Biased respondent group selection under limited budget for minority opinion survey

This paper discusses a new approach to use the information from a special social network with high homophily to select a survey respondent group under a limited budget such that the result of the survey is biased to the minority opinions. This approach has a wide range of potential applications, e.g. collecting complaints from the customers of a new product while most of them are satisfied. We formally define the problem of computing such group with better utilization as the p-biased representative selection problem (p-BRSP). This problem has two separate objectives and is difficult to deal with. Thus, we also propose a new unified-objective which is a function of the two optimization objectives. Most importantly, we introduce two polynomial time heuristic algorithms for the problem, where each of which has an approximation ratio with respect to each of the objectives.