Skip to main content
SpringerLink
Log in

The rectilinear steiner arborescence problem

  • Published:
Algorithmica Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. F. R. K. Chung and R. L. Graham, On Steiner trees for bounded sets,Geom. Dedicata 11 (1981), 353–361.

    Article  MATH  MathSciNet  Google Scholar 

  2. L. Few, The shortest path and shortest roads throughn points,Mathematika 2 (1955), 141–144.

    Article  MATH  MathSciNet  Google Scholar 

  3. M. R. Garey and D. S. Johnson, The rectilinear Steiner tree problem is NP-complete,SIAM J, Appl. Math. 32 (1977), 826–834.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Hanan, On Steiner's problem with rectilinear distance,SIAM J. Appl. Math. 14 (1966), 255–265.

    Article  MATH  MathSciNet  Google Scholar 

  5. F. K. Hwang, On Steiner minimal trees with rectilinear distance,SIAM J. Appl. Math. 30 (1976), 104–114.

    Article  MATH  MathSciNet  Google Scholar 

  6. F. K. Hwang, AnO(n logn) algorithm for rectilinear minimal spanning trees,J. Assoc. Comput. Mach. 26 (1979), 177–182.

    MATH  MathSciNet  Google Scholar 

  7. R. R. Ladeira de Matos, A Rectilinear Arborescence Problem, Dissertation, University of Alabama, 1979.

  8. L. Nastansky, S. M. Selkow, and N. F. Stewart, Cost-minimal trees in directed acyclic graphs,Z. Oper. Res. 18 (1974), 59–67.

    Article  MATH  MathSciNet  Google Scholar 

  9. J. S. Provan, A Polynomial Algorithm for the Steiner Tree Problem on Terminal-Planar Graphs, Technical Report UNC/ORST/TR-83/10, University of North Carolina, 1983.

  10. R. E. Tarjan, Finding optimum branchings,Networks 7 (1977), 25–35.

    Article  MATH  MathSciNet  Google Scholar 

  11. V. A. Trubin, Subclass of the Steiner problems on a plane with rectilinear metric,Cybernetics 21 (1985), 320–322, translated fromKibernetika 21, No. 3 (1985), 37–40.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. AT&T Bell Laboratories, 07733, Holmdel, NJ, USA

    Sailesh K. Rao

  2. Department of Computer Science, Ohio State University, 43210, Columbus, OH, USA

    P. Sadayappan

  3. AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA

    Frank K. Hwang & Peter W. Shor

Authors
  1. Sailesh K. Rao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Sadayappan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Frank K. Hwang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Peter W. Shor
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by F. K. Hwang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rao, S.K., Sadayappan, P., Hwang, F.K. et al. The rectilinear steiner arborescence problem. Algorithmica 7, 277–288 (1992). https://doi.org/10.1007/BF01758762

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01758762

Key words

Search

Navigation