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 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.

Dondi, R., Mauri, G., Zoppis, I. (2020). Complexity issues of string to graph approximate matching. In Language and Automata Theory and Applications (pp.248-259). Springer [10.1007/978-3-030-40608-0_17].

Complexity issues of string to graph approximate matching

Dondi, Riccardo
;
Mauri, Giancarlo;Zoppis, Italo
2020

Abstract

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 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.
slide + paper
Algorithms on strings, Computational complexity, Graph query, Parameterized complexity, Patterns , String to graph matching
English
International Conference on Language and Automata Theory and Applications
2020
A. Leporati; C. Martín-Vide; D. Shapira; C. Zandron
Language and Automata Theory and Applications
9783030406073
mar-2020
2020
12038
248
259
none
Dondi, R., Mauri, G., Zoppis, I. (2020). Complexity issues of string to graph approximate matching. In Language and Automata Theory and Applications (pp.248-259). Springer [10.1007/978-3-030-40608-0_17].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/265039
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