# An Improved Approximation Algorithm for the Minimum Power Cover Problem with Submodular Penalty

## Abstract

**:**

## 1. Introduction

## 2. Preliminary

## 3. Overview of the Algorithm of [14]

## 4. An Improved Primal Dual Algorithm

**Lemma**

**1**

Algorithm 1 Primal Dual Algorithm |

**Figure 1.**A simple example $U=\{{u}_{1},{u}_{2},{u}_{3},{u}_{4},{u}_{5}\}$, $S=\{{s}_{1},{s}_{2},{s}_{3}\}$ and $t=6$.

**Lemma**

**3**

**Proof.**

**Lemma**

**4.**

**Proof.**

**Lemma**

**5.**

**Proof.**

**Lemma**

**6.**

**Proof.**

**Theorem**

**1.**

**Proof.**

## 5. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

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Dai, H.
An Improved Approximation Algorithm for the Minimum Power Cover Problem with Submodular Penalty. *Computation* **2022**, *10*, 189.
https://doi.org/10.3390/computation10100189

**AMA Style**

Dai H.
An Improved Approximation Algorithm for the Minimum Power Cover Problem with Submodular Penalty. *Computation*. 2022; 10(10):189.
https://doi.org/10.3390/computation10100189

**Chicago/Turabian Style**

Dai, Han.
2022. "An Improved Approximation Algorithm for the Minimum Power Cover Problem with Submodular Penalty" *Computation* 10, no. 10: 189.
https://doi.org/10.3390/computation10100189