Linear algorithm for computing a minimum weighted vertex cover in a k-terminal recursively constructed hypergraph

Informally, a recursive hypergraph class is one in which any sufficiently large member in the class can be formed by successively joining smaller members in the class at specific vertices called terminals. Letting the maximum allowable number of terminals be k, we refer to these as k-terminal hypergraphs. We give a linear-time algorithm for finding the weighted vertex cover number of a k-terminal recursively constructed hypergraph.