On the inapproximability of minimizing cascading failures under the deterministic threshold model

Authors:
Lei Nie;Jingjie Liu;Haicang Zhang;Zhiwei Xu
Affiliations:
Institute of Computing Technology, Chinese Academy of Sciences, China and University of Chinese Academy of Sciences, China;Institute of Computing Technology, Chinese Academy of Sciences, China and University of Chinese Academy of Sciences, China;Institute of Computing Technology, Chinese Academy of Sciences, China and University of Chinese Academy of Sciences, China;Institute of Computing Technology, Chinese Academy of Sciences, China
Venue:
Information Processing Letters
Year:
2014

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Abstract

Given a directed graph G and a threshold L(r) for each node r, the rule of deterministic threshold cascading is that a node r fails if and only if it has at least L(r) failed in-neighbors. The cascading failure minimization problem is to find at most k edges to delete, such that the number of failed nodes is minimized. We prove an n^1^-^@e inapproximability result for the general case and a 12n^@e inapproximability result for the special case with the maximum threshold of 1.