Affiliation:
1. Hebrew University of Jerusalem, Jerusalem, Israel
Abstract
This article investigates the problem of learning tree patterns that return nodes with a given set of labels, from example graphs provided by the user. Example graphs are annotated by the user as being either
positive
or
negative
. The goal is then to determine whether there exists a tree pattern returning tuples of nodes with the given labels in each of the positive examples, but in none of the negative examples, and furthermore, to find one such pattern if it exists. These are called the
satisfiability
and
learning
problems, respectively.
This article thoroughly investigates the satisfiability and learning problems in a variety of settings. In particular, we consider example sets that (1) may contain only positive examples, or both positive and negative examples, (2) may contain directed or undirected graphs, and (3) may have multiple occurrences of labels or be uniquely labeled (to some degree). In addition, we consider tree patterns of different types that can allow, or prohibit, wildcard labeled nodes and descendant edges. We also consider two different semantics for mapping tree patterns to graphs. The complexity of satisfiability is determined for the different combinations of settings. For cases in which satisfiability is polynomial, it is also shown that learning is polynomial. (This is nontrivial as satisfying patterns may be exponential in size.) Finally, the
minimal learning
problem, that is, that of finding a minimal-sized satisfying pattern, is studied for cases in which satisfiability is polynomial.
Funder
Israel Science Foundation
Ministry of Science and Technology
Publisher
Association for Computing Machinery (ACM)
Cited by
4 articles.
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