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Ancestral Colorings of Perfect Binary Trees With Applications in Private Retrieval of Merkle Proofs. (arXiv:2205.05211v1 [cs.DS])
May 12, 2022, 1:20 a.m. | Quang Cao, Rinaldo Gagiano, Duy Huynh, Xun Yi, Son Hoang Dau, Phuc Lu Le, Quang-Hung Luu, Emanuele Viterbo, Yu-Chih Huang, Jingge Zhu, Mohammad M. Jal
cs.CR updates on arXiv.org arxiv.org
We introduce a novel tree coloring problem in which each node of a rooted
tree of height $h$ is assigned one of the $h$ colors under the condition that
any two nodes that are ancestor and descendant of each other must have
different colors and moreover, the numbers of nodes in any two distinct color
classes differ by at most one. We refer to such a coloring as a balanced
ancestral coloring. Our key contribution is to characterize, based on …
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