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 language | English |
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Pages (from-to) | 211-214 |
Number of pages | 4 |
Journal | Information Processing Letters |
Volume | 44 |
Issue number | 4 |
DOIs | |
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