# 1D Modeling of Sensor Selection Problem for Weak Barrier Coverage and Gap Mending in Wireless Sensor Networks

## TL;DR

This paper introduces a novel 1D modeling approach for sensor selection in wireless sensor networks, proposing efficient algorithms for weak barrier coverage and gap mending that outperform existing methods in speed and complexity.

## Contribution

It presents a new 1D discrete problem formulation and develops optimal greedy algorithms, OGA and K-OGA, along with a local gap-mending algorithm, LOGM, for improved sensor coverage solutions.

## Key findings

- OGA and K-OGA outperform state-of-the-art in speed and complexity.
- LOGM effectively mends barrier gaps with bounded sensor additions.
- Algorithms demonstrate optimal or near-optimal performance in simulations.

## Abstract

In this paper, we first remodel the line coverage as a 1D discrete problem with co-linear targets. Then, an order-based greedy algorithm, called OGA, is proposed to solve the problem optimally. It will be shown that the existing order in the 1D modeling, and especially the resulted Markov property of the selected sensors can help design greedy algorithms such as OGA. These algorithms demonstrate optimal/efficient performance and have lower complexity compared to the state-of-the-art. Furthermore, it is demonstrated that the conventional continuous line coverage problem can be converted to an equivalent discrete problem and solved optimally by OGA. Next, we formulate the well-known weak barrier coverage problem as an instance of the continuous line coverage problem (i.e. a 1D problem) as opposed to the conventional 2D graph-based models. We demonstrate that the equivalent discrete version of this problem can be solved optimally and faster than the state-of-the-art methods using an extended version of OGA, called K-OGA. Moreover, an efficient local algorithm, called LOGM, is proposed to mend barrier gaps due to sensor failure. In the case of m gaps, LOGM is proved to select at most 2m-1 sensors more than the optimal while being local and implementable in distributed fashion. We demonstrate the optimal/efficient performance of the proposed algorithms via extensive simulations.