Strong minimum energy hierarchical topology in wireless sensor networks

B. S. Panda () and D. Pushparaj Shetty
Additional contact information
B. S. Panda: Indian Institute of Technology Delhi
D. Pushparaj Shetty: Indian Institute of Technology Delhi

Journal of Combinatorial Optimization, 2016, vol. 32, issue 1, No 11, 174-187

Abstract: Abstract Given a set of $$n$$ n sensors, the strong minimum energy topology (SMET) problem in a wireless sensor network is to assign transmit powers to all sensors such that (i) the graph induced only using the bi-directional links is connected, that is, there is a path between every pair of sensors, and (ii) the sum of the transmit powers of all the sensors is minimum. This problem is known to be NP-hard. In this paper, we study a special case of the SMET problem, namely , the $$k$$ k -strong minimum energy hierarchical topology ( $$k$$ k -SMEHT) problem. Given a set of $$n$$ n sensors and an integer $$k$$ k , the $$k$$ k -SMEHT problem is to assign transmission powers to all sensors such that (i) the graph induced using only bi-directional links is connected, (ii) at most $$k$$ k nodes of the graph induced using only bi-directional links have two or more neighbors, that is they are non-pendant nodes, and (iii) the sum of the transmit powers of all the sensors in $$G$$ G is minimum. We show that $$k$$ k -SMEHT problem is NP-hard for arbitrary $$k$$ k . However, we propose a $$\frac{k+1}{2}$$ k + 1 2 -approximation algorithm for $$k$$ k -SMEHT problem, when $$k$$ k is a fixed constant. Finally, we propose a polynomial time algorithm for the $$k$$ k -SMEHT problem for $$k=2$$ k = 2 .

Keywords: Sensor networks; Topology control problem; Graph algorithms; NP-complete; Approximation algorithms (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-015-9869-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:32:y:2016:i:1:d:10.1007_s10878-015-9869-7

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-015-9869-7

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().