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Estimating Absolute Web Crawl Coverage From Longitudinal Set Intersections

Michael Paris, Grigori Paris, Fabian Baumann

Abstract

Web archives preserve portions of the web, but quantifying their completeness remains challenging. Prior approaches have estimated the coverage of a crawl by either comparing the outcomes of multiple crawlers, or by comparing the results of a single crawl to external ground truth datasets. We propose a method to estimate the absolute coverage of a crawl using only the archive's own longitudinal data, i.e., the data collected by multiple subsequent crawls. Our key insight is that coverage can be estimated from the empirical URL overlaps between subsequent crawls, which are in turn well described by a simple urn process. The parameters of the urn model can then be inferred from longitudinal crawl data using linear regression. Applied to our focused crawl configuration of the German Academic Web, with 15 semi-annual crawls between 2013-2021, we find a coverage of approximately 46 percent of the crawlable URL space for the stable crawl configuration regime. Our method is extremely simple, requires no external ground truth, and generalizes to any longitudinal focused crawl.

Estimating Absolute Web Crawl Coverage From Longitudinal Set Intersections

Abstract

Web archives preserve portions of the web, but quantifying their completeness remains challenging. Prior approaches have estimated the coverage of a crawl by either comparing the outcomes of multiple crawlers, or by comparing the results of a single crawl to external ground truth datasets. We propose a method to estimate the absolute coverage of a crawl using only the archive's own longitudinal data, i.e., the data collected by multiple subsequent crawls. Our key insight is that coverage can be estimated from the empirical URL overlaps between subsequent crawls, which are in turn well described by a simple urn process. The parameters of the urn model can then be inferred from longitudinal crawl data using linear regression. Applied to our focused crawl configuration of the German Academic Web, with 15 semi-annual crawls between 2013-2021, we find a coverage of approximately 46 percent of the crawlable URL space for the stable crawl configuration regime. Our method is extremely simple, requires no external ground truth, and generalizes to any longitudinal focused crawl.
Paper Structure (7 sections, 9 equations, 3 figures, 1 table)

This paper contains 7 sections, 9 equations, 3 figures, 1 table.

Table of Contents

  1. Keywords:
  2. Introduction
  3. Related Work
  4. Theoretical intuition and urn model
  5. Results
  6. Discussion
  7. Data availability.

Figures (3)

  • Figure 1: Pairwise URL set intersections for the 15 GAW crawls. (a) The heatmap reveals temporal decay structure; the diagonal shows estimated self-intersection values. (b) Log-transformed containment vs. time difference exhibits a linear relationship.
  • Figure 2: Validation via simulation. (a) Regression on GAW data. (b) Simulation with urn model parameters recovers the same relationship, confirming the method.
  • Figure 3: Per-crawl regression analysis. (a) Separate regressions for each starting crawl yield approximately parallel lines. (b) The y-intercept (estimated $c$) shows a rising trend over 2013--2021.