Parallel Metric Tree Embedding Based on an Algebraic View on Moore-Bellman-Ford

A metric tree embedding of expected stretch α maps a weighted n-node graph G = (V, E, w) to a weighted tree T = (V_T, E_T, w_T) with V ⊆ V_T, and dist(v, w, G) ≤ dist(v, w, T) and E[dist(v, w, T)] ≤ α dist(v, w, G) for all v, w ∈ V. Such embeddings are ...

In the decremental single-source shortest paths (SSSP) problem, we want to maintain the distances between a given source node s and every other node in an n-node m-edge graph G undergoing edge deletions. While its static counterpart can be solved in ...

This paper presents parallel algorithms for embedding an arbitrary n-point metric space into a distribution of dominating trees with O(log n) expected stretch. Such embedding has proved useful in the design of many approximation algorithms in the ...