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  1. theory.stanford.edu › ~jvondrakJan Vondrak's homepage - Stanford University

    Jan Vondrak Professor of Mathematics Dept. of Mathematics Stanford University 450 Jane Lanthrop Way, building 380 Stanford, CA 94305 E-mail: jvondrak-at-stanford-dot-edu.

    • My Papers

      Shahar Dobzinski, Jan Vondrak: Impossibility results for...

    • CS369P

      Course description: This is a graduate-level course in...

    • Some Presentations

      Some presentations Lectures/tutorials Submodular functions...

    • Math 113

      Tuesday 3-5 pm, 383-J (Jan) Friday 2-4 pm, 380-T (Joj)...

  2. theory.stanford.edu › ~jvondrak › dataOptimization of Submodular Functions Tutorial - lecture I

    • Discrete analogy?
    • Cut function:
    • In contrast:
    • Why is it possible to minimize submodular functions?
    • Maximization of submodular functions:
    • Questions that don’t seem to be answered by combinatorial algorithms:

    Not so obvious... f is now a set function, or equivalently

    Komplette Liste auf theory.stanford.edu

    (T ) = je(T ; T )j So, is submodularity more like concavity or convexity?

    Komplette Liste auf theory.stanford.edu

    Maximizing a submodular function (e.g. Max Cut) is NP-hard.

    Komplette Liste auf theory.stanford.edu

    The combinatorial algorithms are sophisticated... But there is a simple explanation: the Lovász extension. Why is it possible to minimize submodular functions? The combinatorial algorithms are sophisticated... But there is a simple explanation: the Lovász extension. Submodular function

    Komplette Liste auf theory.stanford.edu

    comes up naturally in allocation / welfare maximization settings (S) = value of a set of items S ... often submodular due to combinatorial structure or property of diminishing returns in these settings, f (S) is often assumed to be monotone: T =) f (S) f (T ): Maximization of submodular functions: comes up naturally in allocation / welfare maximiza...

    Komplette Liste auf theory.stanford.edu

    What is the optimal approximation for maxff (S) : S 2 Ig, in particular the Submodular Welfare Problem? What is the optimal approximation for multiple constraints, e.g. multiple knapsack constraints? In general, how can we combine different types of constraints? Questions that don’t seem to be answered by combinatorial algorithms: What is the optim...

    Komplette Liste auf theory.stanford.edu

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  3. theory.stanford.edu › ~jvondrak › dataSubmodular Functions and Their Applications - Stanford University

    Jan Vondrák1 1IBM Almaden Research Center San Jose, CA SIAM Discrete Math conference, Minneapolis, MN June 2014 Jan Vondrák (IBM Almaden) Submodular Functions and Applications 1 / 28 . Discrete optimization What is a discrete optimization problem? Find ...

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  4. mathematics.stanford.edu › people › jan-vondrakJan Vondrák | Mathematics - Stanford University

    Department of Mathematics Building 380, Stanford, California 94305 Phone: (650) 725-6284 mathfrontdesk [at] stanford.edu (E-mail)

  5. live-simons-institute.pantheon.berkeley.edu › sites › defaultJunta Approximations for Submodular, XOS and Self-Bounding...

    Jan Vondrák. IBM Almaden Research Center. Simons Institute, Berkeley, October 2013. Junta approximations. How can we simplify a function f : f0; 1gn ! R? In this talk: How well can we approximate f by a function g of few variables? Def.: g approximates f within. in Lp, if. kf. gkp = (E[jf (x) g(x)jp])1=p. (in this talk, the uniform distribution)

  6. Bilder

    • Jan Vondrak - Submodular Functions and Their Applications - YouTube
    • Jan Vondrak
    • JAN VONDRÁK | IBM, Armonk | Computer Science, Almaden
    • archiweb.cz - Jan Vondrák
    • Jan Vondrák

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  7. en.wikipedia.org › wiki › Jan_VondrákJan Vondrák - Wikipedia

    Jan Vondrák is a Czech applied mathematician and theoretical computer scientist. He has been a professor of mathematics at Stanford University since 2015. He was a research staff member in the theory group at the IBM Almaden Research Center from 2009 to 2015.

  8. epubs.siam.org › doi › 10Fast algorithms for maximizing submodular functions

    Authors: Ashwinkumar Badanidiyuru and Jan Vondrák Authors Info & Affiliations. Pages 1497 - 1514. https://doi.org/10.1137/1.9781611973402.110. PDF. BibTeX. Tools. Abstract. There has been much progress recently on improved approximations for problems involving submodular objective functions, and many interesting techniques have been developed.