Equispreading Tree in Manhattan Distance

M. Edahiro*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The equispreading tree on the plane with Manhattan distance, which is a Steiner tree such that all paths from the root to all leaves have the same length, is analyzed. This problem is not only fundamental in computational geometry but also critical for equidistant routings in VLSI clock design. Several characteristics for the trees are discussed together with an algorithm constructing equispreading trees in the bottom-up fashion. This algorithm achieves linear time and space complexity with respect to the number of leaves, and minimizes the path length from the root to leaves. Furthermore, this paper shows that the shortest-path-length equispreading trees are related to the smallest enclosing circles in Manhattan distance.

Original languageEnglish
Pages (from-to)316-338
Number of pages23
JournalAlgorithmica
Volume16
Issue number3
DOIs
Publication statusPublished - 1996 Sep
Externally publishedYes

Keywords

  • CAD
  • Clock routing
  • Computational geometry
  • Manhattan distance
  • Steiner tree
  • VLSI

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics

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