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The rectilinear steiner arborescence problem

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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.

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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
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  2. P. Sadayappan
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  3. Frank K. Hwang
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  4. Peter W. Shor
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Communicated by F. K. Hwang.

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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

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

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