  The performance of processing search queries depends heavily on the stored
index size. Accordingly, considerable research efforts have been devoted to the
development of efficient compression techniques for inverted indexes. Roughly,
index compression relies on two factors: the ordering of the indexed documents,
which strives to position similar documents in proximity, and the encoding of
the inverted lists that result from the ordered stream of documents. Large
commercial search engines index tens of billions of pages of the ever growing
Web. The sheer size of their indexes dictates the distribution of documents
among thousands of servers in a scheme called local index-partitioning, such
that each server indexes only several millions pages. Due to engineering and
runtime performance considerations, random distribution of documents to servers
is common. However, random index-partitioning among many servers adversely
impacts the resulting index sizes, as it decreases the effectiveness of
document ordering schemes. We study the impact of random index-partitioning on
document ordering schemes. We show that index-partitioning decreases the
aggregated size of the inverted lists logarithmically with the number of
servers, when documents within each server are randomly reordered. On the other
hand, the aggregated partitioned index size increases logarithmically with the
number of servers, when state-of-the-art document ordering schemes, such as
lexical URL sorting and clustering with TSP, are applied. Finally, we justify
the common practice of randomly distributing documents to servers, as we
qualitatively show that despite its ill-effects on the ensuing compression, it
decreases key factors in distributed query evaluation time by an order of
magnitude as compared with partitioning techniques that compress better.
