Abstract
We study the properties of the intersection of independence systems. An independence system (V,I) is a k-system if for all S⊆V the ratio of the cardinality of the largest to the smallest maximal independent subset of S is at most k. We show that the intersection of a k1-system and a k2-system is a (k1+k2)-system.As an application of our results, we show an improved approximation algorithm for stochastic probing with deadlines over k-systems.
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