## 1 Introduction  
In recent years we have witnessed an unprecedented increase in the use of wireless communications. Furthermore, it is expected that the overall Internet traffic will double between 2018 and 2023 [1], and the number of connected devices per person will grow from 2.4 to 3.6 during the same period. Although it is almost impossible to envisage our day-to-day life without the use of smart-phones or tablets, there is also an increasing concern about the negative effects that the exposure to electromagnetic fields (EMF) may have on the general population, which has led the International Comission on Non-ionizing Radiation Protection (ICNIRP) to fix new limits to EMF in 2020 [2]. In this regard, the leitmotiv of the Low EMF Exposure Networks (LEXNET) [3] European project was to tackle this challenge, by advocating the use of different management techniques and novel communication technologies to reduce the EMF exposure induced by wireless communication systems, without jeopardizing the quality of experience perceived by end-users. However, the adoption of new wireless technologies and frequency bands under the 5G umbrella, such as Millimeter Waves (mmWave), is leading the scientific community to re-address the effects of EMF [4], while authorities are fostering such research initiatives. In this sense, the European Commission has recently launched a call on this topic with a budget of EUR 40 million (call _Environment and health (2021)_ (_HORIZON-HLTH-2021-ENVHLTH-02_)). Among the communication alternatives that have received more attention from the scientific community, this work deals with wireless multi-hop topologies. Although their origins date back to 1997 (with the IETF MANET working group), the traditional application scenarios that were proposed at that time have significantly changed, moving from war and natural disaster circumstances, to use-cases focused on expanding the coverage of base stations in a simple and economical way. It is worth noting, for example, the relevance of such deployments within the increasingly widespread wireless sensor networks, and the role given to them in the new specifications of the 5G technology, i.e., relaying techniques and Device-to-Device communications [5]. The routing mechanisms that have been traditionally used over wireless multi-hop networks foster the selection of minimum-cost paths, in many cases seeking those alternatives with the least number of hops. In this work, however, we propose to penalize paths exhibiting a higher EMF exposure. Unlike the number of hops, the EMF exposure is not directly related to the Quality of Service (QoS), but to the population's health and, to their perception when using the communication services. In this regard, using the EMF exposure as a quality indicator to develop new communication solutions and to improve existing ones would have a positive impact on the user Quality of Experience (Quality of Experience). Keeping this in mind, the Exposure Index (EI) was defined under the umbrella of the LEXNET project as a metric to quantify the population exposure to the EMF induced by communication systems. This metric combines parameters related to the wireless technologies (i.e., frequency bands), with life segmentation information (i.e., time of the day, technology usages, etc.) to provide an overall estimation of the exposure, as defined in Equation (1). In particular, it is defined as a temporal average, over a period \(T\), of the exposure induced by different combinations of technology-related parameters and segmentation data. We refer to each combination as an exposure component, while \(N_{EC}\) corresponds to the number of considered components. The LEXNET EI takes into account, for every component, the number of devices, \(N_{u}\), and, for each device, the uplink transmitted power, \(\overline{P}_{tx}\) (in \(\Psi\)) as well as the downlink incident power density, \(\overline{S}_{rx}\) (\(\Psi\)/m\({}^{2}\)).