Degree constrained tree embedding into points in the plane

Akihisa Tamura; Yoshiko Tamura

doi:10.1016/0020-0190(92)90087-C

Degree constrained tree embedding into points in the plane

Akihisa Tamura, Yoshiko Tamura

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

Given a set N = {p₁,...,p_n} of n points in general position in the plane, and a positive integral n-vector d = (d₁,...,d_n) satisfying ∑ⁿ_i=1d_i=2n - 2, can we construct a tree on N, such that the degree of point p_i is d_i and none of the (n - 1) line segments connecting two points corresponding to endpoints of an edge intersect each other (except possibly at its endpoints)? We give a simple proof of the existence of such a tree in any instance and propose an algorithm polynomial on n for constructing one.

Original language	English
Pages (from-to)	211-214
Number of pages	4
Journal	Information Processing Letters
Volume	44
Issue number	4
DOIs	https://doi.org/10.1016/0020-0190(92)90087-C
Publication status	Published - 1992 Dec 10
Externally published	Yes

Keywords

Design of algorithms
combinatorial problems
degree sequences
embeddings
trees

ASJC Scopus subject areas

Theoretical Computer Science
Signal Processing
Information Systems
Computer Science Applications

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