Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexity Issues of String to Graph Approximate Matching   The problem of matching a query string to a directed graph, whose vertices
are labeled by strings, has application in different fields, from data mining
to computational biology. Several variants of the problem have been considered,
depending on the fact that the match is exact or approximate and, in this
latter case, which edit operations are considered and where are allowed. In
this paper we present results on the complexity of the approximate matching
problem, where edit operations are symbol substitutions and are allowed only on
the graph labels or both on the graph labels and the query string. We introduce
a variant of the problem that asks whether there exists a path in a graph that
represents a query string with any number of edit operations and we show that
is is NP-complete, even when labels have length one and in the case the
alphabet is binary. Moreover, when it is parameterized by the length of the
input string and graph labels have length one, we show that the problem is
fixed-parameter tractable and it is unlikely to admit a polynomial kernel. The
NP-completeness of this problem leads to the inapproximability (within any
factor) of the approximate matching when edit operations are allowed only on
the graph labels. Moreover, we show that the variants of approximate string
matching to graph we consider are not fixed-parameter tractable, when the
parameter is the number of edit operations, even for graphs that have distance
one from a DAG. The reduction for this latter result allows us to prove the
inapproximability of the variant where edit operations can be applied both on
the query string and on graph labels.

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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg