Approximation and polynomial algorithms for the data mule scheduling with handling time and time span constraints

Abstract

In this paper, we address the data mule scheduling problem with time constraints (DMSTC) in which the aim is to dispatch from a depot the minimum number of data mules to serve target sensors located on a network. Each target sensor is associated with a handling time and each dispatched data mule must return to the depot before time span D. Our main contribution is as follows. First, we give the first constant-factor 2-approximation algorithm and a bicriteria polynomial time approximation scheme (PTAS) for the DMSTC defined on a tree. The former result resolves an open problem proposed in the literature (Chen et al., 2020 [4]). This is achieved by an approximation preserving reduction from the DMSTC to the distance constrained vehicle routing problem, i.e. a special case of the DMSTC with zero handling times. Second, we show that our approximation preserving reduction can be extended to the multi-depot version of the DMSTC and derive a similar bicriteria PTAS for the multi-depot DMSTC on a tree if the number of depots is a fixed constant. Finally, we consider the uniform DMSTC, which is a particular case of the DMSTC with all handling times identical, and develop the first non-trivial polynomial algorithms for the uniform DMSTC define on several classes of special networks, including spiders, paths and cycles.