Skip to main content
SpringerLink
Log in

The complexity of drawing trees nicely

  • Published:
Acta Informatica Aims and scope Submit manuscript

Summary

We investigate the complexity of producing aesthetically pleasing drawings of binary trees, drawings that are as narrow as possible. The notion of what is aesthetically pleasing is embodied in several constraints on the placement of nodes, relative to other nodes. Among the results we give are: (1) There is no obvious “principle of optimality” that can be applied, since globally narrow, aesthetic placements of trees may require wider than necessary subtrees. (2) A previously suggested heuristic can produce drawings on n-node trees that are Θ(n) times as wide as necessary. (3) The problem can be reduced in polynomial time to linear programming; hence, if the coordinates assigned to the nodes are continuous variables, then the problem can be solved in polynomial time. (4) If the placement is restricted to the integral lattice then the problem is NP-hard, as is its approximation to within a factor of about 4 per cent.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Borosh, I., Treybig, L.B.: Bounds on Positive Integral Solutions of Linear Diophantine Equations. Proc. Amer. Math. Soc. 55, 299–304 (1976)

    Google Scholar 

  2. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Co., San Francisco, 1979

    Google Scholar 

  3. Khachian, L.G.: A Polynomial Algorithm for Linear Programming. Doklady Akad. Nauk SSSR 244, 191–194 (1979)

    Google Scholar 

  4. Knott, G.D.: A Numbering System for Binary Trees. Comm. ACM 20, 113–115 (1977)

    Google Scholar 

  5. Knuth, D.E.: The Art of Computer Programming, Vol.1: Fundamental Algorithms. Addison-Wesley Publishing Co., Reading, MA, 1968

    Google Scholar 

  6. Reingold, E.M., Nievergelt, J., Deo, N.: Combinatorial Algorithms: Theory and Practice. Prentice-Hall: Englewood Cliffs, New Jersey, 1977

    Google Scholar 

  7. Reingold, E.M., Tilford, J.S.: Tidier Drawings of Trees. IEEE Trans. Software Engineerg. 7 223–228 (1981)

    Google Scholar 

  8. Sahni, S., Gonzalez, T.: P-complete Approximation Problems. J. ACM 23, 555–565 (1976)

    Google Scholar 

  9. Vaucher, J.G.: Pretty-Printing of Trees. Software-Practice and Experience 10, 553–561 (1980)

    Google Scholar 

  10. Wetherell, C., Shannon, A.: Tidy Drawings of Trees. IEEE Trans. Software Engineerg. 5, 514–520 (1979)

    Google Scholar 

Download references

Author information

Author notes

  1. Kenneth J. Supowit

    Present address: Hewlett-Packard, Computer Research Lab, 94304, Palo Alto, CA, USA

Authors and Affiliations

  1. Department of Computer Science, University of Illinois at Urbana-Champaign, 61801, Urbana, Illinois, USA

    Kenneth J. Supowit & Edward M. Reingold

Authors
  1. Kenneth J. Supowit
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Edward M. Reingold
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported in part by the National Science Foundation, grant numbers NSF MCS 77-22830, NSF MCS 79-04897, and NSF MCS 81-17364

Rights and permissions

Reprints and permissions

About this article

Cite this article

Supowit, K.J., Reingold, E.M. The complexity of drawing trees nicely. Acta Informatica 18, 377–392 (1983). https://doi.org/10.1007/BF00289576

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00289576

Keywords

Search

Navigation