The Sensor Location Problem

Today, transportation in many parts of the world is facilitated largely or even entirely over road networks. In a big city, the road network is likely both complex and heavily utilized. Congestion on the network is therefore a prominent concern to its users, particularly commuters and other timesensitive travelers. As the availability of sophisticated GPS units and other information services grows, accurate determination of the path from point A to point B that minimizes travel time becomes an increasingly feasible possibility to network users. In order for an information service to be able to calculate the timeminimizing path from any origin to any destination, however, the real-time network flow must be known. If a monitoring device were placed at each intersection or on each road, the network flow would be immediately observable. However, this solution may be prohibitively expensive. A question then emerges: What is the minimum number and configuration of monitoring devices on the network such that flow everywhere on the network can be determined?