Improved solution to data gathering with mobile mule

Abstract: In this work we study the problem of collecting protected data in ad-hoc sensor network using a mobile entity called MULE. The objective is to increase information survivability in the network. Sensors from all over the network, route their sensing data through a data gathering tree, towards a particular node, called the $sink$. In case of a failed sensor, all the aggregated data from the sensor and from its children is lost. In order to retrieve the lost data, the MULE is required to travel among all the children of the failed sensor and to re-collect the data. There is a cost to travel between two points in the plane. We aim to minimize the MULE traveling cost, given that any sensor can fail. In order to reduce the traveling cost, it is necessary to find the optimal data gathering tree and the MULE location. We are considering the problem for the unit disk graphs (UDG) and Euclidean distance cost function. We propose a primal-dual algorithm that produces a $\left(20+\varepsilon\right)$-approximate solution for the problem, where $\varepsilon\rightarrow0$ as the sensor network spreads over a larger area. The algorithm requires $O\left(n^{3}\cdot\varDelta\left(G\right)\right)$ time to construct a gathering tree and to place the MULE, where $\varDelta\left(G\right)$ is the maximum degree in the graph and $n$ is the number of nodes.