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An Even Faster and More Unifying Algorithm for Comparing Trees via Unbalanced Bipartite Matchings
TLDR
In this article, the authors presented an algorithm for comparing trees that are labeled in an arbitrary manner, which is faster than the previous algorithms and is at the core of their maximum agreement subtree algorithm.Abstract:
A widely used method for determining the similarity of two labeled trees is to compute a maximum agreement subtree of the two trees. Previous work on this similarity measure is only concerned with the comparison of labeled trees of two special kinds, namely, uniformly labeled trees (i.e., trees with all their nodes labeled by the same symbol) and evolutionary trees (i.e., leaf-labeled trees with distinct symbols for distinct leaves). This paper presents an algorithm for comparing trees that are labeled in an arbitrary manner. In addition to this generality, this algorithm is faster than the previous algorithms.
Another contribution of this paper is on maximum weight bipartite matchings. We show how to speed up the best known matching algorithms when the input graphs are node-unbalanced or weight-unbalanced. Based on these enhancements, we obtain an efficient algorithm for a new matching problem called the hierarchical bipartite matching problem, which is at the core of our maximum agreement subtree algorithm.read more
Citations
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Dissertation
Consensus Algorithms for Trees and Strings
TL;DR: This thesis studies the computational complexity and polynomial-time approximability of a number of discrete combinatorial optimization problems involving labeled trees and strings and presents new inapproximability results and various types of approximation algorithms as well as exact polynometric-time algorithms for certain restrictions of the problems.
Journal ArticleDOI
Improved Algorithms for Maximum Agreement and Compatible Supertrees
Viet Tung Hoang,Wing-Kin Sung +1 more
TL;DR: The results imply the first polynomial time algorithms for both MASP and MCSP when both k and the maximum degree D of the input trees are constant.
Journal ArticleDOI
Unranked second-order anti-unification
TL;DR: An anti-unification algorithm is presented, which computes a generalization of input hedges and records all the differences, and the algorithm is parametric by a skeleton computation function.
Book ChapterDOI
Kernels Based on Distributions of Agreement Subtrees
Kilho Shin,Tetsuji Kuboyama +1 more
TL;DR: Positive semidefinite tree-kernels are introduced, which evaluate distributional features of the sizes of agreement subtrees, and shows efficient dynamic programming algorithms to calculate the kernels.
Book ChapterDOI
Enumeration of Maximum Common Subtree Isomorphisms with Polynomial-Delay
TL;DR: This work presents the first polynomial-delay algorithm for the problem of enumerating all maximum common subtree isomorphisms between a given pair of trees, based on the algorithm of Edmonds for solving the maximum common subgraph problem using a dynamic programming approach in combination with bipartite matching problems.
References
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Book
Introduction to Algorithms
TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
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Formal methods in the study of language
Journal ArticleDOI
Faster scaling algorithms for network problems
Harold N. Gabow,Robert E. Tarjan +1 more
TL;DR: This paper presents algorithms for the assignment problem, the transportation problem, and the minimum- cost flow problem of operations research that find a minimum-cost solution, yet run in time close to the best-known bounds for the corresponding problems without costs.
Journal ArticleDOI
Comparing multiple RNA secondary structures using tree comparisons
Bruce A. Shapiro,Kaizhong Zhang +1 more
TL;DR: This paper presents another approach to the problem of comparing many secondary structures by utilizing a very efficient tree-matching algorithm that will compare two trees in O([T1] X [T2] X L1 X L2) in the worst case and very close to O[T1?] for average trees representing secondary structures.
Journal ArticleDOI
Obtaining common pruned trees
C. R. Finden,A. D. Gordon +1 more
TL;DR: The tree obtained by regrafting branches on to a largest common pruned tree is shown to contain all the classes present in the strict consensus tree.