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Algorithmica

, Volume 7, Issue 1–6, pp 277–288 | Cite as

The rectilinear steiner arborescence problem

  • Sailesh K. Rao
  • P. Sadayappan
  • Frank K. Hwang
  • Peter W. Shor
Article

Abstract

The Rectilinear Steiner Arborescence (RSA) problem is “Given a setN ofn nodes lying in the first quadrant of E2, find the shortest directed tree rooted at the origin, containing all nodes inN, and composed solely of horizontal and vertical arcs oriented only from left to right or from bottom to top.” In this paper we investigate many fundamental properties of the RSA problem, propose anO(n logn)-time heuristic algorithm giving an RSA whose length has an upper bound of twice that of the minimum length RSA, and show that a polynomial-time algorithm that was earlier reported in the literature for this problem is incorrect.

Key words

Steiner trees Rectilinear distance Directed graphs Steiner ratio Heuristics 

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Copyright information

© Springer-Verlag New York Inc. 1992

Authors and Affiliations

  • Sailesh K. Rao
    • 1
  • P. Sadayappan
    • 2
  • Frank K. Hwang
    • 3
  • Peter W. Shor
    • 3
  1. 1.AT&T Bell LaboratoriesHolmdelUSA
  2. 2.Department of Computer ScienceOhio State UniversityColumbusUSA
  3. 3.AT&T Bell LaboratoriesMurray HillUSA

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