## Elastic algorithms for guaranteeing quality monotonicity in big data mining

In Big Data, 2013 IEEE International Conference on, pp. 45-50. IEEE, 2013 (2014)

Given a directed graph *G * and a threshold L(r)

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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)

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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−ϵ}

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inapproximability result for the general case and a

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inapproximability result for the special case with the maximum threshold of 1.