On straightening low-diameter unit trees

S.H. Poon

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

6 Citations (Scopus)

Abstract

A polygonal chain is a sequence of consecutively joined edges embedded in space. A k-chain is a chain of k edges. A polygonal tree is a set of edges joined into a tree structure embedded in space. A unit tree is a tree with only edges of unit length. A chain or a tree is simple if non-adjacent edges do not intersect. We consider the problem about the reconfiguration of a simple chain or tree through a series of continuous motions such that the lengths of all tree edges are preserved and no edge crossings are allowed. A chain or tree can be straightened if all its edges can be aligned along a common straight line such that each edge points "away" from a designed leaf node. Otherwise it is called locked. Graph reconfiguration problems have wide applications in contexts including robotics, molecular conformation, rigidity and knot theory. The motivation for us to study unit trees is that for instance, the bonding-lengths in molecules are often similar, as are the segments of robot arms.
Original languageEnglish
Title of host publicationGraph Drawing (13th International Symposium, GD'05, Limerick, Ireland, September 12-14, 2005, Revised papers)
EditorsP. Healy, N.S. Nikolov
Place of PublicationBerlin
PublisherSpringer
Pages519-521
ISBN (Print)3-540-31425-3
DOIs
Publication statusPublished - 2006

Publication series

NameLecture Notes in Computer Science
Volume3843
ISSN (Print)0302-9743

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