Generalized minimum dominating set and application in automatic text summarization

TL;DR

This paper introduces a generalized minimum dominating set problem on weighted graphs, solved via spin glass theory and belief propagation, with an application to automatic text summarization.

Contribution

It formulates a new generalized MDS problem and applies statistical physics methods to improve automatic text summarization.

Findings

Belief propagation equations derived for the generalized MDS.

Preliminary tests show promise in text summarization.

Method extends traditional MDS to weighted graph scenarios.

Abstract

For a graph formed by vertices and weighted edges, a generalized minimum dominating set (MDS) is a vertex set of smallest cardinality such that the summed weight of edges from each outside vertex to vertices in this set is equal to or larger than certain threshold value. This generalized MDS problem reduces to the conventional MDS problem in the limiting case of all the edge weights being equal to the threshold value. We treat the generalized MDS problem in the present paper by a replica-symmetric spin glass theory and derive a set of belief-propagation equations. As a practical application we consider the problem of extracting a set of sentences that best summarize a given input text document. We carry out a preliminary test of the statistical physics-inspired method to this automatic text summarization problem.