Combinatorica

, Volume 9, Issue 2, pp 111–131

A Dynamic location problem for graphs

  • F. R. K. Chung
  • R. L. Graham
  • M. E. Saks
Article

DOI: 10.1007/BF02124674

Cite this article as:
Chung, F.R.K., Graham, R.L. & Saks, M.E. Combinatorica (1989) 9: 111. doi:10.1007/BF02124674

Abstract

We introduce a class of optimization problems, calleddynamic location problems, involving the processing of requests that occur sequentially at the nodes of a graphG. This leads to the definition of a new parameter of graphs, called the window indexWX(G), that measures how large a “window” into the future is needed to solve every instance of the dynamic location problem onG optimally on-line. We completely characterize this parameter:WX(G)≦k if and only ifG is a weak retract of a product of complete graphs of size at mostk. As a byproduct, we obtain two (polynomially recognizable) structural characterizations of such graphs, extending a result of Bandelt.

AMS subject classification (1980)

05 C 75

Copyright information

© Akadémiai Kiadó 1989

Authors and Affiliations

  • F. R. K. Chung
    • 1
  • R. L. Graham
    • 2
    • 3
  • M. E. Saks
    • 1
    • 3
  1. 1.Bell Communications Research MorristownUSA
  2. 2.AT&T Bell Laboratories Murray HillUSA
  3. 3.Department of Mathematics and RUTCORRutgers University New BrunswickUSA