Journal of Applied Mathematics and Computing

, Volume 32, Issue 2, pp 479–489 | Cite as

All-shortest-path 2-interval routing is NP-complete

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Abstract

k-Interval Routing Scheme (k-IRS) is a compact routing method that allows up to k interval labels to be assigned to an arc. A fundamental problem is to characterize the networks that admit k-IRS. All of the problems related to single-shortest-path k-IRS have already been shown to be NP-complete. For all-shortest-path k-IRS, the characterization problems have been proved to be NP-complete for every k≥3, and remain open for k=1,2. In this paper, we close the open case of k=2 by showing that it is NP-complete to decide whether a graph admits an all-shortest-path 2-IRS. The same proof is also valid for all-shortest-path Strict 2-IRS. All-shortest-path Strict k-IRS is previously known to be polynomial for k=1, open for k=2,3, and NP-complete for every constant k≥4.

Keywords

Interval routing schemes Compact routing NP-completeness 

Mathematics Subject Classification (2000)

05C85 94C15 68Q17 
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Copyright information

© Korean Society for Computational and Applied Mathematics 2009

Authors and Affiliations

  1. 1.Department of Computer ScienceThe University of South DakotaVermillionUSA
  2. 2.Department of Computer ScienceThe Ocean University of QingdaoQingdaoPeople’s Republic of China

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