A note on maximizing a submodular set function subject to a knapsack constraint

@article{Sviridenko2004ANO,
  title={A note on maximizing a submodular set function subject to a knapsack constraint},
  author={Maxim Sviridenko},
  journal={Oper. Res. Lett.},
  year={2004},
  volume={32},
  pages={41-43}
}
  • M. Sviridenko
  • Published 2004
  • Computer Science, Mathematics
  • Oper. Res. Lett.
On maximizing a monotone k-submodular function under a knapsack constraint
A Note on the Budgeted Maximization of Submodular Functions
Many set functionsF in combinatorial optimization satisfy the diminishing returns propertyF (A[fXg) F (A) F (A 0 [fXg) F (A 0 ) forA A
Constrained Submodular Maximization: Beyond 1/e
  • Alina Ene, Huy L. Nguyen
  • Computer Science, Mathematics
    2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
  • 2016
TLDR
This work finds an approximate fractional solution for maximizing the multilinear extension of the function over a down-closed polytope and it is the first improvement over the 1/e approximation achieved by the unified Continuous Greedy algorithm.
Submodular-function maximization subject to multiple constraints
TLDR
An improved local search algorithms are presented and it is shown that the algorithm is polynomial time approximate and has a relatively good time complexity.
Maximizing expected utility over a knapsack constraint
Chance-Constrained Submodular Knapsack Problem
TLDR
This study considers the chance-constrained submodular knapsack problem, where a set of items whose sizes are random variables that follow probability distributions are required to find a subset of items that maximizes the objective function subject to that the probability of total item size exceeding theknapsack capacity is at most a given threshold.
A Faster Tight Approximation for Submodular Maximization Subject to a Knapsack Constraint
TLDR
It is proved it suffices to enumerate only over all subsets of size at most two and still retain a tight (1 − e)-approximation, which improves the running time from O(n) to O( n) queries.
Maximize a Monotone Function with a Generic Submodularity Ratio
TLDR
This paper makes a systematic analysis of greedy algorithms for maximizing a monotone and normalized set function with a generic submodularity ratio under Cardinality constraints, Knapsack constraints, Matroid constraints and K-intersection constraints.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 12 REFERENCES
Approximate Algorithms for the 0/1 Knapsack Problem
A serms of increasingly accurate algorithms to obtain approximate solutions to the 0/1 one-dlmensmnal knapsack problem :s presented Each algorithm guarantees a certain minimal closeness to the
An analysis of approximations for maximizing submodular set functions—I
TLDR
It is shown that a “greedy” heuristic always produces a solution whose value is at least 1 −[(K − 1/K]K times the optimal value, which can be achieved for eachK and has a limiting value of (e − 1)/e, where e is the base of the natural logarithm.
The Budgeted Maximum Coverage Problem
Maximising Real-Valued Submodular Functions: Primal and Dual Heuristics for Location Problems
TLDR
A slightly more specialised model is examined that generalises the location problems of interest, but now also includes the continuous aspects of the problems missing from the earlier model, namely the problem: max{wy: Σj=1najyj ≤ b, 0 ≤ yj < 1} of maximising a real-valued nondecreasing submodular function subject to a knapsack constraint.
Constrained Maximum-Entropy Sampling
  • Jon Lee
  • Computer Science
    Oper. Res.
  • 1998
TLDR
Using techniques of linear algebra, combinatorial optimization, and convex optimization, upper and lower bounds on the optimal value for the Gaussian case are developed and integrated into a branch-and-bound algorithm for the exact solution of these design problems.
An Exact Algorithm for Maximum Entropy Sampling
TLDR
An upper bound for the entropy is established, based on the eigenvalue interlacing property, and incorporated in a branch-and-bound algorithm for the exact solution of the experimental design problem of selecting a most informative subset, having prespecified size, from a set of correlated random variables.
New upper bounds for maximum-entropy sampling, mODa 6— advances in model-oriented design and analysis (Puchberg/Schneeberg
  • Contrib. Statist
  • 2001
New upper bounds for maximum-entropy sampling, mODa 6—advances in model-oriented design and analysis
  • (Puchberg/Schneeberg,
  • 2001
The budgeted maximum coverage problem, Inform
  • Process. Lett
  • 1999
The budgeted maximum coverage problem, Information
  • Processing Letters
  • 1999
...
1
2
...