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Smoothed Analysis of Three Combinatorial Problems [chapter]

Cyril Banderier, René Beier, Kurt Mehlhorn
2003 Lecture Notes in Computer Science  
We apply the concept to combinatorial problems and study the smoothed complexity of three classical discrete problems: quicksort, left-to-right maxima counting, and shortest paths.  ...  The smoothed complexity of a problem is the worst smoothed complexity of any instance. Spielman and Teng introduced this notion for continuous problems.  ...  For an edge e, let r(e) be the number of leading zeroes in the random part of e. Conclusion We analyzed the smoothed complexity of three combinatorial problems.  ... 
doi:10.1007/978-3-540-45138-9_14 fatcat:gzreskkdwfhs3g5l3p7vkyq2a4

Editorial

Marshall Bern
2001 Computational geometry  
Most previous algorithms for this problem depend upon the smoothness of the original curve; this paper tackles the more general problem of curves with corners and gives impressive experimental results.  ...  The final three papers extend the study of combinatorial curves beyond surface reconstruction.  ...  and analysis of planar shape deformation", Siu-Wing Cheng, Herbert Edelsbrunner, Ping Fu and Ka-Po Lam apply the ideas of the previous paper to the case of two dimensions and describe various ways to choose  ... 
doi:10.1016/s0925-7721(01)00014-1 fatcat:3edvxqhvmnfs3gpvgkevlj7itu

Optimization of a Monitoring Network for Sulfur Dioxide

E. P. J. Boer, A. L. M. Dekkers, A. Stein
2002 Journal of Environmental Quality  
We show that it leads to a flexible criterion for a combinatorial search algorithm is applied to find a (sub)optimal adaptation of an existing monitoring network. This flexisolution.  ...  This flexible method allows the characterization of trends by using simple local models.  ...  ACKNOWLEDGMENTS tory (LLO) of the RIVM for providing the data. They also  ... 
doi:10.2134/jeq2002.1210 pmid:11841060 fatcat:5pf3fmz7dfgapju2ykxqsvd7ea

Page 276 of American Mathematical Society. Transactions of the American Mathematical Society Vol. 30, Issue 2 [page]

1928 American Mathematical Society. Transactions of the American Mathematical Society  
There will, however, never be any real difficulty about translating any statement that we make into the less expressive language of pure, combinatorial analysis situs.  ...  combinatorial point of view.  ... 

The Piecewise Smooth Mumford–Shah Functional on an Arbitrary Graph

L. Grady, C.V. Alvino
2009 IEEE Transactions on Image Processing  
The Mumford-Shah functional has had a major impact on a variety of image analysis problems including image segmentation and filtering and, despite being introduced over two decades ago, it is still in  ...  In order to reduce these problems, we reformulate the corresponding Mumford-Shah functional on an arbitrary graph and apply the techniques of combinatorial optimization to produce a fast, lowenergy solution  ...  After this definition, we consider each of the three terms and formulate the combinatorial analogue of the piecewise smooth Mumford-Shah functional.  ... 
doi:10.1109/tip.2009.2028258 pmid:19635698 fatcat:inyuw77aj5arbntnya2rtoimfe

A Framework for Evaluating the Smoothness of Data-Mining Results [chapter]

Gaurav Misra, Behzad Golshan, Evimaria Terzi
2012 Lecture Notes in Computer Science  
The data-mining literature is rich in problems that are formalized as combinatorial-optimization problems.  ...  Existing combinatorial algorithms for solving such entity-selection problems identify a set of entities (e.g., reviews or nodes) as important.  ...  We formally, define the smoothness of a combinatorial optimization-problem X, L , F using the following formula: Smoothness(X) = X ∈X Pr(X )Sim(S * X , S * X ) The formula consists of three main parts:  ... 
doi:10.1007/978-3-642-33486-3_42 fatcat:dids73fqufaqhdiqqfbak2qily

Hospital daily outpatient visits forecasting using a combinatorial model based on ARIMA and SES models

Li Luo, Le Luo, Xinli Zhang, Xiaoli He
2017 BMC Health Services Research  
Methods: We formulate a seasonal ARIMA (SARIMA) model on a daily time series and then a single exponential smoothing (SES) model on the day of the week time series, and finally establish a combinatorial  ...  Furthermore, the combinatorial model can capture the comprehensive features of the time series data better.  ...  Availability of data and materials The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.  ... 
doi:10.1186/s12913-017-2407-9 pmid:28693579 pmcid:PMC5504658 fatcat:2spbjhyvhvbbblotduxoi6uwve

Smoothed Online Combinatorial Optimization Using Imperfect Predictions [article]

Kai Wang, Zhao Song, Georgios Theocharous, Sridhar Mahadevan
2022 arXiv   pre-print
We study smoothed online combinatorial optimization problems when an imperfect predictive model is available, where the model can forecast the future cost functions with uncertainty.  ...  Smoothed online combinatorial optimization considers a learner who repeatedly chooses a combinatorial decision to minimize an unknown changing cost function with a penalty on switching decisions in consecutive  ...  Lastly, given predictions and dynamic planning windows, the smoothed online combinatorial optimization problem reduces to an offline combinatorial problem.  ... 
arXiv:2204.10979v1 fatcat:gknwdwylozebtfrrmv65kz6csq

