## 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
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

JIMO

In this paper, we consider the warehouse-retailer network design
game based on the warehouse-retailer network design problem (WRND)
proposed by Teo and Shu (2004). By carefully defining the
generalized distance function, we present a cost-sharing method for
the warehouse-retailer network design game. We show that the
proposed cost-sharing scheme is cross-monotonic, competitive, and
$3$-approximate cost recovery.

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.

JIMO

In this paper, we consider the $k$-level facility location problem
with submodular penalties ($k$-FLPSP). We propose a primal-dual
$6$-approximation (combinatorial) algorithm for the $k$-FLPSP.

keywords:
submodular.
,
approximation algorithm
,
primal-dual
,
Facility location
,
combinatorial algorithm

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

We study two unrelated machine scheduling problems with machine dependent release dates to minimize the makespan.
For the case with fixed processing time where processing job $j$ on machine $i$ requires time $p_{ij}$ and incurs a cost of $c_{ij}$,
we derive a $2$-approximation algorithm. For the problem with variable processing times where the cost increases linearly as the processing time decreases, we propose a $(2+\epsilon)$-approximation algorithm.

keywords:
Scheduling
,
linear programming
,
rounding.
,
unrelated parallel machine
,
approximation algorithm

## Year of publication

## Related Authors

## Related Keywords

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