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 |
|---|---|
| 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 |
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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 journal › Article
}
TY - JOUR
T1 - Degree constrained tree embedding into points in the plane
AU - Tamura, Akihisa
AU - Tamura, Yoshiko
PY - 1992/12/10
Y1 - 1992/12/10
N2 - 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.
AB - 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.
KW - combinatorial problems
KW - degree sequences
KW - Design of algorithms
KW - embeddings
KW - trees
UR - http://www.scopus.com/inward/record.url?scp=0043160038&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0043160038&partnerID=8YFLogxK
U2 - 10.1016/0020-0190(92)90087-C
DO - 10.1016/0020-0190(92)90087-C
M3 - Article
AN - SCOPUS:0043160038
VL - 44
SP - 211
EP - 214
JO - Information Processing Letters
JF - Information Processing Letters
SN - 0020-0190
IS - 4
ER -