Get a Sample for a Discount

Abstract

While price and data quality should define the major trade-off for consumers in data markets, prices are usually prescribed by vendors and data quality is not negotiable. In this paper we study a model where data quality can be traded for a discount. We focus on the case of XML documents and consider completeness as the quality dimension. In our setting, the data provider offers an XML document, and sets both the price of the document and a weight to each node of the document, depending on its potential worth. The data consumer proposes a price. If the proposed price is lower than that of the entire document, then the data consumer receives a sample, i.e., a random rooted subtree of the document whose selection depends on the discounted price and the weight of nodes. By requesting several samples, the data consumer can iteratively explore the data in the document. We show that the uniform random sampling of a rooted subtree with prescribed weight is unfortunately intractable. However, we are able to identify several practical cases that are tractable. The first case is uniform random sampling of a rooted subtree with prescribed size; the second case restricts to binary weights. For both these practical cases we present polynomial-time algorithms and explain how they can be integrated into an iterative exploratory sampling approach.