The complexity of the characterization of networks supporting shortest-path interval routing

  • Authors:

  • T. Eilam;S. Moran;S. Zaks

  • Affiliations:

  • Department of Computer Science, The Technion-Israel Institute of Technology, Technion-City, Haifa 32000, Israel;Department of Computer Science, The Technion-Israel Institute of Technology, Technion-City, Haifa 32000, Israel;Department of Computer Science, The Technion-Israel Institute of Technology, Technion-City, Haifa 32000, Israel

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2002

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Abstract

Interval Routing is a routing method that was proposed in order to reduce the size of the routing tables by using intervals and was extensively studied and implemented. Some variants of the original method were also defined and studied. The question of characterizing networks which support optimal (i.e., shortest path) Interval Routing has been thoroughly investigated for each of the variants and under different models, with only partial answers, both positive and negative, given so far. In this paper, we study the characterization problem under the most basic model (the one unit cost), and with the most restrictive memory requirements (one interval per edge). We prove that this problem is NP-hard (even for the restricted class of graphs of diameter at most 3). Our result holds for all variants of Interval Routing. It significantly extends some related NP-hardness result, and implies that, unless P = NP, partial characterization results of some classes of networks which support shortest path Interval Routing, cannot be pushed further to lead to efficient characterizations for these classes.