  This paper explores combinatorial optimization for problems of max-weight
graph matching on multi-partite graphs, which arise in integrating multiple
data sources. Entity resolution-the data integration problem of performing
noisy joins on structured data-typically proceeds by first hashing each record
into zero or more blocks, scoring pairs of records that are co-blocked for
similarity, and then matching pairs of sufficient similarity. In the most
common case of matching two sources, it is often desirable for the final
matching to be one-to-one (a record may be matched with at most one other);
members of the database and statistical record linkage communities accomplish
such matchings in the final stage by weighted bipartite graph matching on
similarity scores. Such matchings are intuitively appealing: they leverage a
natural global property of many real-world entity stores-that of being nearly
deduped-and are known to provide significant improvements to precision and
recall. Unfortunately unlike the bipartite case, exact max-weight matching on
multi-partite graphs is known to be NP-hard. Our two-fold algorithmic
contributions approximate multi-partite max-weight matching: our first
algorithm borrows optimization techniques common to Bayesian probabilistic
inference; our second is a greedy approximation algorithm. In addition to a
theoretical guarantee on the latter, we present comparisons on a real-world ER
problem from Bing significantly larger than typically found in the literature,
publication data, and on a series of synthetic problems. Our results quantify
significant improvements due to exploiting multiple sources, which are made
possible by global one-to-one constraints linking otherwise independent
matching sub-problems. We also discover that our algorithms are complementary:
one being much more robust under noise, and the other being simple to implement
and very fast to run.
