Motivated by a growing market that involves buying and selling data over the web, we study pricing schemes that assign value to queries issued over a database. Previous work studied pricing mechanisms that compute the price of a query by extending a data seller's explicit prices on certain queries, or investigated the properties that a pricing function should exhibit without detailing a generic construction. In this work, we present a formal framework for pricing queries over data that allows the construction of general families of pricing functions, with the main goal of avoiding arbitrage. We consider two types of pricing schemes: instance-independent schemes, where the price depends only on the structure of the query, and answer-dependent schemes, where the price also depends on the query output. Our main result is a complete characterization of the structure of pricing functions in both settings, by relating it to properties of a function over a lattice. We use our characterization, together with information-theoretic methods, to construct a variety of arbitrage-free pricing functions. Finally, we discuss various tradeoffs in the design space and present techniques for efficient computation of the proposed pricing functions.
The first formal framework for query-based data pricing was introduced by @cite_15 . The authors define the notion of arbitrage, and provide a framework that takes a set of fixed prices for views over the data identified by seller, and extends these price points to a pricing function over any query. The authors also show that evaluation of the prices can be done efficiently in polynomial time for specific classes of conjunctive queries and a restricted set of views that include only selections. Subsequently, the authors demonstrated how the framework can be implemented into a prototype pricing system called QueryMarket @cite_1 @cite_26 . Further work @cite_4 discusses the pricing and complexity of pricing for the class of aggregate queries. The work by Lin and Kifer @cite_16 proposes several possible forms of arbitrage violations and integrates them into a single framework. The authors allow the queries to be randomized, and propose two potential pricing functions that are arbitrage-free across all forms.
@cite_26 @cite_4 @cite_1 @cite_15 @cite_16
2399897640 2065504152 2168402580 2272515049
In a data marketplace, producers of data provide query answers to consumers in exchange for payment. A market for data allows capital to flow from data consumers to data producers. This helps to finance the costs of data collection and dissemination, thereby increasing the availability of data throughout society. While nascent data markets exist on the Web, they are currently limited in the pricing mechanisms and interactions they support. In this paper we propose new criteria for interactive pricing in a data market: price functions should be non-disclosive, arbitrage-free, and regret-free. We study the structure of price functions meeting these criteria, and distinguish between NP-complete and PTIME cases for computing a conforming price function. Increasingly data is being bought and sold online. To facilitate such transactions, online data market-places have emerged to provide a service for sellers to price views on their data, and buyers to buy such views. These marketplaces neither support the sale of ad-hoc queries (that are not one of the specified views), nor do they support queries that join datasets. We present QueryMarket, a prototype data marketplace that automatically extrapolates prices to ad-hoc queries, including those with joins, from the manually priced views. We call this capability "query-based pricing" and describe how it is superior to existing pricing methods, and how it provides more flexible pricing for the sellers. We then show how QueryMarket implements query-based pricing and how it generates explanations for the prices it computes. Data is increasingly being bought and sold online, and Web-based marketplace services have emerged to facilitate these activities. However, current mechanisms for pricing data are very simple: buyers can choose only from a set of explicit views, each with a specific price. In this paper, we propose a framework for pricing data on the Internet that, given the price of a few views, allows the price of any query to be derived automatically. We call this capability "query-based pricing." We first identify two important properties that the pricing function must satisfy, called arbitrage-free and discount-free. Then, we prove that there exists a unique function that satisfies these properties and extends the seller's explicit prices to all queries. When both the views and the query are Unions of Conjunctive Queries, the complexity of computing the price is high. To ensure tractability, we restrict the explicit prices to be defined only on selection views (which is the common practice today). We give an algorithm with polynomial time data complexity for computing the price of any chain query by reducing the problem to network flow. Furthermore, we completely characterize the class of Conjunctive Queries without self-joins that have PTIME data complexity (this class is slightly larger than chain queries), and prove that pricing all other queries is NP-complete, thus establishing a dichotomy on the complexity of the pricing problem when all views are selection queries. Data is a commodity. Recent research has considered the mathematical problem of setting prices for different queries over data. Ideal pricing functions need to be flexible --defined for arbitrary queries (select-project-join, aggregate, random sample, and noisy privacy-preserving queries). They should be fine-grained -- a consumer should not be required to buy the entire database to get answers to simple "low-information" queries (such as selecting only a few tuples or aggregating over only one attribute). Similarly, a consumer may not want to pay a large amount of money, only to discover that the database is empty. Finally, pricing functions should satisfy consistency conditions such as being "arbitrage-free" -- consumers should not be able to circumvent the pricing function by deducing the answer to an expensive query from a few cheap queries. Previously proposed pricing functions satisfy some of these criteria (i.e. they are defined for restricted subclasses of queries and or use relaxed conditions for avoiding arbitrage). In this paper, we study arbitrage-free pricing functions defined for arbitrary queries. We propose new necessary conditions for avoiding arbitrage and provide new arbitrage-free pricing functions. We also prove several negative results related to the tension between flexible pricing and avoiding arbitrage, and show how this tension often results in unreasonable prices.