOINC provides significantly lower worst-case execution time, and lessens the gap between the average and the worst-case  ...  The system gives low O(1) worst-case execution time for task management operations, such as task scheduling, state transitioning, and validation.  ...  Acknowledgments This research was supported by supported the ALEAE project (INRIA ARC), and the ANR Clouds@home project (contract ANR-09-JCJC-0056-01).  ... 
doi:10.1007/978-3-642-15277-1_35 fatcat:bhv6s2o6jbcidcjgpbvy6hlgru

Average case complexity of linear multivariate problems II. Applications

H Wogniakowski
1992 Journal of Complexity  
In particular, we find the order of the average case complexity of multivariate function approximation in AStd.  ...  Complexity 8, in press) to linear multivariate problems LMP equipped with the folded Wiener sheet measure.  ...  For the folded Wiener sheet measure, Paskov (1991) utilized a relation between the average case and worst case settings and derived optimal sample points by using the worst case analysis of Bykovskij  ... 
doi:10.1016/0885-064x(92)90002-s fatcat:5ti43kh2sveljmm6pjobmrhism

Average case complexity of linear multivariate problems [article]

Henryk Woźniakowski
1993 arXiv   pre-print
We also address the optimal design problem for an by using a relation to the worst case setting.  ...  The first consists of function values and the second of all continuous linear functionals. Tractability of means that the average case complexity is O((1/)^p) with p independent of d.  ...  Optimal design for APP is analyzed by exhibiting a relation between average case and worst case errors of linear algorithms for APP.  ... 
arXiv:math/9307234v1 fatcat:a6q5ynilbnaathefgy7yen4orm

Average case complexity under the universal distribution equals worst-case complexity

Ming Li, Paul M.B. Vitányi
1992 Information Processing Letters  
Li, M. and P.M.B. Vitanyi, Average case complexity under the universal distribution equals worst-case complexity, Information Processing Letters 42 (1992) 145-149.  ...  The average complexity of any algorithm whatsoever under the universal distribution is of the same order of magnitude as the worst-case complexity.  ...  , Benny Chor, Gloria Kissin, John Tromp, and Vladimir Uspenskii commented on the manuscript. Mike O'Donnell raised the question we address here during a lecture given by the second author.  ... 
doi:10.1016/0020-0190(92)90138-l fatcat:y3nkfyl2yrahfir2wspetdgbey

Page 1187 of Mathematical Reviews Vol. , Issue 97B [page]

1997 Mathematical Reviews  
Both algorithms require extra space and were conjectured to be optimal in the worst and the average case, respectively.  ...  How- ever, there has been no algorithm for building heaps that is optimal in both the worst and average cases simultaneously.  ... 

Average-case quantum query complexity

Andris Ambainis, Ronald de Wolf
2001 Journal of Physics A: Mathematical and General  
We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial [3] .  ...  We also prove some general bounds for average-case complexity and show that the average-case quantum complexity of MAJORITY under the uniform distribution is nearly quadratically better than the classical  ...  Acknowledgments We thank Harry Buhrman for suggesting this topic, and him, Lance Fortnow, Lane Hemaspaandra, Hein Röhrig, Alain Tapp, and Umesh Vazirani for helpful discussions.  ... 
doi:10.1088/0305-4470/34/35/302 fatcat:wndxdkajcjdmhlkr4qb36fsgay

Average-Case Quantum Query Complexity [article]

Andris Ambainis and Ronald de Wolf (CWI and U of Amsterdam)
2001 arXiv   pre-print
We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial.  ...  We also prove some general bounds for average-case complexity and show that the average-case quantum complexity of MAJORITY under the uniform distribution is nearly quadratically better than the classical  ...  Acknowledgments We thank Harry Buhrman for suggesting this topic, and him, Lance Fortnow, Lane Hemaspaandra, Hein Röhrig, Alain Tapp, and Umesh Vazirani for helpful discussions.  ... 
arXiv:quant-ph/9904079v3 fatcat:ikeph27eljaj5hqwb4biy6v5uq

Average-Case Quantum Query Complexity [chapter]

Andris Ambainis, Ronald de Wolf
2000 Lecture Notes in Computer Science  
We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial.  ...  We also prove some general bounds for average-case complexity and show that the average-case quantum complexity of MAJORITY under the uniform distribution is nearly quadratically better than the classical  ...  Thus the polynomial relation that holds between quantum and classical query complexities in the case of worstcase complexity [3] does not carry over to the average-case setting. • Under non-uniformµ  ... 
doi:10.1007/3-540-46541-3_11 fatcat:hfpk6nr6bvbvnmnnipsyfw2ryi

Page 3594 of Mathematical Reviews Vol. , Issue 90F [page]

1990 Mathematical Reviews  
The other approach leads to a close relation between the asymptotic and average case settings.  ...  Complexity of linear problems is analyzed. The probabilistic complexity is compared with the average complexity and some relations are developed.  ... 
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