Advertisement

Journal of Combinatorial Optimization

, Volume 30, Issue 3, pp 768–802 | Cite as

Heuristics for the data arrangement problem on regular trees

  • Eranda Çela
  • Rostislav Staněk
Article

Abstract

The data arrangement problem on regular trees (DAPT) consists in assigning the vertices of a given graph G to the leaves of a d-regular tree T such that the sum of the pairwise distances of all pairs of leaves in T which correspond to edges of G is minimised. This problem is a special case of the generic graph embedding problem and is NP-hard for every fixed \(d\ge 2\). In this paper we propose construction and local search heuristics for the DAPT and introduce a lower bound for this problem. The analysis of the performance of the heuristics is based on two considerations: (a) the quality of the solutions produced by the heuristics as compared to the respective lower bound (b) for a special class of instances with known optimal solution we evaluate the gap between the optimal value of the objective function and the objective function value attained by the heuristic solution, respectively.

Keywords

Combinatorial optimisation Data arrangement problem  Regular trees Heuristics 

Mathematics Subject Classification

90C27 

Notes

Acknowledgments

The research was funded by the Austrian Science Fund (FWF): P23829.

References

  1. Çela E, Staněk R (2013) Polynomially solvable special cases of the data arrangement problem on regular trees, working paperGoogle Scholar
  2. Chung FRK (1984) An optimal linear arrangement of trees. Comput Math Appl 10:43–60zbMATHMathSciNetCrossRefGoogle Scholar
  3. Feige U, Krauthgamer R, Nissim K (2003) On cutting a few vertices from a graph. Discret Appl Math 127:643–649zbMATHMathSciNetCrossRefGoogle Scholar
  4. Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. Series of books in the mathematical sciences, p 210Google Scholar
  5. Juvan M, Mohar B (1992) Optimal linear labelings and eigenvalues of graphs. Discret Appl Math 36(2): 153–168Google Scholar
  6. Luzcak MJ, Noble SD (1992) Optimal arrangement of data in a tree directory. Discret Appl Math 121(1–3):307–315Google Scholar
  7. Petit J (1998) Approximation heuristics and benchmarkings for the MinLA problem. In: Battiti R, Bertossi A (eds) Algorithms and experiments (ALEX98)—Building bridges between theory and applications, pp 112–128Google Scholar
  8. Petit J (2003) Experiments on the minimum linear arrangement problem. ACM J Exp Algorithm 8:307–315MathSciNetGoogle Scholar
  9. Shiloach Y (1979) A minimum linear arrangement algorithm for undirected trees. SIAM J Comput 8:15–22zbMATHMathSciNetCrossRefGoogle Scholar
  10. Staněk R (2012) Heuristiken für das optimale data-arrangement-problem in einem baum. Master’s thesis, Graz Univeristy of Technology, in GermanGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institut für Optimierung und Diskrete MathematikTU GrazGrazAustria
  2. 2.Institut für Statistik und Operations ResearchUniversität GrazGrazAustria

Personalised recommendations