While price and data quality should define the major tradeoff 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 present a pseudo-polynomial time algorithm to select a rooted subtree with prescribed weight uniformly at random, but show that this problem is unfortunately intractable. Yet, we are able to identify several practical cases where our algorithm runs in polynomial time. The first case is uniform random sampling of a rooted subtree with prescribed size rather than weights; the second case restricts to binary weights.As a more challenging scenario for the sampling problem, we also study the uniform sampling of a rooted subtree of prescribed weight and prescribed height. We adapt our pseudo-polynomial time algorithm to this setting and identify tractable cases.
Order Statistics for Probabilistic Graphical Models
