LP Randomized Rounding for Maximum Coverage Problem and Minimum Set Cover with Threshold Problem

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There are abundance of web accessible life science sources. Traversal of a particular path can answer a navigational query, returning a target object set (TOS). The cardinality of TOS is considered as the benefit of a path and there is some cost function associated with each path. It is common that multiple alternate paths satisfy the query and we are not allowed to pick all these paths to answer the query, since there could be exponential number of paths in a graph. We are interested in selecting a subset of these paths.

We present two problems in this context. The first problem is to select a subset of paths of maximum benefit within a cost budget. This is known as {\em Budgeted Maximum Coverage Problem} in the literature. The second problem is to select a subset of paths of minimum cost with a threshold benefit guarantee. This is the {\em Minimum Set Cover with Threshold Problem}. We develop randomized approximation algorithms based on LP rounding and conduct experiments.