Approximation Algorithm and Applications for Connected Submodular Function Maximization Problems

In this paper, we study a connected submodular function maximization problem, which arises from many applications including deploying UAV networks to serve users and placing sensors to cover Points of Interest (PoIs). Specifically, given a budget K, the problem is to find a subset S with K nodes fro...

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Bibliographic Details
Published in:IEEE Transactions on Networking Vol. 33; no. 1; pp. 241 - 254
Main Authors: Wang, Ziming, Li, Jing, Xue, He, Xu, Wenzheng, Liang, Weifa, Xu, Zichuan, Peng, Jian, Zhou, Pan, Jia, Xiaohua, Das, Sajal K.
Format: Journal Article
Language:English
Published: IEEE 01.02.2025
Subjects:
Approximation algorithms
Autonomous aerial vehicles
Capacitive sensors
Computer science
Contamination
Disasters
sensor placement
Sensors
Social networking (online)
submodular function maximization
UAV deployment
Water pollution
Wireless sensor networks
ISSN:2998-4157, 2998-4157
Online Access:Get full text
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Summary:In this paper, we study a connected submodular function maximization problem, which arises from many applications including deploying UAV networks to serve users and placing sensors to cover Points of Interest (PoIs). Specifically, given a budget K, the problem is to find a subset S with K nodes from a graph G, so that a given submodular function <inline-formula> <tex-math notation="LaTeX">f(S) </tex-math></inline-formula> on S is maximized and the induced subgraph <inline-formula> <tex-math notation="LaTeX">G[S] </tex-math></inline-formula> by the nodes in S is connected, where the submodular function f can be used to model many practical application problems, such as the number of users within different service areas of the deployed UAVs in S, the sum of data rates of users served by the UAVs, the number of covered PoIs by placed sensors, etc. We then propose a novel <inline-formula> <tex-math notation="LaTeX">\frac {1-1/e}{2h+2} </tex-math></inline-formula>-approximation algorithm for the problem, improving the best approximation ratio <inline-formula> <tex-math notation="LaTeX">\frac {1-1/e}{2h+3} </tex-math></inline-formula> for the problem so far, through estimating a novel upper bound on the problem and designing a smart graph decomposition technique, where e is the base of the natural logarithm, h is a parameter that depends on the problem and its typical value is 2. In addition, when <inline-formula> <tex-math notation="LaTeX">h=2 </tex-math></inline-formula>, the algorithm approximation ratio is at least <inline-formula> <tex-math notation="LaTeX">\frac {1-1/e}{5} </tex-math></inline-formula> and may be as large as 1 in some special cases when <inline-formula> <tex-math notation="LaTeX">K\le 23 </tex-math></inline-formula>, and is no less than <inline-formula> <tex-math notation="LaTeX">\frac {1-1/e}{6} </tex-math></inline-formula> when <inline-formula> <tex-math notation="LaTeX">K\ge 24 </tex-math></inline-formula>, compared with the current best approximation ratio <inline-formula> <tex-math notation="LaTeX">\frac {1-1/e}{7}\left ({{=\frac {1-1/e}{2h+3}}}\right) </tex-math></inline-formula> for the problem. Finally, experimental results in the application of deploying a UAV network demonstrate that, the number of users within the service area of the deployed UAV network by the proposed algorithm is up to 7.5% larger than those by existing algorithms, and the throughput of the deployed UAV network by the proposed algorithm is up to 9.7% larger than those by the algorithms. Furthermore, the empirical approximation ratio of the proposed algorithm is between 0.7 and 0.99, which is close to the theoretical maximum value one.
ISSN:2998-4157
2998-4157
DOI:10.1109/TNET.2024.3477532