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Beyond Worst-Case Analysis [article]

Tim Roughgarden
2018 arXiv   pre-print
This article covers a number of modeling methods for going beyond worst-case analysis and articulating which inputs are the most relevant.  ...  In the worst-case analysis of algorithms, the overall performance of an algorithm is summarized by its worst performance on any input.  ...  Research in beyond worst-case analysis acknowledges this fact while retaining the emphasis on robust guarantees that is central to worst-case analysis.  ... 
arXiv:1806.09817v1 fatcat:s4idpks5ozghrflwqfkcjigeve

Beyond Worst-Case Analysis for Joins with Minesweeper [article]

Hung Q. Ngo and Dung T. Nguyen and Christopher Ré and Atri Rudra
2014 arXiv   pre-print
We describe a new algorithm, Minesweeper, that is able to satisfy stronger runtime guarantees than previous join algorithms (colloquially, 'beyond worst-case guarantees') for data in indexed search trees  ...  In addition, the certificate allows us to define a strictly stronger notion of runtime complexity than traditional worst-case guarantees.  ...  Roughgarden, Lecture notes for CS369N "beyond worst-case analysis". [47] , Problem set #1 (CS369N: Beyond worst-case analysis). http://theory.stanford.edu/ tim/f11/hw1.pdf, 2011. [48] W.  ... 
arXiv:1302.0914v5 fatcat:o64u6ewdezaqdhdllcsz3dbhve

Beyond Pigouvian Taxes: A Worst Case Analysis [article]

Moshe Babaioff, Ruty Mundel, Noam Nisan
2021 arXiv   pre-print
We show that no tax structure leads to bounded losses in the worst case.  ...  We observe that this social inefficiency may be unbounded, and study whether alternative tax structures may lead to milder losses in the worst case, i.e. to a lower price of anarchy.  ...  For the case in which there is more than one equilibrium point, we will look at the worst equilibrium pointx and the optimal equilibrium point x * .  ... 
arXiv:2107.12023v2 fatcat:ttqjsjottngtpfv2sm5hghac64

Bandits with Knapsacks beyond the Worst-Case [article]

Karthik Abinav Sankararaman, Aleksandrs Slivkins
2021 arXiv   pre-print
While worst-case regret bounds for BwK are well-understood, we present three results that go beyond the worst-case perspective.  ...  The optimal worst-case regret rate is well-understood. In particular, it is Õ( √ KT ) when B = Ω(T ). We present several results that go beyond the worst-case perspective: 1.  ...  No worst-case regret bounds are provided; their algorithm does not appear to achieve even o(T ) regret in the worst case.  ... 
arXiv:2002.00253v7 fatcat:modyv2tkpbbgpjrpuflfx62i3m

Smoothed Analysis: Analysis of Algorithms Beyond Worst Case

Bodo Manthey, Heiko Röglin
2011 it - Information Technology  
It is a hybrid of the classical worst-case analysis and average-case analysis, where the performance on inputs is measured that are subject to random noise.  ...  The reason for this discrepancy is that worst-case analysis is often a way too pessimistic measure for the performance of an algorithm.  ...  Thus, for smaller σ, smoothed analysis gets closer to worst-case analysis.  ... 
doi:10.1524/itit.2011.0654 fatcat:fkiqutsij5ao7idaz6t77qepdu

Beyond the Worst-Case Analysis of Algorithms (Introduction) [article]

Tim Roughgarden
2020 arXiv   pre-print
Worst-case analysis summarizes the performance profile of an algorithm by its worst performance on any input of a given size, implicitly advocating for the algorithm with the best-possible worst-case performance  ...  This chapter surveys several alternatives to worst-case analysis that are discussed in detail later in the book.  ...  The competitive analysis of online algorithms (Section 2.4) was pioneered by Sleator and Tarjan (1985) . Bélády's algorithm (Section 2.4) appears in Bélády (1967) .  ... 
arXiv:2007.13241v1 fatcat:r2wvbku4xnhudkxauco5ccstiy

Certified Algorithms: Worst-Case Analysis and Beyond

Konstantin Makarychev, Yury Makarychev, Michael Wagner
2020 Innovations in Theoretical Computer Science  
Certified algorithms provide worst-case and beyond-worst-case performance guarantees.  ...  Thus, we have both worst-case and beyond-worst-case guarantees for A. We believe that this property is very desirable in practice.  ...  We believe that certified algorithms will prove useful in developing new algorithms for solving worst-case and beyond-worst-case instances.  ... 
doi:10.4230/lipics.itcs.2020.49 dblp:conf/innovations/MakarychevM20 fatcat:ftbq4ex2orceznk7e7gxinrpva

Clustering under Local Stability: Bridging the Gap between Worst-Case and Beyond Worst-Case Analysis [article]

