Online Multi-path Routing in a Maze

We consider the problem of routing a message in a mesh network with faulty nodes. The number and positions of faulty nodes is unknown. It is known that a flooding strategy like expanding ring search can route a message linear in the minimum number of steps h while it causes a traffic (i.e. the total number of messages) of O(h). For optimizing traffic a single-path strategy is optimal producing traffic O(h+ p), where p is the number of border nodes neighbored to faulty nodes. We present a deterministic multi-path online routing algorithm that delivers a message within O(h) steps causing traffic O((h + p) log h). For the comparative combined ratio we present a variant of this algorithm that improves the known bound from h O “q log log h log h ” to O(log h). This combined comparative ratio is the minimum of the comparative traffic ratio defined as a quotient over p+ h and the competitive time ratio as a quotient over h. ∗DFG Graduiertenkolleg 776 “Automatic Configuration in Open Systems” †Supported by the DFG Sonderforschungsbereich 376: “Massive Parallelität: Algorithmen, Entwurfsmethoden, Anwendungen.” and by the EU within the 6th Framework Programme under contract 001907 “Dynamically Evolving, Large Scale Information Systems” (DELIS)