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15
Pairwise global alignment of protein interaction networks by matching neighborhood topology
 Proceedings of the 11th Annual International Conference on Computational Molecular Biology (RECOMB’07
, 2007
"... Abstract. We describe an algorithm, IsoRank, for global alignment of two proteinprotein interaction (PPI) networks. IsoRank aims to maximize the overall match between the two networks; in contrast, much of previous work has focused on the local alignment problem  identifying many possible alignm ..."
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Cited by 90 (3 self)
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Abstract. We describe an algorithm, IsoRank, for global alignment of two proteinprotein interaction (PPI) networks. IsoRank aims to maximize the overall match between the two networks; in contrast, much of previous work has focused on the local alignment problem  identifying many possible alignments, each corresponding to a local region of similarity. IsoRank is guided by the intuition that a protein should be matched with a protein in the other network if and only if the neighbors of the two proteins can also be well matched. We encode this intuition as an eigenvalue problem, in a manner analogous to Google's PageRank method. We use IsoRank to compute the rst known global alignment between the S. cerevisiae and D. melanogaster PPI networks. The common subgraph has 1420 edges and describes conserved functional components between the two species. Comparisons of our results with those of a wellknown algorithm for local network alignment indicate that the globally optimized alignment resolves ambiguity introduced by multiple local alignments. Finally, we interpret the results of global alignment to identify functional orthologs between yeast and
y; our functional ortholog prediction method is much simpler than a recently proposed approach and yet provides results that are more comprehensive. 1
Maximum agreement and compatible supertrees
 Proceedings of the 15th Combinatorial Pattern Matching Symposium (CPM’O4), volume 3109 of LNCS
, 2004
"... Given a set of leaflabelled trees with identical leaf sets, the MAST problem, respectively MCT problem, consists of finding a largest subset of leaves such that all input trees restricted to these leaves are isomorphic, respectively compatible. In this paper, we propose extensions of these problem ..."
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Cited by 20 (8 self)
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Given a set of leaflabelled trees with identical leaf sets, the MAST problem, respectively MCT problem, consists of finding a largest subset of leaves such that all input trees restricted to these leaves are isomorphic, respectively compatible. In this paper, we propose extensions of these problems to the context of supertree inference, where input trees have nonidentical leaf sets. This situation is of particular interest in phylogenetics. The resulting problems are called SMAST and SMCT. A sufficient condition is given that identifies cases where these problems can be solved by resorting to MAST and MCT as subproblems. This condition is met, for instance, when only two input trees are considered. Then we give algorithms for SMAST and SMCT that benefit from the link with the subtree problems. These algorithms run in time linear to the time needed to solve MAST, respectively MCT, on an instance of the same or smaller size. It is shown that arbitrary instances of SMAST and SMCT can be turned in polynomial time into instances composed of trees with a bounded number of leaves. SMAST is shown to be W[2]hard when the considered parameter is the number of input leaves that have to be removed to obtain the agreement of the input trees. A simlar result holds for SMCT. Moreover, the corresponding optimization problems, that is the complements of SMAST and SMCT, can not be approximated in polynomial time within a constant factor, unless P = NP. These results also hold when the input trees have a bounded number of leaves. The presented results apply to both collections of rooted and unrooted trees. Preprint submitted to Elsevier Science 17 November 2006 1
On the approximation of computing evolutionary trees
 in Proceedings of the 11th International Computing and Combinatorics Conference (COCOON’05
, 2005
"... Abstract. Given a set of leaflabelled trees with identical leaf sets, the wellknown MAST problem consists of finding a subtree homeomorphically included in all input trees and with the largest number of leaves. MAST and its variant called MCT are of particular interest in computational biology. Th ..."
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Cited by 12 (4 self)
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Abstract. Given a set of leaflabelled trees with identical leaf sets, the wellknown MAST problem consists of finding a subtree homeomorphically included in all input trees and with the largest number of leaves. MAST and its variant called MCT are of particular interest in computational biology. This paper presents positive and negative results on the approximation of MAST, MCT and their complement versions, denoted CMAST and CMCT. For CMAST and CMCT on rooted trees we give 3approximation algorithms achieving significantly lower running times than those previously known. In particular, the algorithm for CMAST runs in linear time. The approximation threshold for CMAST, resp. CMCT, is shown to be the same whenever collections of rooted trees or of unrooted trees are considered. Moreover, hardness of approximation results are stated for CMAST, CMCT and MCT on small number of trees, and for MCT on unbounded number of trees.
Rooted Maximum Agreement Supertrees
, 2005
"... Given a set T of rooted, unordered trees, where each Ti ∈ T is distinctly leaflabeled by a set �(Ti) and where the sets �(Ti) may overlap, the maximum agreement supertree problem (MASP) is to construct a distinctly leaflabeled tree Q with leaf set �(Q) ⊆ ∪Ti ∈T �(Ti) such that �(Q)  is maximiz ..."
