Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
- G. Călinescu, C. Chekuri, Martin Pál, J. Vondrák
- PhysicsSIAM journal on computing (Print)
- 1 November 2011
An improved coating pan apparatus and spray arm assembly are disclosed for providing facilitated maintenance and cleaning of sensitive spray nozzles. The spray arm assembly includes means for varying…
Maximizing Non-Monotone Submodular Functions
- U. Feige, V. Mirrokni, J. Vondrák
- MathematicsIEEE Annual Symposium on Foundations of Computer…
- 21 October 2007
Submodular maximization generalizes many important problems including Max Cut in directed/undirected graphs and hypergraphs, certain constraint satisfaction problems and maximum facility location…
Optimal approximation for the submodular welfare problem in the value oracle model
- J. Vondrák
- MathematicsSymposium on the Theory of Computing
- 17 May 2008
A randomized continuous greedy algorithm is developed which achieves a (1-1/e)-approximation for the Submodular Welfare Problem in the value oracle model and is shown to have a potential of wider applicability on the examples of the Generalized Assignment Problem and the AdWords Assignment Problem.
Fast algorithms for maximizing submodular functions
- Ashwinkumar Badanidiyuru, J. Vondrák
- Computer ScienceACM-SIAM Symposium on Discrete Algorithms
- 5 January 2014
A new variant of the continuous greedy algorithm, which interpolates between the classical greedy algorithm and a truly continuous algorithm, is developed, which can be implemented for matroid and knapsack constraints using O(n2) oracle calls to the objective function.
Lazier Than Lazy Greedy
- Baharan Mirzasoleiman, Ashwinkumar Badanidiyuru, Amin Karbasi, J. Vondrák, Andreas Krause
- Computer ScienceAAAI Conference on Artificial Intelligence
- 28 September 2014
The first linear-time algorithm for maximizing a general monotone submodular function subject to a cardinality constraint is developed, and it is shown that the randomized algorithm, STOCHASTIC-GREEDY, can achieve a (1 − 1/e − ε) approximation guarantee, in expectation, to the optimum solution in time linear in the size of the data.
Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)
- G. Călinescu, C. Chekuri, Martin Pál, J. Vondrák
- Mathematics, Computer ScienceConference on Integer Programming and…
- 25 June 2007
The generalized assignment problem (GAP) is a special case of the problem, and although the reduction requires |N| to be exponential in the original problem size, it is able to interpret the recent (1 i¾? 1/e)-approximation for GAP by Fleischer et al.[10] in the framework.
Submodular maximization by simulated annealing
- S. Gharan, J. Vondrák
- Computer Science, MathematicsACM-SIAM Symposium on Discrete Algorithms
- 9 July 2010
A new algorithm for submodular maximization which is based on the idea of simulated annealing is proposed and it is proved that this algorithm achieves improved approximation for two problems: a 0.41-approximation for unconstrained submodul maximization, and a0.325-app approximation subject to a matroid independence constraint.
Dependent Randomized Rounding via Exchange Properties of Combinatorial Structures
- C. Chekuri, J. Vondrák, R. Zenklusen
- MathematicsIEEE Annual Symposium on Foundations of Computer…
- 23 October 2010
A new {\em swap rounding} technique which can be applied in a variety of settings including matroids and matroid intersection, while providing Chernoff-type concentration bounds for linear and sub modular functions of the rounded solution is described.
Approximating the stochastic knapsack problem: the benefit of adaptivity
- B. C. Dean, M. Goemans, J. Vondrák
- Computer Science45th Annual IEEE Symposium on Foundations of…
- 17 October 2004
We consider a stochastic variant of the NP-hard 0/1 knapsack problem in which item values are deterministic and item sizes are independent random variables with known, arbitrary distributions. Items…
Optimal approximation for submodular and supermodular optimization with bounded curvature
- M. Sviridenko, J. Vondrák, Justin Ward
- Mathematics, Computer ScienceACM-SIAM Symposium on Discrete Algorithms
- 19 November 2013
It is proved that the approximation results obtained are the best possible in the value oracle model, even in the case of a cardinality constraint.
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