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Combinatorica

, Volume 9, Issue 2, pp 111–131 | Cite as

A Dynamic location problem for graphs

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

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 

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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

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