Minimizing hierarchical routing error

In hierarchical routing schemes, nodes are grouped into clusters at multiple levels, and a given node sees only a summarized view of the entire network. Hierarchical routing introduces error, which is the difference between the hierarchical path length and the optimal path length using flat routing. Since in practice the routing table size at each node is limited, we formulate the constrained optimization problems of finding a hierarchy structure that minimizes either the worst case or average case routing error. We prove results characterizing solutions of these problems, and present dynamic programming solution algorithms and computational results.