A Framework for Dynamic Parameterized Dictionary Matching

@inproceedings{Ganguly2016AFF,
  title={A Framework for Dynamic Parameterized Dictionary Matching},
  author={Arnab Ganguly and Wing-Kai Hon and Rahul Shah},
  booktitle={SWAT},
  year={2016}
}
Two equal-length strings S and S' are a parameterized-match (p-match) iff there exists a one-to-one function that renames the characters in S to those in S'. Let P be a collection of d patterns of total length n characters that are chosen from an alphabet Sigma of cardinality sigma. The task is to index P such that we can support the following operations. * search(T): given a text T, report all occurrences such that there exists a pattern P_i in P that is a p-match with the substring T[j,j… 
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A framework for designing space-efficient dictionaries for parameterized and order-preserving matching
TLDR
This paper presents indexes of the same sizes, but with slightly increased query time for order-preserving matching and parameterized matching, and considers this problem under the following definitions of matching.
Parameterized Text Indexing with One Wildcard
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An interesting generalization of this problem, where the pattern contains one wildcard character ϕ ∉ Σ that matches with any other character in Σ, and it is shown that such queries can be answered in optimal O(p+occ) time per query using an O(n log n) space index.
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TLDR
It is proved that for a constant size alphabet, there exists a randomized Monte-Carlo algorithm for the streaming dictionary matching problem that takes constant time per character and uses O(d log m) words of space, where m is the length of the longest pattern in the dictionary.
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Online Parameterized Dictionary Matching with One Gap
TLDR
This work defines and study the strict PDMOG problem, in which sub-patterns of the same dictionary pattern should be parameterized matched via the same bijection, which captures situations where sub- patterns of a dictionary pattern are encoded simultaneously.
A brief history of parameterized matching problems
Abstract Parameterized pattern matching is a string searching variant that was initially defined to detect duplicate code but later proved to support several other applications. In particular, two…
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TLDR
The paper presents two algorithms solving the Parameterized Dictionary Matching with One Gap, for dictionaries with non-uniformly bounded gaps, and suggests the related problem of Parameterize Dictionary Recognition with one Gap, which requires reporting a single parameterized appearance of each gapped pattern.
Dynamic Dictionary Matching in the Online Model
TLDR
In the online version of the dictionary matching problem, the characters of T arrive online, one at a time, and the goal is to establish, immediately after every new character arrival, which of the patterns in \(\mathcal {D}\) are a suffix of the current text.
pBWT: Achieving Succinct Data Structures for Parameterized Pattern Matching and Related Problems
TLDR
A new BWT-like transform is called pBWT, which is extended to obtain a succinct index for the Parameterized Dictionary Matching problem of Idury and Schaffer and introduces an n log σ + O(n)-bit index with O(|Plog σ+occ·log n logσ) query time.
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TLDR
A new algorithm for the KMM problem in the streaming model that, up to poly-log factors, has the same bounds as the most recent results that use different techniques, and for most inputs, is significantly faster on average.
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