Degree constrained tree embedding into points in the plane

Akihisa Tamura, Yoshiko Tamura

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

Given a set N = {p1,...,pn} of n points in general position in the plane, and a positive integral n-vector d = (d1,...,dn) satisfying ∑ni=1di=2n - 2, can we construct a tree on N, such that the degree of point pi is di 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 languageEnglish
Pages (from-to)211-214
Number of pages4
JournalInformation Processing Letters
Volume44
Issue number4
DOIs
Publication statusPublished - 1992 Dec 10
Externally publishedYes

Fingerprint

Trees (mathematics)
Polynomials
Polynomial Algorithm
Line segment
Pi
Intersect

Keywords

  • combinatorial problems
  • degree sequences
  • Design of algorithms
  • embeddings
  • trees

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

Degree constrained tree embedding into points in the plane. / Tamura, Akihisa; Tamura, Yoshiko.

In: Information Processing Letters, Vol. 44, No. 4, 10.12.1992, p. 211-214.

Research output: Contribution to journalArticle

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