Maria-Florina Balcan, Colin White
2017 arXiv   pre-print
Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms.  ...  First, we provide algorithms that inherit the worst-case guarantees of clustering approximation algorithms, while simultaneously guaranteeing near-optimal solutions when the data is stable.  ...  Traditionally, the theory of clustering (and more generally, the theory of algorithms) has focused on the analysis of worst-case instances.  ... 
arXiv:1705.07157v1 fatcat:3vqzbbkx3vc2la6egthqj5dphi

Beyond Worst-case: A Probabilistic Analysis of Affine Policies in Dynamic Optimization [article]

Omar El Housni, Vineet Goyal
2019 arXiv   pre-print
In this paper, we aim to address this stark-contrast between the worst-case and the empirical performance of affine policies.  ...  The approximation bound depends on the distribution, but it is significantly better than the worst-case bound for a large class of distributions.  ...  beyond worst-case.  ... 
arXiv:1706.05737v3 fatcat:ocignbueqrd5dnfeuyywzlptvu

Beyond Worst-case Analysis of Multicore Caching Strategies [article]

Shahin Kamali, Helen Xu
2020 arXiv   pre-print
In particular, we take the first steps beyond worst-case analysis for analysis of multicore caching algorithms.  ...  In this paper, we introduce cyclic analysis, a generalization of bijective analysis introduced by Angelopoulos and Schweitzer [JACM'13].  ...  We take the first steps beyond worst-case analysis for multicore caching with the separation of LRU from all other lazy algorithms on inputs with locality via cyclic analysis.  ... 
arXiv:2011.02046v1 fatcat:seendyw5j5anfd7cgde4ogip54

Smoothed and Average-case Approximation Ratios of Mechanisms: Beyond the Worst-case Analysis [article]

Xiaotie Deng, Yansong Gao, Jie Zhang
2017 arXiv   pre-print
These results also pave the way for further studies of smoothed and average-case analysis for approximate mechanism design problems, beyond the worst-case analysis.  ...  of the worst-case inputs, and define the average-case approximation ratio to compare the performance of these two mechanisms when the inputs follow a distribution.  ...  Although average-case and smoothed analysis are usually more complex than the worst-case analysis, they provide different measures from the worst-case complexity.  ... 
arXiv:1705.07200v2 fatcat:jaxqim7zwnh5pnozwalwewl4rq

Beyond Worst-Case Analysis in Private Singular Vector Computation [article]

Moritz Hardt, Aaron Roth
2012 arXiv   pre-print
Our algorithm also leads to improvements in worst-case settings and to better low-rank approximations in the spectral norm.  ...  Known worst-case lower bounds show that the error of any differentially private algorithm must scale polynomially with the dimension of the singular vector.  ...  bounds Our robust power iteration analysis can also be applied easily to worst-case settings without any incoherence assumptions.  ... 
arXiv:1211.0975v1 fatcat:r6r2oia3tvavbdzjfay4cco2ka

Beyond Worst-Case Analysis for Root Isolation Algorithms

Alperen Ergür, Josué Tonelli-Cueto, Elias Tsigaridas
2022 Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation  
However, the worst-case analysis of root-finding algorithms does not correlate with their practical performance.  ...  We develop a smoothed analysis framework for polynomials with integer coefficients to bridge the gap between the complexity estimates and the practical performance.  ...  To the best of our knowledge, this large field almost entirely relies on the worst-case analysis.  ... 
doi:10.1145/3476446.3535475 fatcat:dsxkshe4bva5he3ym6dpswqtgu

Beyond worst-case analysis for joins with minesweeper

Hung Q. Ngo, Dung T. Nguyen, Christopher Re, Atri Rudra
2014 Proceedings of the 33rd ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '14  
We describe a new algorithm, Minesweeper, that is able to satisfy stronger runtime guarantees than previous join algorithms (colloquially, 'beyond worst-case guarantees') for data in indexed search trees  ...  In addition, the certificate allows us to define a strictly stronger notion of runtime complexity than traditional worst-case guarantees.  ...  We believe ours is the first beyond worst-case analysis of join queries.  ... 
doi:10.1145/2594538.2594547 dblp:conf/pods/NgoNRR14 fatcat:fvbsi4kd3jdhzbtfjodncmdtcq

Beyond Worst-Case Analysis for Root Isolation Algorithms [article]

Alperen A. Ergür, Josué Tonelli-Cueto, Elias Tsigaridas
2022 arXiv   pre-print
However, the worst-case analysis of root-finding algorithms does not correlate with their practical performance.  ...  We develop a smoothed analysis framework for polynomials with integer coefficients to bridge the gap between the complexity estimates and the practical performance.  ...  To the best of our knowledge, this large field almost entirely relies on the worst-case analysis.  ... 
arXiv:2202.06428v3 fatcat:gyx4edgzv5dijfvy43nliolhrq
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