Abstract
BackgroundA bisection-type algorithm for the grammar-based compression of tree-structured data has been proposed recently. In this framework, an elementary ordered-tree grammar (EOTG) and an elementary unordered-tree grammar (EUTG) were defined, and an approximation algorithm was proposed.ResultsIn this paper, we propose an integer programming-based method that finds the minimum context-free grammar (CFG) for a given string under the condition that at most two symbols appear on the right-hand side of each production rule. Next, we extend this method to find the minimum EOTG and EUTG grammars for given ordered and unordered trees, respectively. Then, we conduct computational experiments for the ordered and unordered artificial trees. Finally, we apply our methods to pattern extraction of glycan tree structures.ConclusionsWe propose integer programming-based methods that find the minimum CFG, EOTG, and EUTG for given strings, ordered and unordered trees. Our proposed methods for trees are useful for extracting patterns of glycan tree structures.
Highlights
A bisection-type algorithm for the grammar-based compression of tree-structured data has been proposed recently
We propose an integer programming (IP)-based method that finds the minimum context-free grammar (CFG) for a given string under the condition that at most two symbols appear on the right-hand side of each production rule
We extend the elementary ordered-tree grammar (EOTG) to a grammar for the unordered trees, called the elementary unordered tree grammar (EUTG) [10], and use a simple elementary unorderedtree grammar (EUTG) for rooted unordered tree compression
Summary
A bisection-type algorithm for the grammar-based compression of tree-structured data has been proposed recently. In this framework, an elementary ordered-tree grammar (EOTG) and an elementary unorderedtree grammar (EUTG) were defined, and an approximation algorithm was proposed. Li et al proposed the universal similarity metric (USM), and approximated the dissimilarity using compression sizes. They applied a compression algorithm to unaligned mitochondrial genomes, and obtained a phylogeny that was consistent with the commonly accepted one [1]. Protein tertiary structures and metabolic networks were compressed, and their similarities were minimum grammar, nor they achieve a guaranteed approximation ratio
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