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Near-Optimal Distance Emulator for Planar Graphs

Naor, and Steven Rudich. Implicat representation of graphs. SIAM Journal on Discrete Mathematics, 5(4):596–603, 1992. Haim Kaplan, Shay Mozes, Yahav Nussbaum, and Micha Sharir. Submatrix maximum queries ... . SIAM Journal Discrete Math., 3(1):81–97, 1990. Philip Klein, Shay Mozes, and Oren Weimann. Shortest paths in directed planar graphs with negative lengths: a linear-space O(n lg2 n)-time algorithm. ACM

Dispersion on Trees

In the k-dispersion problem, we need to select k nodes of a given graph so as to maximize the minimum distance between any two chosen nodes. This can be seen as a generalization of the independent set problem, where the goal is to select nodes so that the minimum distance is larger than 1. We design an optimal O(n) time algorithm for the dispersion problem on trees consisting of...