Approximating 2-cliques in unit disk graphs

Pattillo, Jeffrey; Wang, Yiming; Butenko, Sergiy

doi:10.1016/j.dam.2013.10.017

Cited by 2 publications

(2 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The problem of identification of the cluster heads that are overlapped with each other can be simplified to the problem of clique search. 55 So the algorithm developed for the clique search problem is used to find the coverage level of communication of each cluster head in the network. 52 The clique partition is a type of grouping where cluster head nodes are divided into cliques, where each clique implies mutual proximity.…”

Section: Proposed Approachmentioning

confidence: 99%

Identification of optimal location points for efficient data gathering in IoT environment

Wala

Chand

Sharma

2021

Int J Communication

View full text Add to dashboard Cite

Recent development in sensor technologies encourages the adoption of mobile data collectors (MDCs), that is, vehicles or robots, to collect data in the Internet of Things (IoT) environment. However, the slow travel speed of the MDCs leads to significant delays in the transmission of data. This work proposes an optimal region location point based route planning (ORLP-RP) scheme to construct a shorter tour with minimized data delivery latency. Primary goal of the work is to distinguish the overlapped wireless sensor network (WSN) clusters and specify the overlapped regions to find optimal location points within each identified region to ensure one-hop data gathering from each cluster. Thereafter, MDC trajectory is formed by using the nearest-neighbor (NN) heuristic approach that generates a near optimal solution. In performance evaluation, the ORLP-RP scheme has been compared with the existing algorithms such as EAPC, RDP, MOPSO, and NDCMC for data collection in terms of the number of optimal location points, total path length, data gathering latency, network lifespan, energy consumption, and data gathering ratio. Simulation results demonstrate the effectiveness of the proposed approach by improving the number of optimal location points with an average up to 58%, total path length improvement by 17%, energy consumption and network lifespan improvement on average by 18% and 12%, data gathering ratio by the MDC up to 9%, and reducing the delay of the MDC path by 21% compared with considered approaches. Thus, simulation results indicate better performance of the proposed scheme at all the indices listed above.

show abstract

Section: Proposed Approachmentioning

confidence: 99%

Identification of optimal location points for efficient data gathering in IoT environment

Wala

Chand

Sharma

2021

Int J Communication

View full text Add to dashboard Cite

show abstract

“…Unfortunately, our algorithm can not be directly extended to the maximum d-clique problem. Except for the 1 2 -approximation algorithm of Pattillo et al [19], for d = 2, there is no related work discussing the maximum d-clique problem in unit disk graphs. Hence, approximating the maximum d-clique problem in unit disk graphs is also an interesting open problem.…”

Section: Upper Bound On Cmentioning

confidence: 99%

Approximating Maximum Diameter-Bounded Subgraph in Unit Disk Graphs

Abu-Affash

Carmi

Maheshwari

et al. 2021

Discrete Comput Geom

View full text Add to dashboard Cite

We consider a well studied generalization of the maximum clique problem which is defined as follows. Given a graph G on n vertices and an integer d ≥ 1, in the maximum diameter-bounded subgraph problem (MaxDBS for short), the goal is to find a (vertex) maximum subgraph of G of diameter at most d. For d = 1, this problem is equivalent to the maximum clique problem and thus it is NP-hard to approximate it within a factor n 1− , for any > 0. Moreover, it is known that, for any d ≥ 2, it is NP-hard to approximate MaxDBS within a factor n 1/2− , for any > 0.In this paper we focus on MaxDBS for the class of unit disk graphs. We provide a polynomialtime constant-factor approximation algorithm for the problem. The approximation ratio of our algorithm does not depend on the diameter d. Even though the algorithm itself is simple, its analysis is rather involved. We combine tools from the theory of hypergraphs with bounded VC-dimension, k-quasi planar graphs, fractional Helly theorems and several geometric properties of unit disk graphs.

show abstract

Approximating 2-cliques in unit disk graphs

Cited by 2 publications

References 16 publications

Identification of optimal location points for efficient data gathering in IoT environment

Identification of optimal location points for efficient data gathering in IoT environment

Approximating Maximum Diameter-Bounded Subgraph in Unit Disk Graphs

Contact Info

Product

Resources

About