Nonblocking Graphs: Greedy Algorithms to Compute Disjoint Paths

We define and characterize a class of graphs, called nonblocking graphs of order n, in which one can incrementally compute n vertex-/edge-disjoint paths for any n pairs of vertices such that each path connects one pair of vertices. We then investigate a subclass of these graphs, called geodetically nonblocking graphs of order n, in which all paths incrementally constructed are required to be minimal, i.e., to have a length equal to the distance of the resp. pair of vertices. The results may be of practical relevance when considering processor networks in the model of open-line communication in which communication requests arise at random times and have to be satisified by communication paths which are node-/line-disjoint to the paths already established for previous requests.

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