Anti Tai Mapping for Unordered Labeled Trees
Mislav Bla\v{z}evi\'c, Stefan Canzar, Khaled Elbassioni, Domagoj, Matijevi\'c

TL;DR
This paper introduces the concept of anti Tai mappings for unordered labeled trees, providing polynomial algorithms for special cases and a lower bound approach for the general problem, aiding in solving the maximum-weight Tai mapping.
Contribution
It defines anti Tai mappings and develops polynomial algorithms for cases where one tree is a path and for a restricted class of mappings, advancing methods to approximate maximum-weight Tai mappings.
Findings
Polynomial-time algorithm for anti Tai mapping when one tree is a path.
Extension to a lower bound for general unordered trees.
Efficient algorithm for a restricted class of anti Tai mappings in quadratic time.
Abstract
The well-studied Tai mapping between two rooted labeled trees and defines a one-to-one mapping between nodes in and that preserves ancestor relationship. For unordered trees the problem of finding a maximum-weight Tai mapping is known to be NP-complete. In this work, we define an anti Tai mapping as a binary relation between two unordered labeled trees such that any two violate ancestor relationship and thus cannot be part of the same Tai mapping, i.e. , given an ancestor order meaning that is an ancestor of . Finding a maximum-weight anti Tai mapping arises in the cutting plane method for solving the maximum-weight Tai mapping problem via integer programming. We give an efficient polynomial-time algorithm for finding…
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