Budgeted constrained coverage on bounded carving-width and series-parallel multi-interface networks

Abstract

The IoT vision often requires near-real-time data from physical and battery operated virtual devices in order to implement complex and critical services. In this paper, we consider the use of multi-interface wireless network communication for fast and energy efficient data transfer in a typical IoT scenario. Multi-interface wireless networks allow the interconnection of battery-powered devices that can have different communication technologies such as Bluetooth, WiFi, 4G, 5G and GPRS. Devices can activate one or more interface depending on the availability, required communication bandwidth, the cost (in terms of energy consumption) for maintaining an active interface, and the neighbourhood.Consider a network composed of heterogeneous devices. Each device might communicate by means of multiple interfaces. An intriguing research direction is that of activating (switch-on) a subset of interfaces for each device in such a way that suitable communication connections are established. This means that the two devices at the endpoints of each connection must activate at least a same interface. This peculiarity inspired the modelling of what is called in the literature as Multi-Interface networks. Such a model has bee extensively investigated in the recent years. We consider a new variant where each interface is associated with both a cost and a profit, and also the establishment of a connection provides a profit. Moreover, each device is limited to activate at most a fixed number q of its available interfaces whereas the overall cost of the interfaces that can be activated must be kept below a predefined budget b. Within this context we consider the Coverage problem where the requirement is to establish all the connections defined by the edges of an undirected graph G=(V,E), where nodes V represent the devices. We prove the problem is NP-hard even for the basic case of q=2. Then, we investigate the case of two well-established and related graph classes. Namely, we consider graphs with bounded Carving-width and Series-Parallel keeping parameter q=2. In both cases, we design two complementary pseudo-polynomial time (in the size of the input) algorithms based on dynamic programming. Furthermore, for series-parallel graphs we also provide a fully polynomial time approximation scheme.