Information gathering in adversarial systems: lines and cycles

In this paper we consider the problem of routing packets to a single destination in a dynamically changing network, where both the network and the packet injections are under adversarial control. Routing packets to a single destination is also known as information gathering. Information gathering is an important communication primitive for sensor networks. Since sensor networks have a wide range of civilian and military applications, they have recently attracted a great deal of research attention. Several communication protocols have already been suggested for sensor networks, but not much theoretical work has been done so far in this area. Information gathering is an important primitive to allow an observer to collect information from the sensors. Because sensors usually do not move, they form a static topology of possible communication links, but since sensors may frequently be in sleep mode or their communication may be disrupted by interference or obstacles, communication links may be up and down in an unpredictable way. In this paper, we consider sensor networks forming lines or cycles of unreliable edges. Already these seemingly simple topologies are difficult to handle by online algorithms, and the best previously known algorithms require by a factor of θ(n) more buffer size to achieve the same throughput as optimal routing algorithms, where n is the size of the network. We improve this factor to O(log n) and prove a matching lower bound that holds for all online algorithms.