B.L. Allen and M. Steel, Subtree transfer operations and their induced metrics on evolutionary trees, Ann. Combin. 5 (1) (2001) 1--15.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....terms of bipartitions; hence trees close together with respect to RF distance tend to have a wellresolved strict consensus tree. In addition, computing most alternative distances, such as nearest neighbor interchange distance (NNI) or tree bisection and reconnection distance (TBR) is NP complete [7, 1]. The RF distance between two trees counts the number bipartitions that are not shared by the two trees: ##b i # T 1 # b i ## T 2 ## # ##b i ## T 1 # b i # T 2 ## n The distance is normalized by n, the number of taxa. Since RF distance is a particular kind of Hamming distance, it is a metric. ....

B. Allen and M. Steel. Subtree transfer operations and their induced metric on evolutionary trees. Annals of combinatorics, in press.

.... PLANAR GRAPHS, see [DF98] MIMIMUM FILLIN (Kaplan, Tarjan and Shamir [KST94] for search trees, and k LEAF SPANNING TREE, DF98] various Pi i;j;k GRAPH MODIFICATION PROBLEMS (Leizhen Cai [LeC95] SET BASIS, UNIQUE HITTING SET ( DF98] and various phylogenetic tree metric problems (Allen [Al98]) 2.4 Why This Is Interesting: The Deal with the Devil The above discussion focuses on the fact that parameterized complexity describes a a new paradigm for seeking tractability in computational problems. We call this The Deal with the Devil of Intractability. The basic idea is that we are ....

B. Allen, Subtree Transfer Operations and their Induced Metrics on Evolutionary Trees, MSc. Thesis, University of Canterbury, 1998.

....two evolutionary trees is to define a distance measure between two trees and compare the two trees by computing the distance. Several distance measures have been proposed, e.g. the symmetric di#erence metric [12] the nearest neighbor interchange metric [16] the subtree transfer distance [1], the Robinson and Foulds metric [13] and the quartet metric [8] Each distance measure has di#erent properties and reflects di#erent aspects of biology, e.g. the subtree transfer distance is related to the number of recombinations between the two sets of species. The quartet metric has several ....

B. L. Allen and M. Steel. Subtree transfer operations and their induced metrics on evolutionary trees. Annals of Combinatorics, 5:1--13, 2001.

....and by ProNEx Project 107 97 (Proc. CNPq 664107 97 4) interchange) SPR (subtree prune and regraft) and TBR (tree bisection and reconnection) for measuring the distance between two phylogenies have been de ned [5, 4, 2] Many results relating these concepts are presented by Allen and Steel [1]. In particular, they show that the size of a maximum agreement forest of two trees is precisely the TBR distance between them. We are concerned here with the problem of nding the size of a maximum agreement forest of two trees, which is known to be NP hard [3, 1] The formal de nition of this ....

....are presented by Allen and Steel [1] In particular, they show that the size of a maximum agreement forest of two trees is precisely the TBR distance between them. We are concerned here with the problem of nding the size of a maximum agreement forest of two trees, which is known to be NP hard [3, 1]. The formal de nition of this problem is given in the next section. We present a 3approximation algorithm for this problem and show that a previous algorithm by Hein et al. 3] claimed to have performance ratio 3, has performance ratio 4. The algorithm we shall describe is simple, but the ....

B. Allen and M. Steel. Subtree transfer operations and their induced metrics on evolutionary trees. Submitted to the Annals of Combinatorics, 2001.

....comparing two evolutionary trees is to de ne a distance measure between two trees and compare the two trees by computing the distance. Several distance measures have been proposed, e.g. the symmetric di erence metric [12] the nearest neighbor interchange metric [16] the subtree transfer distance [1], the Robinson and Foulds metric [13] and the quartet metric [8] Each distance measure has di erent properties and re ects di erent aspects of biology, e.g. the subtree transfer distance is related to the number of recombinations between the two sets of species. The quartet metric has several ....

B. L. Allen and M. Steel. Subtree transfer operations and their induced metrics on evolutionary trees. Annals of Combinatorics, 5:1-13, 2001.

....how similar two trees are in terms of the relationships among leaves. Various metrics have been proposed to measure the similarity based on the undirected tree topology. The symmetric difference metric (SM) 5] the nearest neighbour interchange (NNI) metric [9] the subtree transfer distance (ST) [1], and the Robinson and Foulds metric (RF) 6] are examples of such measures. We study the quartet metric [4] in this paper. For the duration of this paper let evolutionary trees be synonymous with degree 3 trees with leaves uniquely labeled by elements from a label set S where jSj = n. An ....

B.L. Allen and S. Steel. Subtree transfer operations and their induced metrics on evolutionary trees. Research Report 170, Dept. of Math., University of Canterbury.

....MAFs. 2.6 MAF Size and SPR and TBR Distance Lemma 7 of [6] states that the size of a MAF for any two given rooted binary trees T 1 ,T 2 is one more than their SPR distance. However this is not true for unrooted trees, and indeed, neither is it true for SPR transformations (suitably defined, see [1]) on rooted trees as the counterexamples in Figure 3 show. Despite these counterexamples, Lemma 7 of [6] becomes true if we consider the TBR operation instead of the SPR operation, as the next theorem shows. 7 Theorem 2.4 Suppose we have two binary trees T,T # with L(T) L(T # ) L. Then, dTBR ....

....for the SPR operation, however for Rule 2 we o#er the following: Conjecture 3.2 Let T 1 ,T 2 # UB(n) and let T # 1 and T # 2 be obtained from T 1 and T 2 by applying Rule 2. Then dSPR (T 1 ,T 2 ) dSPR (T # 1 ,T # 2 ) For the NNI distance problem, Rule 2 is not distance preserving (see [1]) 3.1.3 Maximally Reduced Trees have Bounded Size Suppose that we are given T 1 ,T 2 # UB(n) such that d# (T 1 ,T 2 ) k for # # SPR,TBR ,andthat T 1 and T 2 can be reduced no further by Rule 1 or Rule 2. In this section, we show that the size of the leaf set of the two trees is bounded by ....

B. Allen, Subtree transfer operations and their induced metrics on evolutionary trees. MSc thesis, University of Canterbury, Christchurch, New Zealand, 1998.

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B.L. Allen and M. Steel, Subtree transfer operations and their induced metrics on evolutionary trees, Ann. Combin. 5 (1) (2001) 1--15.

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