On the Admission of Dependent Flows in Powerful Sensor Networks Reuven Cohen Ilia Nudelman Gleb Polevoy Department of Computer Science Technion – Israel Institute of Technology Haifa 32000 Israel Abstract—In this paper we define and study a new problem, referred to as the Dependent Unsplittable Flow Problem (D-UFP). We present and discuss this problem in the context of large-scale powerful (radar/camera) sensor networks, but we believe it has important applications on the admission of large flows in other networks as well. In order to optimize the selection of flows transmitted to the gateway, D-UFP takes into account possible dependencies between flows. We show that D-UFP is more difficult than NP-hard problems for which no good approximation is known. Then, we address two special cases of this problem: the case where all the sensors have a shared channel and the case where the sensors form a mesh and route to the gateway over a spanning tree. I. I NTRODUCTION In wireless sensor networks, sensors probe the sur- rounding environment and generate reports of the col- lected readings. Using wireless communication, these reports are sent to a control center, usually through a gateway deployed in the physical proximity of the sensors. While much of the focus of the sensor network community has been on the design of miniature low- power wireless sensor networks, an important network- ing revolution has been taking place for powerful sensors such as radars and cameras [10], [11], [19], [21], [28]. Such sensor networks are used in a variety of civilian and military applications such as earthquake sensing, weather monitoring, road traffic monitoring, and Network Centric Operations (NCO)[9], [21]. As indicated by [11], these emerging systems raise a number of new research challenges that do not exist in mote-class wireless sensor networks. Although these systems are not limited by energy considerations, the data they generate exceeds, by several orders of mag- nitude, the bandwidth capacity of the wireless networks that connect them to their gateway. Since delivering all this data is not possible, a decision must be made as to which flow to deliver and which to drop. This decision should be based on the bandwidth of each flow and its profit to the whole system. This brings to mind the well-known NP-hard Un- splittable Flow Problem (UFP) [7], [12]. However, UFP does not capture an important property of the considered radar/camera sensors: the dependency between different flows. For example, consider two Doppler radars that scan partially overlapping areas. Some of their detected events are likely to be similar. Thus, the profit of deliv- ering both flows should be smaller than the sum of their individual profits. In other cases, however, the combined profit of two different flows might be greater than the sum of their individual ones. For instance, in the context of adaptive sensing of the atmosphere, data from multiple radars allows for more accurate estimation of wind velocity vectors [19]. When some of the dependencies between flows are positive and others are negative, the dependency set is said to be mixed and the resulting optimization problem is harder. In this paper we define and study a new problem, referred to as the Dependent Unsplittable Flow Problem (D-UFP). We present and discuss this problem in the context of powerful radar/camera wireless sensor net- works (WSNs), but we believe it has important applica- tions in the admission of large flows in other networks as well. While UFP’s goal is to maximize the profit gained by accommodating independent flows, our generalization takes into account the dependency between flows. Thus, the profit from delivering two flows is not necessarily equal to the sum of their profits. The algorithms proposed in this paper allow the sensor network to determine which flows to deliver and which to drop. In some applications, such as NCO [21], the network may need to run the algorithm very often, sometimes even once a minute, in order to adapt itself to the changing reality. The rest of the paper is organized as follows. In Section II we discuss related work. In Section III we introduce our framework and define D-UFP. In Section IV we describe a new algorithm for solving D-UFP in the case where all the sensors transmit to the gateway over one common channel. In Section V we describe a new algorithm for solving D-UFP in the more general case