Analysis of Movement-Based Connectivity Restoration Problem in Wireless Ad-Hoc and Sensor Networks

TL;DR

This paper proves that the Movement-Based Connectivity Restoration problem in wireless ad-hoc and sensor networks is NP-Complete by reducing it from the Steiner Tree Problem, highlighting its computational complexity.

Contribution

It provides a formal proof of NP-Completeness for the MCR problem through a reduction from the Steiner Tree Problem, clarifying its computational difficulty.

Findings

MCR problem is NP-Complete.

Reduction from Steiner Tree Problem established.

Highlights the complexity of optimizing node movements for connectivity.

Abstract

Topology control, including topology construction and maintenance phases, is a vital conception for wireless ad-hoc networks of any kind, expressly the wireless sensor networks (WSN). Topology maintenance, the latter phase, concerns several problems, such as optimizing the energy consumption, increasing the data rate, making clusters, and sustaining the connectivity. A disconnected network, among other strategies, can efficiently be connected again using a Movement-based Connectivity Restoration (MCR) method, where a commensurate number of nodes move (or are moved) to the desired positions. However, finding an optimal route for the nodes to be moved can be a formidable problem. As a matter of fact, this paper presents details regarding a direct proof of the NP-Completeness of the MCR Problem by a reduction of the well-studied Steiner Tree Problem using the minimum number of Steiner points and the bounded edge length.