Market Pricing for Data Streams

Abstract

Internet-enabled marketplaces such as Amazon deal with huge datasets registering transaction of merchandises between lots of buyers and sellers. It is important that algorithms become more time and space efficient as the size of datasets increase. An algorithm that runs in polynomial time may not have a reasonable running time for such large datasets. Here, we study the development of pricing algorithms that are appropriate for use with massive datasets. We especially focus on the streaming setting, the common model for big data analysis. We present an envy-free mechanism for social welfare maximization problem in the streaming setting using O(k2 l) space, where k is the number of different goods and l is the number of available items of each good. We also provide an α-approximation mechanism for revenue maximization in this setting given an α-approximation mechanism for the corresponding offline problem exists. Moreover, we provide mechanisms to approximate the optimum social welfare (or revenue) within 1 – ε factor, in space independent of l which would be favorable in case l is large compared to k. Finally, we present hardness results showing approximation of optimal prices that maximize social welfare (or revenue) in the streaming setting needs Ω(l) space. We achieve our results by developing a powerful sampling technique for bipartite networks. The simplicity of our sampling technique empowers us to maintain the sample over the input sequence. Indeed, one can construct this sample in the distributed setting (a.k.a, MapReduce) and get the same results in two rounds of computations, or one may simply apply this sampling technique to provide faster offline algorithms.