Reformulating and Optimizing the Mumford-Shah Functional on a Graph — A Faster, Lower Energy Solution [chapter]

Leo Grady, Christopher Alvino
2008 Lecture Notes in Computer Science  
In order to reduce these problems, we reformulate the corresponding MSF on an arbitrary graph and apply combinatorial optimization to produce a fast, low-energy solution.  ...  Finally, by avoiding evolution of the contour via gradient descent, we demonstrate that our optimization of the MSF is capable of evolving the contour with non-local movement.  ...  An added benefit of reformulating an energy in a combinatorial setting is that such a generic formulation may be applied without modification to higher dimensional data or general data analysis problems  ... 
doi:10.1007/978-3-540-88682-2_20 fatcat:ot5vpcnfh5azndywbldfrnolwq

A combinatorial Yamabe problem on two and three dimensional manifolds [article]

Huabin Ge, Xu Xu
2016 arXiv   pre-print
In this paper, we introduce a new combinatorial curvature on two and three dimensional triangulated manifolds, which transforms in the same way as that of the smooth scalar curvature under scaling of the  ...  Then we use the flow method to study the corresponding constant curvature problem, which is called combinatorial Yamabe problem.  ...  Acknowledgements The first author would like to show his greatest respect to Professor Gang Tian who brought him to the area of combinatorial curvature flows.  ... 
arXiv:1504.05814v2 fatcat:rv3ry6x4pfhtpemevf2snddjoe

Forthcoming Papers

2001 Artificial Intelligence  
Recursive conditioning is therefore the first algorithm for exact inference in Bayesian networks to offer a smooth tradeoff between time and space, and to explicate a smooth, quantitative relationship  ...  On one extreme, recursive conditioning takes O(n) space and O(n exp(w log n)) timewhere n is the size of a Bayesian network and w is the width of a given elimination order-therefore, establishing a new  ...  We present a formal model for this class of problems and provide a theoretical analysis of the class of optimal schedules.  ... 
doi:10.1016/s0004-3702(00)00086-2 fatcat:ydglr4s7x5f23fh2vmgoph2mb4

Smooth curve extraction by mean field annealing

Laurent H�rault, Radu Horaud
1995 Annals of Mathematics and Artificial Intelligence  
First, we suggest a mathematical model encoding the figureground discrimination problem that makes explicit a definition of shape (or figure) based on cocircularity, smoothness, proximity, and contrast  ...  Moreover, this cost function fits the constraints of a interacting spin system which in turn is a well suited physical model to solve hard combinatorial optimization problems.  ...  In practice, we implemented three combinatorial optimization methods: simulated annealing (SA), mean field annealing (MFA), and microcanonical annealing (MCA) [8] .  ... 
doi:10.1007/bf01530832 fatcat:emf6htp6aff5pmcknopbmf6oiy

Instantons and the topology of 4-manifolds

Ronald J. Stern
1983 The Mathematical intelligencer  
using modern analysis and geometry.  ...  Poincar~ promoted another type of structure on a manifold, where the above transition functions cI)~ o ~1 , instead of being smooth are required to preserve the natural combinatorial structure of R n (  ...  Poincar~ promoted another type of structure on a manifold, where the above transition functions cI)~ o ~1 , instead of being smooth are required to preserve the natural combinatorial structure of R n (  ... 
doi:10.1007/bf03026571 fatcat:5jejz624hbbflcgnwbc2rwco2q

(Locally) Differentially Private Combinatorial Semi-Bandits [article]

Xiaoyu Chen, Kai Zheng, Zixin Zhou, Yunchang Yang, Wei Chen, Liwei Wang
2020 arXiv   pre-print
In this paper, we study Combinatorial Semi-Bandits (CSB) that is an extension of classic Multi-Armed Bandits (MAB) under Differential Privacy (DP) and stronger Local Differential Privacy (LDP) setting.  ...  For B_1-bounded smooth CSB under ε-DP, we also prove the optimal regret bound is Θ̃(mKB^2_1ln T/Δϵ) with both upper bound and lower bound, where K is the maximum number of feedback in each round.  ...  of Artificial Intelligence (Locally) DP Combinatorial Semi-Bandits  ... 
arXiv:2006.00706v2 fatcat:g6efvtbujrf7bfst5wrqrlaswa

Figure-ground discrimination: a combinatorial optimization approach

L. Herault, R. Horaud
1993 IEEE Transactions on Pattern Analysis and Machine Intelligence  
ination problem from a combinatorial optimization perspective.  ...  Therefore, the shape/noise discrimination problem becomes a combinatorial optimization problem, namely, the problem of finding the global minimum for the cost function just described.  ... 
doi:10.1109/34.232076 fatcat:teulrh2br5e5lgryofhg64tdqm
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