Advertisement

Abstract

We deal with the problem of maintaining the heaviest paths in a DAG under edge insertion and deletion. Michel and Van Hentenryck [2] designed algorithms for this problem which work on DAGs with strictly positive edge weights. They handle edges of zero or negative weight by replacing each of them by (potentially many) edges with positive weights. In this paper we show an alternative solution, which has the same complexity and handles arbitrary edge weights without graph transformations. For the case in which all edge weights are integers, we show a second algorithm which is asymptotically faster.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fredman, M.L., Tarjan, R.E.: Fibonacci heaps and their uses in improved network optimization algorithms. J. Assoc. Comput. Mach. 34, 596–615 (1987)MathSciNetGoogle Scholar
  2. 2.
    Michel, L., Van Hentenryck, P.: Maintaining longest paths incrementally. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 540–554. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    Ramalingam, G., Reps, T.: On the computational complexity of dynamic graph problems. Theor. Comput. Sci. 158(1-2), 233–277 (1996)CrossRefMathSciNetzbMATHGoogle Scholar
  4. 4.
    Mikkel Thorup. Integer priority queues with decrease key in constant time and the single source shortest paths problem. In Proc. 35th ACM Symp. on Theory of Computing (STOC), pages 149–158, 2003.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Irit Katriel
    • 1
  1. 1.Max-Planck-Institut für Informatik SaarbrückenGermany

Personalised recommendations