## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

NACO

We introduce two set cover problems with submodular costs and linear/submodular penalties and
offer two approximation algorithms of ratios $\eta$ and $2\eta$ respectively via the primal-dual
technique, where $\eta$ is the largest number of sets that each element belongs to.

JIMO

In this paper, we consider the $2$-catalog segmentation problem. For
the disjoint version, we propose an approximation
algorithm based on the non-uniform rotation technique using a
semidefinite programming ($SDP$) relaxation. We give the
performance curve depending on the ratio between the value of optimal
SDP solution and the total weight. In this curve, the
lowest point implies the approximation ratio is $0.7317$ which is the best ratio for the disjoint version until now.
We also consider the performance curve of the joint version.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]