# Anti Tai Mapping for Unordered Labeled Trees

@article{Blazevic2021AntiTM, title={Anti Tai Mapping for Unordered Labeled Trees}, author={Mislav Blazevic and Stefan Canzar and Khaled M. Elbassioni and Domagoj Matijevic}, journal={ArXiv}, year={2021}, volume={abs/2107.08292} }

The well-studied Tai mapping between two rooted labeled trees T1(V1, E1) and T2(V2, E2) defines a one-to-one mapping between nodes in T1 and T2 that preserves ancestor relationship [1]. For unordered trees the problem of finding a maximum-weight Tai mapping is known to be NP-complete [2]. In this work, we define an anti Tai mapping M ⊆ V1 × V2 as a binary relation between two unordered labeled trees such that any two (x, y), (x′, y′) ∈M violate ancestor relationship and thus cannot be part of…

## References

SHOWING 1-10 OF 16 REFERENCES

Tai Mapping Hierarchy for Rooted Labeled Trees Through Common Subforest

- Mathematics, Computer ScienceTheory of Computing Systems
- 2016

The Tai mapping hierarchy is characterized as a common subforest by focusing on the connections of nodes and the arrangements of subtrees in a commonSubforest by introducing several new variations.

Fast Computation of the Tree Edit Distance between Unordered Trees Using IP Solvers

- Mathematics, Computer ScienceDiscovery Science
- 2014

The method can efficiently compute ariations of the tree edit distance by adding additional constraints and is much faster than an existing method if input trees have a large degree and it is shown that two variations of theTree edit distance could be computed efficiently by IP solvers.

The Tree-to-Tree Correction Problem

- Computer ScienceJACM
- 1979

An algorithm is presented which solves the problem of determining the distance from T to T' as measured by the mlmmum cost sequence of edit operaUons needed to transform T into T'.

Improved Methods for Computing Distances Between Unordered Trees Using Integer Programming

- Mathematics, Computer ScienceCOCOA
- 2017

This work proposes new integer linear programming formulations for these three distances and the bottom-up distance by combining with dynamic programming and shows that these methods remarkably outperformed to the previous methods.

A clique-based method for the edit distance between unordered trees and its application to analysis of glycan structures

- Computer Science, MedicineBMC Bioinformatics
- 2011

The result suggests that the proposed method can efficiently compute the edit distance for moderate size unordered trees and has the accuracy comparative to those by the edit Distance for ordered trees and by an existing method for glycan search.

Some MAX SNP-Hard Results Concerning Unordered Labeled Trees

- Mathematics, Computer ScienceInf. Process. Lett.
- 1994

Given two rooted, labeled, and unordered trees, it is shown that both problems are MAX SNP-hard, which means that neither problem has a polynomial time approximation scheme (PTAS) unless P = NP.

On a matching distance between rooted phylogenetic trees

- Mathematics, Computer ScienceInt. J. Appl. Math. Comput. Sci.
- 2013

This paper defines and explores in detail properties of the Matching Cluster (MC) distance, which can be regarded as a refinement of the RF metric for rooted trees, but the distance evaluation is more complex.

The Generalized Robinson-Foulds Metric

- Computer Science, MathematicsWABI
- 2013

This work proposes a natural extension of the RF metric that does not simply count identical clades but instead, also takes similar clades into consideration, and finds that matchings that respect the tree structure differ significantly from those that do not, underlining the importance of this natural condition.

On the Editing Distance Between Unordered Labeled Trees

- Mathematics, Computer ScienceInf. Process. Lett.
- 1992

This paper gives efficient polynomial-time algorithms for the case when one tree is a string or has a bounded number of leaves and shows that the problem is NP-complete even for binary trees having a label alphabet of size two.

A gene ontology inferred from molecular networks

- Biology, MedicineNature Biotechnology
- 2013

It is shown that large networks of gene and protein interactions in Saccharomyces cerevisiae can be used to infer an ontology whose coverage and power are equivalent to those of the manually curated Gene Ontology (GO).