On reduction integer programs to knapsack problem
Optimization and Control
2008-06-25 v1
Authors:
S. I. Veselov
Abstract
Let A be an integral nonnegative m×n matrix, b be an integral nonnegative vector. It is suggested new method for reduction of integer program max{cx∣Ax=b,x≥0,x∈Zn} to knapsack problem max{c′x∣fAx=fb,x≥0,x∈Zn}.
Cite
@article{arxiv.0806.3853,
title = {On reduction integer programs to knapsack problem},
author = {S. I. Veselov},
journal= {arXiv preprint arXiv:0806.3853},
year = {2008}
}
Related papers
View all related →
Optimization and Control · Mathematics
LLL-reduction for Integer Knapsacks
Iskander Aliev, Martin Henk
2011-08-01
Data Structures and Algorithms · Computer Science
Approximability of Sparse Integer Programs
David Pritchard, Deeparnab Chakrabarty
2010-02-09
Data Structures and Algorithms · Computer Science
Approximation Schemes for Binary Quadratic Programming Problems with Low cp-Rank Decompositions
Khaled Elbassioni, Trung Thanh Nguyen
2014-11-20
Data Structures and Algorithms · Computer Science
Approximation Algorithms for Generalized Multidimensional Knapsack
Arindam Khan, Eklavya Sharma, K. V. N. Sreenivas
2021-02-12
Optimization and Control · Mathematics
The Support of Integer Optimal Solutions
Iskander Aliev, Jesus De Loera, Fritz Eisenbrand, Timm Oertel +1
2017-12-27
Optimization and Control · Mathematics
A multi-criteria approach to approximate solution of multiple-choice knapsack problem
Ewa M. Bednarczuk, Janusz Miroforidis, Przemysław Pyzel
2017-12-20
Optimization and Control · Mathematics
Integrality Gaps of Integer Knapsack Problems
Iskander Aliev, Martin Henk, Timm Oertel
2016-11-14
Optimization and Control · Mathematics
On Feasibility of Integer Knapsacks
Iskander Aliev, Martin Henk
2009-11-24
Optimization and Control · Mathematics
Convex Algorithms for Nonnegative Matrix Factorization
Vijay Krishnamurthy, Alexandre d'Aspremont
2012-07-03
Data Structures and Algorithms · Computer Science
Covering and packing mixed-integer linear programs with a fixed number of constraints: Approximation and convex hull
Kobe Grobben, Phablo F. S. Moura, Hande Yaman
2026-02-12
Optimization and Control · Mathematics
Congruency-Constrained TU Problems Beyond the Bimodular Case
Martin Nägele, Richard Santiago, Rico Zenklusen
2023-04-26
Discrete Mathematics · Computer Science
Proximity results and faster algorithms for Integer Programming using the Steinitz Lemma
Friedrich Eisenbrand, Robert Weismantel
2019-06-10
Data Structures and Algorithms · Computer Science
Parameterized Integer Quadratic Programming: Variables and Coefficients
Daniel Lokshtanov
2017-04-11
Optimization and Control · Mathematics
Novel bi-objective optimization algorithms minimizing the max and sum of vectors of functions
Hamidreza Khaleghzadeh, Ravi Reddy Manumachu, Alexey Lastovetsky
2022-09-07
Optimization and Control · Mathematics
Knapsack with compactness: a semidefinite approach
Hubert Villuendas, Mathieu Besançon, Jérôme Malick
2025-04-28
Optimization and Control · Mathematics
A Note on Non-Degenerate Integer Programs with Small Sub-Determinants
Stephan Artmann, Friedrich Eisenbrand, Christoph Glanzer, Timm Oertel +2
2016-04-01
Data Structures and Algorithms · Computer Science
Approximation Algorithms for the Incremental Knapsack Problem via Disjunctive Programming
Daniel Bienstock, Jay Sethuraman, Chun Ye
2013-11-20
Optimization and Control · Mathematics
Parametric Integer Programming in Fixed Dimension
Friedrich Eisenbrand, Gennady Shmonin
2008-01-29
Cryptography and Security · Computer Science
Worst--Case to Average--Case Reductions for SIS over integers
Konstantinos A. Draziotis, Myrto Eleftheria Gkogkou
2026-03-10
Data Structures and Algorithms · Computer Science
An Almost Optimal Approximation Algorithm for Monotone Submodular Multiple Knapsack
Yaron Fairstein, Ariel Kulik, Joseph, Naor +2
2021-04-19
Artificial Intelligence · Computer Science
An Integer Programming Model for Binary Knapsack Problem with Value-Related Dependencies among Elements
Davoud Mougouei, David M. W. Powers, Asghar Moeini
2017-02-23
Data Structures and Algorithms · Computer Science
Packing While Traveling: Mixed Integer Programming for a Class of Nonlinear Knapsack Problems
Sergey Polyakovskiy, Frank Neumann
2015-04-16
Optimization and Control · Mathematics
A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems
Ankur Sinha, Arka Das, Guneshwar Anand, Sachin Jayaswal
2022-08-31
Data Structures and Algorithms · Computer Science
Improved Analysis of two Algorithms for Min-Weighted Sum Bin Packing
Guillaume Sagnol
2023-04-06
Optimization and Control · Mathematics
Mirror-Descent Methods in Mixed-Integer Convex Optimization
Michel Baes, Timm Oertel, Christian Wagner, Robert Weismantel
2012-09-05