Corpus ID: 202151380

On Integer Programming, Discrepancy, and Convolution

@article{Jansen2018OnIP,
  title={On Integer Programming, Discrepancy, and Convolution},
  author={K. Jansen and Lars Rohwedder},
  journal={arXiv: Data Structures and Algorithms},
  year={2018}
}
Integer programs with a constant number of constraints are solvable in pseudo-polynomial time. We give a new algorithm with a better pseudo-polynomial running time than previous results. Moreover, we establish a strong connection to the problem (min, +)-convolution. (min, +)-convolution has a trivial quadratic time algorithm and it has been conjectured that this cannot be improved significantly. We show that further improvements to our pseudo-polynomial algorithm for any fixed number of… Expand
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References

SHOWING 1-10 OF 22 REFERENCES
On the Optimality of Pseudo-polynomial Algorithms for Integer Programming
  • 7
  • PDF
On Problems Equivalent to (min,+)-Convolution
  • 7
  • Highly Influential
  • PDF
Clustered Integer 3SUM via Additive Combinatorics
  • 99
  • PDF
Minkowski's Convex Body Theorem and Integer Programming
  • R. Kannan
  • Mathematics, Computer Science
  • Math. Oper. Res.
  • 1987
  • 659
A Near-Linear Pseudopolynomial Time Algorithm for Subset Sum
  • 48
  • PDF
On lower bounds for the Maximum Consecutive Subsums Problem and the (min,+)-convolution
  • 11
  • Highly Influential
  • PDF
Better Approximations for Tree Sparsity in Nearly-Linear Time
  • 26
  • PDF
Capacitated Dynamic Programming: Faster Knapsack and Graph Algorithms
  • 14
  • PDF
Constructive Discrepancy Minimization by Walking on the Edges
  • Shachar Lovett, Raghu Meka
  • Mathematics, Computer Science
  • 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
  • 2012
  • 73
  • PDF
On Integer Programming and Convolution
  • 27
  • PDF
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