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Worst-Case Running Times for Average-Case Algorithms

Luís Antunes, Lance Fortnow
2009 2009 24th Annual IEEE Conference on Computational Complexity  
Under a standard hardness assumption we exactly characterize the worst-case running time of languages that are in average polynomial-time over all polynomial-time samplable distributions.  ...  More precisely we show that if exponential time is not in subexponential space, then the following are equivalent for any algorithm A: • For all P-samplable distributions µ, A runs in time polynomial on  ...  Acknowledgments We thank Eric Allender, Dieter van Melkebeek, Peter Bro Miltersen and Paul Vitányi for helpful discussions and comments.  ... 
doi:10.1109/ccc.2009.12 dblp:conf/coco/AntunesF09 fatcat:6uoktuxp5jhd5cdyzxykje46oq

Performance Analysis of Heap Sort and Insertion Sort Algorithm

2021 International Journal of Emerging Trends in Engineering Research  
Then identifiesthe efficiency of these algorithms according to this data three cases used that is Best, Average and Worst Case.  ...  For theresults of this research study,the comparison ofthese two sorting algorithms with different type of the data at running time such as Large, Average, and Small.  ...  Heap sort takes less time than insertion sort in average and large data for both in average and worst case and it has smaller difference in running time for large data set so heap sort is best for large  ... 
doi:10.30534/ijeter/2021/08952021 fatcat:pkzlrm6g7vchda4qat6ydasdla

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

Ming Li, Paul M.B. Vitányi
1992 Information Processing Letters  
This holds both for time complexity and for space complexity.  ...  The average complexity of any algorithm whatsoever under the universal distribution is of the same order of magnitude as the worst-case complexity.  ...  fast sorting algorithms of which the provable average run-time is of equal order of magnitude as the worst-case run-time, even though this average running time can only be proved to be O(n log 2 n) under  ... 
doi:10.1016/0020-0190(92)90138-l fatcat:y3nkfyl2yrahfir2wspetdgbey

Performance Visualization of Gnome Sort in Worst Case Implemented Using R in Three Personal Computers

2017 International Journal of Current Research and Review  
The performances (data size versus average run time in seconds) of Gnome sort algorithm in the worst case in all the three personal computers are visualized using scatter plots and quadratic curves.  ...  worst case follows quadratic nature or not.  ...  The performances (data size versus average run time in seconds) of Gnome sort in the worst case implemented using R in all the three (3) cases are shown using a single scatter plot in the following figure  ... 
doi:10.7324/ijcrr.2017.91113 fatcat:kgisaofizrc7pk2qjngnmtup4m

Efficient Algorithms for Pattern Matching with General Gaps and Character Classes [chapter]

Kimmo Fredriksson, Szymon Grabowski
2006 Lecture Notes in Computer Science  
We give algorithms that have efficient average and worst case running times. The algorithms have important applications in music information retrieval and computational biology.  ...  We develop efficient dynamic programming algorithms for a pattern matching with general gaps and character classes.  ...  Acknowledgments We thank anonymous referees for many helpful suggestions.  ... 
doi:10.1007/11880561_22 fatcat:bhuenlovkfc23phumc63b3sjjm

Worst-Case Efficient Sorting with QuickMergesort [article]

Stefan Edelkamp, Armin Weiß
2018 arXiv   pre-print
While Quicksort is very fast on average, Mergesort additionally gives worst-case guarantees, but needs extra space for a linear number of elements.  ...  poor guarantee for the worst case.  ...  Figure 8 : 8 Running times of MoMQuickMergesort(average and simulated worst case), hybrid QMS and other algorithms for random permutations of 32-bit integers. Running times are divided by n log n.  ... 
arXiv:1811.00833v1 fatcat:bz5wjb46jza4zbjnqavhud5rme

Smoothed Analysis: Analysis of Algorithms Beyond Worst Case

Bodo Manthey, Heiko Röglin
2011 it - Information Technology  
The reason for this discrepancy is that worst-case analysis is often a way too pessimistic measure for the performance of an algorithm.  ...  Many algorithms perform very well in practice, but have a poor worst-case performance.  ...  worst-case running time.  ... 
doi:10.1524/itit.2011.0654 fatcat:fkiqutsij5ao7idaz6t77qepdu

Smoothed Analysis of Local Search Algorithms [chapter]

Bodo Manthey
2015 Lecture Notes in Computer Science  
Smoothed analysis is a method for analyzing the performance of algorithms for which classical worst-case analysis fails to explain the performance observed in practice.  ...  One particular class of algorithms where smoothed analysis has been used successfully are local search algorithms.  ...  Thus, a good average-case running-time does not necessarily explain a good practical performance.  ... 
doi:10.1007/978-3-319-21840-3_43 fatcat:acnc5xb2ybheldethxmykewzoy

