Approximation Algorithms for the Connected Sensor Cover Problem

Huang, Like; Li, Jian; Shi, Qicai

doi:10.1007/978-3-319-21398-9_15

Cited by 11 publications

(6 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the objective function of the problem considered in this paper may not be a special submodular function. In addition, Huang et al [12] investigated the problem of placing K sensors to monitor targets so that the number of targets covered by the K sensors is maximized and the network formed by the K placed sensors is connected, where a target is covered by a sensor if their Euclidean distance is no more than a given sensing range R s , and two sensors can communicate with each other if their Euclidean distance is no greater than a given communication range R c , and R s ≤ R c . They proposed a 1−1/e 8( 2 √ 2α +1) 2 -approximation algorithm, where α = Rs Rc , and the ratio thus is between…”

Section: Related Workmentioning

confidence: 99%

“…128 , when α = Rs Rc = 1, which indicates that the performance of the solutions delivered by the both algorithms may be far from the optimal solution. Therefore, the both algorithms in [12] and [37], [38] are applicable to the case with many to-be-placed sensors, i.e., the value of K is very large, e.g., K = 10, 000. Notice that there are usually tens or hundreds of UAVs to-be-deployed in a real UAV network, and the approximation ratio ) -approximation algorithm in [17], the main technical differences between them are twofold.…”

Section: Related Workmentioning

confidence: 99%

“…Constraint (11) ensures that each user u i can be served by no more than one UAV. Constraint (12) indicates that user u i cannot be served by any UAV at location v j outside of its communication range R user , and d ij is the Euclidean distance between u i and v j .…”

Section: Problem Definitionmentioning

confidence: 99%

See 2 more Smart Citations

Throughput Maximization of UAV Networks

Sun

Zou

et al. 2021

Preprint

View full text Add to dashboard Cite

In this paper we study the deployment of multiple unmanned aerial vehicles (UAVs) to form a temporal UAV network for the provisioning of emergent communications to affected people in a disaster zone, where each UAV is equipped with a lightweight base station device and thus can act as an aerial base station for users. Unlike most existing studies that assumed that a UAV can serve all users in its communication range, we observe that both computation and communication capabilities of a single lightweight UAV are very limited, due to various constraints on its size, weight, and power supply. Thus, a single UAV can only provide communication services to a limited number of users. We study a novel problem of deploying K UAVs in the top of a disaster area such that the sum of the data rates of users served by the UAVs is maximized, subject to that (i) the number of users served by each UAV is no greater than its service capacity; and (ii) the communication network induced by the K UAVs is connected. We then propose a-approximation algorithm for the problem, improving the current best result of the problem by five times (the best approximation ratio so far is)), where e is the base of the natural logarithm. We finally evaluate the algorithm performance via simulation experiments. Experimental results show that the proposed algorithm is very promising. Especially, the solution delivered by the proposed algorithm is up to 12% better than those by existing algorithms.

show abstract

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Throughput Maximization of UAV Networks

Sun

Zou

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Hence it is natural to investigate approximation algorithms for the VC-weighted Steiner tree problem in these graph classes. Moreover, unit disk graphs are regarded as a reasonable model of wireless networks, and the vertex-weighted Steiner tree problem in unit disk graphs has been actively studied in this context (see, e.g., [1,14,22,23,24]). Since our problem is motivated by an application in communication networks, it is reasonable to investigate the problem in unit disk graphs.…”

Section: Our Contributionsmentioning

confidence: 99%

“…To solve the connected dominating set problem, we present a linear programming (LP) rounding algorithm. This algorithm relies on an idea presented by Huang, Li, and Shi [14], who considered a variant of the connected dominating set problem in unit disk graphs. Although their algorithm is only for minimizing the number of vertices in a solution, we prove that it can be extended to our problem.…”

Section: Our Contributionsmentioning

confidence: 99%

Computing a Tree Having a Small Vertex Cover

Fukunaga

Maehara

2016

Combinatorial Optimization and Applications

View full text Add to dashboard Cite

We consider a new Steiner tree problem, called vertex-cover-weighted Steiner tree problem. This problem defines the weight of a Steiner tree as the minimum weight of vertex covers in the tree, and seeks a minimum-weight Steiner tree in a given vertex-weighted undirected graph. Since it is included by the Steiner tree activation problem, the problem admits an O(log n)approximation algorithm in general graphs with n vertices. This approximation factor is tight up to a constant because it is NP-hard to achieve an o(log n)-approximation for the vertex-coverweighted Steiner tree problem in general graphs even if the given vertex weights are uniform and a spanning tree is required instead of a Steiner tree. In this paper, we present constantfactor approximation algorithms for the problem in unit disk graphs and in graphs excluding a fixed minor. For the latter graph class, our algorithm can be also applied for the Steiner tree activation problem.consists of at least n/2 vertices. Our problem is to compute a tree that minimizes the number (or, more generally, the weight) of devices required to monitor all of the traffic.More formally, our problem is defined as follows. Let G = (V, E) be an undirected graph associated with nonnegative vertex weights w ∈ R V + . Throughout this paper, we will denote |V | by n. Let T ⊆ V be a set of vertices called terminals. The problem seeks a pair comprising a tree F and a vertex set U ⊆ V (F ) such that (i) F is a Steiner tree with regard to the terminal set T (i.e., T ⊆ V (F )), and (ii) U is a vertex cover of F (i.e., each edge in F is incident to at least one vertex in U ). The objective is to find such a pair (F, U ) that minimizes the weight w(U ) := v∈U w(v) of the vertex cover. We call this the vertex-cover-weighted (VC-weighted) Steiner tree problem. We call the special case in which V = T the vertex-cover-weighted (VC-weighted) spanning tree problem. The aim of this paper is to investigate these fundamental problems.Besides the motivation from the communication networks, there is another reason for the importance of the VC-weighted Steiner tree problem. The VC-weighted Steiner tree problem is a special case of the Steiner tree activation problem, which was formulated by Panigrahi [18]. In the Steiner tree activation problem, we are given a set W of nonnegative real numbers, and each edge uv in the graph is associated with an activation function f uv : W × W → { , ⊥}, where indicates that an edge uv is activated, and ⊥ indicates that it is not. The activation function is assumed to be monotone (i.e., if f uv (i, j) = , i ≤ i , and j ≤ j , then f uv (i , j ) = ). A solution for the problem is defined as a |V |-dimensional vector x ∈ W V . We say that a solution x activates an edge uv if f uv (x(u), x(v)) = . The problem seeks a solution x that minimizes x(V ) := v∈V x(v) subject to the constraint that the edges activated by x include a Steiner tree. To see that the Steiner tree activation problem includes the VC-weighted Steiner tree problem, define W as {0} ∪ {w(v) : v ∈ V }, a...

show abstract