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An Even Faster and More Unifying Algorithm for Comparing Trees via Unbalanced Bipartite Matchings
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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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Proceedings ArticleDOI
Fixed parameter polynomial time algorithms for maximum agreement and compatible supertrees
Viet Tung Hoang,Wing-Kin Sung +1 more
TL;DR: In this article, the authors gave the first polynomial time algorithms for both MASP and MCSP when both the maximum degree and maximum degree of the constant labeled trees are constant.
Book ChapterDOI
Fast Universalization of Investment Strategies with Provably Good Relative Returns
TL;DR: In this article, the authors present a general framework for universalizing investment strategies and discuss conditions under which investment strategies are universalizable, including trading strategies that decide positions in individual stocks, and portfolio strategies that allocate wealth among multiple stocks.
Book ChapterDOI
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 computed generalizations are least general among a certain class of generalizations.
Posted Content
A single-exponential fixed-parameter algorithm for Distance-Hereditary Vertex Deletion
TL;DR: In this article, the first single-exponential fixed-parameter tractable algorithm for vertex deletion to distance-hereditary graphs was presented, and matching lower bounds based on the exponential time hypothesis were provided.
Journal ArticleDOI
Computing the Maximum Agreement of Phylogenetic Networks
TL;DR: The maximum agreement phylogenetic subnetwork problem (MASN) of finding a branching structure shared by a set of phylogenetic networks is introduced and it is proved that the problem is NP-hard even if restricted to three phylogenetics networks.
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
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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.