The bisection problem for graphs of degree 4 (configuring transputer systems)

  • Juraj Hromkovič
  • Burkhard Monien
Part of the Lecture Notes in Computer Science book series (LNCS, volume 520)


It is well known that for each k≥3 there exists such a constant c k and such an infinite sequence {Gn} n=8 of k-degree graphs (each G n has exactly n vertices) that the bisection width of G n is at least c k ·n. It this paper some upper bounds on ck's are found. Let σk(n) be the maximum of bisection widths of all k-bounded graphs of n vertices. We prove that
$$\sigma _k \left( n \right) \leqslant \frac{{\left( {k - 2} \right)}}{4} \cdot n + o\left( n \right)$$
for all k=2r, r≥2. This result is improved for k=4 by constructing two algorithms A and B, where for a given 4-degree-bounded graph G n of n vertices
  1. (i)

    A constructs a bisection of G n involving at most n/2+4 edges for even n≤76 (i.e., σ4(n)≤n/2+4 for even n≤76)

  2. (ii)

    B constructs a bisection of G n involving at most n/2+2 edges for n≥256 (i.e. σ4(n)≤n/2+2 for n≥256).


The algorithms A and B run in O(n2) time on graphs of n vertices, and they are used to optimize hardware by building large transputer systems.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Juraj Hromkovič
    • 1
  • Burkhard Monien
    • 1
  1. 1.University of PaderbornPaderbornWest Germany

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