NDLI: Strong minimum energy $$2$$ -hop rooted topology for hierarchical wireless sensor networks

Content Provider	SpringerLink
Author	Panda, B. S. Pushparaj Shetty, D.
Copyright Year	2013
Abstract	Given a set of sensors, the strong minimum energy topology (SMET) problem is to assign transmit power to each sensor such that the sum of the transmit powers of all the sensors is minimum subject to the constraint that the resulting topology containing only bidirectional links is strongly connected. This problem is known to be NP-hard. However, most of the wireless sensor networks are hierarchical in nature, where shorter path lengths are preferred for communication between any two nodes. Given a set of sensors and a specified sensor, say $$r$$ , the strong minimum energy $$2$$ -hop rooted topology problem ( $$2$$ h-SMERT) is to assign transmit power to each sensor such that the sum of the transmit powers of all the sensors is minimum subject to the constraints that the resulting topology containing only bidirectional links is strongly connected and the length of the path from $$r$$ to any other node is at most $$2$$ . We prove that the $$2$$ h-SMERT problem is NP-hard. We also prove that $$2$$ h-SMERT problem is APX-hard. We then show that $$2$$ h-SMERT problem is not approximable within a factor of $$\frac{1}{2}(1-\epsilon ) \ln n$$ unless NP $$\subseteq DTIME(n^{\log \log n})$$ . On the positive side, we propose a $$2(1+ \ln n)$$ -approximation algorithm for the $$2$$ h-SMERT problem. We also study two special cases of the $$2$$ h-SMERT problem, namely, the $$d$$ -rest- $$2$$ h-SMERT problem and the $$k$$ -int- $$2$$ h-SMERT problem. We propose a $$2(1+ \ln d)$$ -approximation algorithm for the $$d$$ -rest- $$2$$ h-SMERT problem. The $$k$$ -int- $$2$$ h-SMERT problem is NP-hard for arbitrary $$k$$ . However, for fixed constant $$k$$ , we propose a $$\frac{k+1}{2}$$ -approximation algorithm for the $$k$$ -int- $$2$$ h-SMERT problem and obtain a polynomial time optimal algorithm for the $$k$$ -int- $$2$$ h-SMERT problem for $$k=2$$ .
Starting Page	1077
Ending Page	1094
Page Count	18
File Format	PDF
ISSN	13826905
Journal	Journal of Combinatorial Optimization
Volume Number	30
Issue Number	4
e-ISSN	15732886
Language	English
Publisher	Springer US
Publisher Date	2013-11-20
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Wireless sensor network Topology control problem Transmission power assignment Graph algorithm NP-hard APX-hard Approximation algorithm Combinatorics Convex and Discrete Geometry Mathematical Modeling and Industrial Mathematics Theory of Computation Optimization Operations Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Computer Science Applications Computational Theory and Mathematics Control and Optimization Applied Mathematics

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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