Networks with small stretch number

S CICERONE
2004 Journal of Discrete Algorithms  
In a previous work, the authors introduced the class of graphs with bounded induced distance of order k (BID(k) for short), to model non-reliable interconnection networks. A network modeled as a graph in BID(k) can be characterized as follows: if some nodes have failed, as long as two nodes remain connected, the distance between these nodes in the faulty graph is at most k times the distance in the non-faulty graph. The smallest k such that G ∈ BID(k) is called stretch number of G. We show an
more » ... d characteristic of the stretch numbers: every rational number greater or equal 2 is a stretch number, but only discrete values are admissible for smaller stretch numbers. Moreover, we give a new characterization of classes BID(2−1/i), i 1, based on forbidden induced subgraphs. By using this characterization, we provide a polynomial time recognition algorithm for graphs belonging to these classes, while the general recognition problem is Co-NP-complete.
doi:10.1016/s1570-8667(04)00016-4 fatcat:ci2l7yqw3fgnvonz5m7cvw4dum