Minimum Information Dominating Set for Opinion Sampling
Abstract
We consider the problem of inferring the opinions of a social network through strategically sampling a minimum subset of nodes by exploiting correlations in node opinions. We first introduce the concept of information dominating set (IDS). A subset of nodes in a given network is an IDS if knowing the opinions of nodes in this subset is sufficient to infer the opinion of the entire network. We focus on two fundamental algorithmic problems: (i) given a subset of the network, how to determine whether it is an IDS; (ii) how to construct a minimum IDS. Assuming binary opinions and the local majority rule for opinion correlation, we show that the first problem is coNPcomplete and the second problem is NPhard in general networks. We then focus on networks with special structures, in particular, acyclic networks. We show that in acyclic networks, both problems admit linearcomplexity solutions by establishing a connection between the IDS problems and the vertex cover problem. Our technique for establishing the hardness of the IDS problems is based on a novel graph transformation that transforms the IDS problems in a general network to that in an odddegree network. This graph transformation technique not only gives an approximation algorithm to the IDS problems, but also provides a useful tool for general studies related to the local majority rule. Besides opinion sampling for applications such as political polling and market survey, the concept of IDS and the results obtained in this paper also find applications in data compression and identifying critical nodes in information networks.
 Publication:

arXiv eprints
 Pub Date:
 May 2014
 arXiv:
 arXiv:1405.5572
 Bibcode:
 2014arXiv1405.5572G
 Keywords:

 Computer Science  Social and Information Networks;
 Computer Science  Data Structures and Algorithms