2. Facility Location

The facility location problem has occupied a central place in operations research since the early 1960's, as it models design decisions on the placement of factories, warehouses, schools, or hospitals to serve a set of customers efficiently. For an overview of previous work see the survey chapter by Cornue-jols, Nemhauser & Wolsey in [21]. Recently, it has received renewed research interest because it can be used to place servers or proxies in communication networks [28]. We apply the facility location problem to configuration and deployment issues in wireless sensor networks. More specifically, we discuss how algorithms for the facility location problem can be used to assign functionality to certain nodes in a wireless sensor network, i.e., choose a subset of designated nodes as service providers of a particular service. Such assignment of functionality to designated nodes is a key element in the often-cited ability for self-configuration [3] that is required in many sensor-network applications. Consider clustering, which is a prominent sensor network configuration problem (see Chapter ??), where a subset of cluster leaders is selected to provide a service to their neighboring nodes, while the latter (slave nodes) can shut down some functionality and thus save power. Clustering can for instance be used to improve the efficiency of data delivery (e.g., flooding, routing). In this setting, cluster leaders act as sole direct communication partners for the associated slave nodes, which allows slave nodes to synchronize to their cluster leader's transmission schedule and shut down their transceivers based on this schedule. As slave nodes save power, it is desirable to have only few cluster leaders (as long as each slave node has a cluster leader as a neighbor) to enable energy savings at many slave nodes. In this sense an optimal configuration is modeled by the minimum dominating set problem discussed in Chapter ??. An example of such a configuration is shown in Figure 2.1(a). However, such a strategy increases the distance between cluster leaders and their associated nodes. If network nodes can vary their transmission power, such a configuration is not energy optimal. In particular, an energy-optimal configuration would require placing cluster leaders as close as possible to their associated nodes. An example of this strategy is shown in Fig