On the power laws of language: word frequency distributions

About eight decades ago, Zipf postulated that the word frequency distribution of languages is a power law, i.e., it is a straight line on a log-log plot. Over the years, this phenomenon has been documented and studied extensively. For many corpora, however, the empirical distribution barely resembles a power law: when plotted on a loglog scale, the distribution is concave and appears to be composed of two differently sloped straight lines joined by a smooth curve. A simple generative model is proposed to capture this phenomenon. Theword frequency distributions produced by this model are shown to match the observations both analytically and empirically. © 2017 Copyright held by the owner/author(s)

Compressed Web Indexes

Web search engines use indexes to efficiently retrieve pages containing specified query terms, as well as pages linking to specified pages. The problem of compressed indexes that permit such fast retrieval has a long history. We consider the problem: assuming that the terms in (or links to) a page are generated from a probability distribution, how well compactly can we build such indexes that allow fast retrieval? Of particular interest is the case when the probability distribution is Zipfian (or a similar power law), since these are the distributions that arise on the web. We obtain sharp bounds on the space requirement of Boolean indexes for text documents that follow Zipf’s law. In the process we develop a general technique that applies to any probability distribution, not necessarily a power law; this is the first analysis of compression in indexes under arbitrary distributions. Our bounds lead to quantitative versions of rules of thumb that are folklore in indexing. Our experiments on several document collections show that the distribution of terms appears to follow a double-Pareto law rather than Zipf’s law. Despite widely varying sets of documents, the index sizes observed in the experiments conform well to our theoretical predictions