Suchergebnisse
Suchergebnisse:
Winter 2021: Math 113: Linear Algebra. Fall 2020: Math 61DM: Modern Mathematics: Linear Algebra and Discrete Mathematics. Fall 2019: Math 61DM: Modern Mathematics: Linear Algebra and Discrete Mathematics. Spring 2019: Math 120: Groups and Rings. Fall 2018: Math 113: Linear algebra done right (book by Sheldon Axler).
- 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)...
- My Papers
- 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
(T ) = je(T ; T )j So, is submodularity more like concavity or convexity?
Maximizing a submodular function (e.g. Max Cut) is NP-hard.
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
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...
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...
- 588KB
- 65
Jan Vondrák1 1IBM Almaden Research Center San Jose, CA ACM-SIAM SODA, New Orleans, LA January 7, 2013 Jan Vondrák (IBM Almaden) Submodular Functions and Applications 1 / 29. Prelude: what is this about? There are two kinds of mathematicians: The Problem ...
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.
23. Mai 2011 · Chandra Chekuri, Jan Vondrák, Rico Zenklusen. We consider the problem of maximizing a non-negative submodular set function f:2N →R+ over a ground set N subject to a variety of packing type constraints including (multiple) matroid constraints, knapsack constraints, and their intersections. In this paper we develop a general ...
- Chandra Chekuri, Jan Vondrák, Rico Zenklusen, Rico Zenklusen
- 2011
Department of Mathematics Building 380, Stanford, California 94305 Phone: (650) 725-6284 mathfrontdesk [at] stanford.edu (E-mail)
Wenzheng Li, Paul Liu, Jan Vondrák: A polynomial lower bound on adaptive complexity of submodular maximization. CoRR abs/2002.09130 ( 2020) 2010 – 2019. 2019. [c50] Vitaly Feldman, Jan Vondrák: High probability generalization bounds for uniformly stable algorithms with nearly optimal rate.
