An elementary proposition on the dynamic routing problem in wireless networks of sensors

The routing problem (finding an optimal route from one point in a computer network to another) is surrounded by impossibility results. These results are usually expressed as lower and upper bounds on the set of nodes (or the set of links) of a network and represent the complexity of a solution to the routing problem (a routing function). The routing problem dealt with here, in particular, is a dynamic one (it accounts for network dynamics) and concerns wireless networks of sensors. Sensors form wireless links of limited capacity and time-variable quality to route messages amongst themselves. It is desired that sensors self-organize ad hoc in order to successfully carry out a routing task, e.g. provide daily soil erosion reports for a monitored watershed, or provide immediate indications of an imminent volcanic eruption, in spite of network dynamics. Link dynamics are the first barrier to finding an optimal route between a node x and a node y in a sensor network. The uncertainty of the outcome (the best next hop) of a routing function lies partially with the quality fluctuations of wireless links. Take, for example, a static network. It is known that, given the set of nodes and their link weights (or costs), a node can compute optimal routes by running, say, Dijkstra’s algorithm. Link dynamics however suggest that costs are not static. Hence, sensors need a metric (a measurable quantity of uncertainty) to monitor for fluctuations, either improvements or degradations of quality or load; when a fluctuation is sufficiently large (say, by ∆), sensors ought to update their costs and seek another route. Therein lies the other fundamental barrier to find an optimal route – complexity. A crude argument would suggest that sensors (and their links) have an upper bound on the number of messages they can transmit, receive and store