Utilizing Minimum Set-Cover Structures with Several Constraints for Knowledge Discovery on Large Literature Databases

A lot of problems in natural language processing and knowledge discovery 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.