On optimal realizations of finite metric spaces by graphs
Discrete & Computational Geometry
An optimality criterion for graph embeddings of metrics
SIAM Journal on Discrete Mathematics
A fast algorithm for constructing trees from distance matrices
Information Processing Letters
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
On the use of an inverse shortest paths algorithm for recovering linearly correlated costs
Mathematical Programming: Series A and B
Commute times of random walks on trees
Discrete Applied Mathematics
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The analysis of complex networks is of major interest in various fields of science. In many applications we face the challenge that the exact topology of a network is unknown but we are instead given information about distances within this network. The theoretical approaches to this problem have so far been focusing on the reconstruction of graphs from shortest path distance matrices. Often, however, movements in networks do not follow shortest paths but occur in a random fashion. In these cases an appropriate distance measure can be defined as the mean length of a random walk between two nodes - a quantity known as the mean first hitting time. In this contribution we investigate whether a graph can be reconstructed from its mean first hitting time matrix and put forward an algorithm for solving this problem. A heuristic method to reduce the computational effort is described and analyzed. In the case of trees we can even give an algorithm for reconstructing graphs from incomplete random walk distance matrices.