On algebraic traceback in dynamic networks

This paper presents the concept of incremental traceback for determining changes in the trace of a network as it evolves with time. A distributed algorithm, based on the methodology of algebraic traceback developed by Dean et al., is proposed that can determine a path of d nodes using O(d) marked packets, and subsequently determine the changes in it using O(log d) marked packets. The algorithm is established to be order-wise optimal, i.e. no other distributed algorithm can determine changes in the path topology using lesser order of bits (or marked packets). The algorithm is shown to have a computational complexity of O(d log d), which is significantly less than that of any existing non-incremental algorithm for algebraic traceback. The extension of the traceback mechanism to systems deploying network coding is also considered.