A Minimum Set-Cover Problem with several constraints

A lot of problems in natural language processing can be interpreted using structures from discrete mathematics. In this paper we will discuss the search query and topic finding problem using a generic context-based approach. This problem can be described as a Minimum Set Cover Problem with several constraints. The goal is to find a minimum covering of documents with the given context for a fixed weight function. The aim of this problem reformulation is a deeper understanding of both the hierarchical problem using union and cut as well as the non-hierarchical problem using the union. We thus choose a modeling using bipartite graphs and suggest a novel reformulation using an integer linear program as well as novel graph-theoretic approaches.