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Cited by 11 (2 self)
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Given a set T of rooted, unordered trees, where each Ti ∈ T is distinctly leaflabeled by a set �(Ti) and where the sets �(Ti) may overlap, the maximum agreement supertree problem (MASP) is to construct a distinctly leaflabeled tree Q with leaf set �(Q) ⊆ ∪Ti ∈T �(Ti) such that �(Q)  is maximized and for each Ti ∈ T, the topological restriction of Ti to �(Q) is isomorphic to the topological restriction of Q to �(Ti). Let n = � �∪Ti ∈T �(Ti) � � , k =T , and D = maxTi ∈T {deg(Ti)}. We first show that MASP with k = 2 can be solved in O ( √ Dn log(2n/D)) time, which is O(n log n) when D = O(1) and O(n1.5) when D is unrestricted. We then present an algorithm for MASP with D = 2 whose running time is polynomial if k = O(1). On the other hand, we prove that MASP is NPhard for any fixed k ≥ 3 when D is unrestricted, and also NPhard for any fixed D ≥ 2 when k is unrestricted even if each input tree is required to contain at most three leaves. Finally, we describe a polynomialtime (n/log n)approximation algorithm for MASP.
Improved Parameterized Complexity of the Maximum Agreement Subtree and . . .
 IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS
, 2006
"... Given a set of evolutionary trees on a same set of taxa, the maximum agreement subtree problem (MAST), respectively maximum compatible tree problem (MCT), consists of finding a largest subset of taxa such that all input trees restricted to these taxa are isomorphic, respectively compatible. These ..."
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Cited by 9 (4 self)
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Given a set of evolutionary trees on a same set of taxa, the maximum agreement subtree problem (MAST), respectively maximum compatible tree problem (MCT), consists of finding a largest subset of taxa such that all input trees restricted to these taxa are isomorphic, respectively compatible. These problems
The maximum agreement of two nested phylogenetic networks
 New Topics in Theoretical Computer Science, chap. 4, Nova Publishers, 2008
"... Given a set N of phylogenetic networks, the maximum agreement phylogenetic subnetwork problem (MASN) asks for a subnetwork embedded in every Ni ∈ N with as many leaves as possible. MASN can be used to identify shared branching structure among phylogenetic networks or to measure their similarity. In ..."
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Cited by 6 (4 self)
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Given a set N of phylogenetic networks, the maximum agreement phylogenetic subnetwork problem (MASN) asks for a subnetwork embedded in every Ni ∈ N with as many leaves as possible. MASN can be used to identify shared branching structure among phylogenetic networks or to measure their similarity. In this chapter, we prove that the general case of MASN is NPhard already for two phylogenetic networks (in fact, even if one of the two input networks is a binary tree), but that the problem can be solved efficiently if each of the two input phylogenetic networks exhibits a nested structure. For this purpose, we introduce the concept of a nested phylogenetic network and study some of its underlying fundamental combinatorial properties. We first show that the total number of nodes V (N)  in any nested phylogenetic network N with n leaves and nesting depth d is O(n(d + 1)). We then describe a simple algorithm for testing if a given phylogenetic network is nested, and if so, determining its nesting depth in O(V (N)  · (d + 1)) time. Next, we present a polynomialtime algorithm for MASN for two nested phylogenetic networks N1,N2. Its running time is O(V (N1)  ·
Solving the maximum agreement subtree and the maximum compatible tree problems on many bounded degree trees
 Proceedings of the 17th Annual Symposium on Combinatorial Pattern Matching (CPM’06
, 2006
"... Given a set of leaflabeled trees with identical leaf sets, the wellknown Maximum Agreement SubTree problem (MAST) consists of finding a subtree homeomorphically included in all input trees and with the largest number of leaves. Its variant called Maximum Compatible Tree (MCT) is less stringent, as ..."
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Cited by 4 (0 self)
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Given a set of leaflabeled trees with identical leaf sets, the wellknown Maximum Agreement SubTree problem (MAST) consists of finding a subtree homeomorphically included in all input trees and with the largest number of leaves. Its variant called Maximum Compatible Tree (MCT) is less stringent, as it allows the input trees to be refined. Both problems are of particular interest in computational biology, where trees encountered have often small degrees. In this paper, we study the parameterized complexity of MAST and MCT with respect to the maximum degree, denoted by D, of the input trees. Although MAST is polynomial for bounded D [1, 6, 3], we show that the problem is W[1]hard with respect to parameter D. Moreover, relying on recent advances in parameterized complexity we obtain a tight lower bound: while MAST can be solved in O(N O(D)) time where N denotes the input length, we show that an O(N o(D) ) bound is not achievable, unless SNP ⊆ SE. We also show that MCT is W[1]hard with respect to D, and that MCT cannot be solved in O(N o(2D/2)) time, unless SNP ⊆ SE. 1
From constrained to unconstrained maximum agreement subtree in linear time
 ALGORITHMICA
, 2008
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Linear time 3approximation for the MAST problem
, 2009
"... Given a set of leaflabeled trees with identical leaf sets, the wellknown Maximum Agreement Subtree (MAST) problem consists in finding a subtree homeomorphically included in all input trees and with the largest number of leaves. MAST and its variant called Maximum Compatible Tree (MCT) are of parti ..."
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Cited by 1 (0 self)
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Given a set of leaflabeled trees with identical leaf sets, the wellknown Maximum Agreement Subtree (MAST) problem consists in finding a subtree homeomorphically included in all input trees and with the largest number of leaves. MAST and its variant called Maximum Compatible Tree (MCT) are of particular interest in computational biology. This paper presents a lineartime approximation algorithm to solve the complement version of MAST, namely identifying the smallest set of leaves to remove from input trees to obtain isomorphic trees. We also present an O(n2 + kn) algorithm to solve the complement version of MCT. For both problems, we thus achieve significantly lower running times than previously known algorithms. Fast running times are especially important in phylogenetics where large collections of trees are routinely produced by resampling procedures, such as the non parametric bootstrap or Bayesian MCMC methods.