Optimal distortion embedding of complete binary trees into lines

Authors:
Masao Kumamoto;Eiji Miyano
Affiliations:
Department of Systems Design and Informatics, Kyushu Institute of Technology, Fukuoka 820-8502, Japan;Department of Systems Design and Informatics, Kyushu Institute of Technology, Fukuoka 820-8502, Japan
Venue:
Information Processing Letters
Year:
2012

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Abstract

We study the problem of embedding an unweighted complete binary tree into a line with low distortion. Very recently, Mathieu and Papamanthou (2008) [9] showed that the inorder traversal of the complete binary tree of height h gives a line embedding of distortion O(2^h), and conjectured that the current lower bound of @W(2^hh) increases to @W(2^h), i.e., the upper bound of O(2^h) is best possible. In this paper, we disprove their conjecture by providing a line embedding of the complete binary tree of height h with optimal distortion @Q(2^hh).