A Better Approximation Ratio and an IP Formulation for a Sensor Cover Problem

2012 ◽  
pp. 49-60 ◽  
Author(s):  
Rafael da Ponte Barbosa ◽  
Yoshiko Wakabayashi
Keyword(s):  
Approximation Ratio ◽  
Sensor Cover ◽  
Cover Problem

Constant-approximation for minimum weight partial sensor cover

2020 ◽  
pp. 2150047
Author(s):  
Siwen Liu ◽  
Hongmin W. Du
Keyword(s):  
Time Constant ◽  
Polynomial Time ◽  
Wireless Sensors ◽  
Minimum Weight ◽  
Total Weight ◽  
Sensor Cover ◽  
Nonnegative Weight ◽  
Cover Problem

Consider a set of homogeneous wireless sensors, [Formula: see text] with nonnegative weight [Formula: see text] for each sensor [Formula: see text]. Let [Formula: see text] be a set of target points. Given a integer [Formula: see text], we study the minimum weight partial sensor cover problem, that is, find the minimum total weight subset of sensors covering at least [Formula: see text] target points in [Formula: see text]. In this paper, we show the existence of polynomial-time constant-approximation for this problem.

scholarly journals Approximation algorithms for the connected sensor cover problem

2020 ◽  
Vol 809 ◽  
pp. 563-574
Author(s):  
Lingxiao Huang ◽  
Jian Li ◽  
Qicai Shi
Keyword(s):  
Approximation Algorithms ◽  
Sensor Cover ◽  
Cover Problem

Complexity of the Maximum k-Path Vertex Cover Problem

2020 ◽  
Vol E103.A (10) ◽  
pp. 1193-1201
Author(s):  
Eiji MIYANO ◽  
Toshiki SAITOH ◽  
Ryuhei UEHARA ◽  
Tsuyoshi YAGITA ◽  
Tom C. van der ZANDEN
Keyword(s):  
Vertex Cover ◽  
Vertex Cover Problem ◽  
Cover Problem

Approximation Algorithms for Submodular Data Summarization with a Knapsack Constraint

2021 ◽  
Vol 5 (1) ◽  
pp. 1-31
Author(s):  
Kai Han ◽  
Shuang Cui ◽  
Tianshuai Zhu ◽  
Enpei Zhang ◽  
Benwei Wu ◽  
...  
Keyword(s):  
Approximation Algorithms ◽  
Fundamental Problem ◽  
Randomized Algorithm ◽  
Deterministic Algorithm ◽  
Submodular Function ◽  
Approximation Ratio ◽  
Performance Bounds ◽  
Data Summarization ◽  
Submodular Optimization ◽  
Knapsack Constraint

Data summarization, i.e., selecting representative subsets of manageable size out of massive data, is often modeled as a submodular optimization problem. Although there exist extensive algorithms for submodular optimization, many of them incur large computational overheads and hence are not suitable for mining big data. In this work, we consider the fundamental problem of (non-monotone) submodular function maximization with a knapsack constraint, and propose simple yet effective and efficient algorithms for it. Specifically, we propose a deterministic algorithm with approximation ratio 6 and a randomized algorithm with approximation ratio 4, and show that both of them can be accelerated to achieve nearly linear running time at the cost of weakening the approximation ratio by an additive factor of ε. We then consider a more restrictive setting without full access to the whole dataset, and propose streaming algorithms with approximation ratios of 8+ε and 6+ε that make one pass and two passes over the data stream, respectively. As a by-product, we also propose a two-pass streaming algorithm with an approximation ratio of 2+ε when the considered submodular function is monotone. To the best of our knowledge, our algorithms achieve the best performance bounds compared to the state-of-the-art approximation algorithms with efficient implementation for the same problem. Finally, we evaluate our algorithms in two concrete submodular data summarization applications for revenue maximization in social networks and image summarization, and the empirical results show that our algorithms outperform the existing ones in terms of both effectiveness and efficiency.

Toward Refined Nash Equilibria for the SET K-COVER Problem via a Memorial Mixed-Response Algorithm

2021 ◽  
pp. 1-11
Author(s):  
Changhao Sun ◽  
Xiaochu Wang ◽  
Huaxin Qiu ◽  
Wei Sun ◽  
Qingrui Zhou
Keyword(s):  
Nash Equilibria ◽  
Mixed Response ◽  
Cover Problem
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