Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: EmbAssi: Embedding Assignment Costs for Similarity Search in Large Graph
  Databases   The graph edit distance is an intuitive measure to quantify the dissimilarity
of graphs, but its computation is NP-hard and challenging in practice. We
introduce methods for answering nearest neighbor and range queries regarding
this distance efficiently for large databases with up to millions of graphs. We
build on the filter-verification paradigm, where lower and upper bounds are
used to reduce the number of exact computations of the graph edit distance.
Highly effective bounds for this involve solving a linear assignment problem
for each graph in the database, which is prohibitive in massive datasets.
Index-based approaches typically provide only weak bounds leading to high
computational costs verification. In this work, we derive novel lower bounds
for efficient filtering from restricted assignment problems, where the cost
function is a tree metric. This special case allows embedding the costs of
optimal assignments isometrically into $\ell_1$ space, rendering efficient
indexing possible. We propose several lower bounds of the graph edit distance
obtained from tree metrics reflecting the edit costs, which are combined for
effective filtering. Our method termed EmbAssi can be integrated into existing
filter-verification pipelines as a fast and effective pre-filtering step.
Empirically we show that for many real-world graphs our lower bounds are
already close to the exact graph edit distance, while our index construction
and search scales to very large databases.

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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
31
The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: dg-ga