Identifying algorithmic vulnerabilities through simulated annealing

S. Andrew Johnson, Dinesh P. Mehta, Ramakrishna Thurimella
2011 Optimization Letters  
In this paper, we present a method for finding inputs that perform much worse than the average input to different algorithms.  ...  Unfortunately, it is algorithmically intractable, if not unsolvable, to find the inputs which would cause worst case behavior.  ...  Our initial experiments with other structures that have mismatched average and worst-case performances (e.g., unbalanced binary trees) indicate that this approach is not limited to sorting.  ... 
doi:10.1007/s11590-011-0333-z fatcat:c55k3m77rvg2bp446y464ye2du

Worst-Case to Average-Case Reductions Revisited [chapter]

Dan Gutfreund, Amnon Ta-Shma
2007 Lecture Notes in Computer Science  
the average-case complexity of the language, is only samplable in super-polynomial time.  ...  After extending the negative results to the non-standard average-case setting of [GSTS05], we ask whether their positive result can be extended to the standard setting, to prove some new worst-case/average-case  ...  Charlie Rackoff for suggesting the relevance of the argument that the polynomial-time hierarchy collapses under P = NP, Alex Healy for commenting on the manuscript, and Oded Goldreich for a helpful conversation  ... 
doi:10.1007/978-3-540-74208-1_41 fatcat:xivhqx3mmbddbju5vd3ypdbmue

Bidirectional PageRank Estimation: From Average-Case to Worst-Case [article]

Peter Lofgren, Siddhartha Banerjee, Ashish Goel
2015 arXiv   pre-print
We present a new algorithm for estimating the Personalized PageRank (PPR) between a source and target node on undirected graphs, with sublinear running-time guarantees over the worst-case choice of source  ...  Our work builds on a recent line of work on bidirectional estimators for PPR, which obtained sublinear running-time guarantees but in an average-case sense, for a uniformly random choice of target node  ...  a worst-case running-time of: O   log 1 p fail d t δ   .  ... 
arXiv:1507.08705v3 fatcat:nmmgedcfo5g2xdmmoqfbwry5jy

Empirical Analysis of Bubble Sort on Two Personal Computers using Performance Visualization and Mann Whitney U Test

Dipankar Das
2018 International Journal for Research in Applied Science and Engineering Technology  
The study presents a statistical analysis and visualizations of the Bubble sort algorithm in the worst case implemented using R on two different PCs.  ...  The scatter plots of the worst case performances of Bubble sort for both the computers under study reveal approximate smooth patterns with few jitters (in both the cases).  ...  Data Collection 1) Ten (10) number of observations i.e. the worst case run times in seconds of the Bubble sort for each data size for each of the computers had been noted 2) The average run times for each  ... 
doi:10.22214/ijraset.2018.3223 fatcat:zfthmvetdjagpbcqfilsxfjxyq

Average-Case Complexity [article]

Andrej Bogdanov, Luca Trevisan
2021 arXiv   pre-print
While the relation between worst-case and average-case complexity for general NP problems remains open, there has been progress in understanding the relation between different "degrees" of average-case  ...  We survey the average-case complexity of problems in NP. We discuss various notions of good-on-average algorithms, and present completeness results due to Impagliazzo and Levin.  ...  Acknowledgements We thanks Scott Aaronson, Jonathan Katz, Chris Moore and the anonymous referee for their helpful comments.  ... 
arXiv:cs/0606037v3 fatcat:ishwc6ck2vhztpfb5z3bjywehi

Hardness Amplification of Optimization Problems

Elazar Goldenberg, Karthik C. S., Michael Wagner
2020 Innovations in Theoretical Computer Science  
such that every randomized algorithm running in time poly(α(n)) fails to solve Π on 99 /100 fraction of inputs sampled from D .  ...  running in time t(n) fails to solve Π on 1 α(n) fraction of inputs sampled from D, then, assuming some relationships on α(n) and t(n), there is a distribution D over instances of Π of size O(n · α(n))  ...  In fact, can we prove a worst case to an average case hardness amplification based on ETH? Our next theorem is a step towards proving such a worst-case to an average case reduction for MaxSAT.  ... 
doi:10.4230/lipics.itcs.2020.1 dblp:conf/innovations/GoldenbergS20 fatcat:nqnlm74n65f7tm22q4hetqiiv4

Bidirectional PageRank Estimation: From Average-Case to Worst-Case [chapter]

Peter Lofgren, Siddhartha Banerjee, Ashish Goel
2015 Lecture Notes in Computer Science  
We present a new algorithm for estimating the Personalized PageRank (PPR) between a source and target node on undirected graphs, with sublinear running-time guarantees over the worst-case choice of source  ...  Our work builds on a recent line of work on bidirectional estimators for PPR, which obtained sublinear running-time guarantees but in an average case sense, for a uniformly random choice of target node  ...  a worst-case running-time of: O 1 d t δ .  ... 
doi:10.1007/978-3-319-26784-5_13 fatcat:x6w5ulrf3jhflezgskyg4oqlbu
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