A Polynomial Time Algorithm for Finding a Minimally Generalized Linear Interval Graph Pattern

Yamasaki, Hideo; Shoudai, Takayoshi

doi:10.1587/transinf.e92.d.120

Cited by 5 publications

(2 citation statements)

References 14 publications

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“…This is more like learning special types of graph languages, and the research has been moved into that direction, mostly driven by Shoudai and his co-authors; we only refer to [215,217], but there are more papers in that research area. There have also been investigations of a purely graph-theoretical nature, for instance, the inference and recovery of edge-colored trees from sequences of edge colors obtained from walking a tree [150].…”

Section: Text Learning Of Tree Patternsmentioning

confidence: 99%

Learning Tree Languages

Björklund

Fernau

2016

Topics in Grammatical Inference

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Tree languages have proved to be a versatile and rewarding extension of the classical notion of string languages. Many nice applications have been established over the years, in areas such as Natural Language Processing, Information Extraction, and Computational Biology. Although some properties of string languages transfer easily to the tree case, in particular for regular languages, several computational aspects turn out to be harder. It is therefore both of theoretical and of practical interest to investigate how far and in what ways Grammatical Inference algorithms developed for the string case are applicable to trees. This chapter surveys known results in this direction. We begin by recalling the basics of tree language theory. Then, the most popular learning scenarios and algorithms are presented. Several applications of Grammatical Inference of tree languages are reviewed in some detail. We conclude by suggesting a number of directions for future research.

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Section: Text Learning Of Tree Patternsmentioning

confidence: 99%

Learning Tree Languages

Björklund

Fernau

2016

Topics in Grammatical Inference

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“…We considered the inference of ordered term tree patterns [13], TTSP graph patterns [14], and interval graph patterns [15]. Since cographs are P 4 -free, cograph patterns have expressive power incomparable with these patterns.…”

Section: Introductionmentioning

confidence: 99%

Polynomial Time Learnability of Graph Pattern Languages Defined by Cographs

Shoudai

Yoshimura

Suzuki

et al. 2018

IEICE Trans. Inf. & Syst.

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A cograph (complement reducible graph) is a graph which can be generated by disjoint union and complement operations on graphs, starting with a single vertex graph. Cographs arise in many areas of computer science and are studied extensively. With the goal of developing an effective data mining method for graph structured data, in this paper we introduce a graph pattern expression, called a cograph pattern, which is a special type of cograph having structured variables. Firstly, we show that a problem whether or not a given cograph pattern g matches a given cograph G is NP-complete. From this result, we consider the polynomial time learnability of cograph pattern languages defined by cograph patterns having variables labeled with mutually different labels, called linear cograph patterns. Secondly, we present a polynomial time matching algorithm for linear cograph patterns. Next, we give a polynomial time algorithm for obtaining a minimally generalized linear cograph pattern which explains given positive data. Finally, we show that the class of linear cograph pattern languages is polynomial time inductively inferable from positive data.

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