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33
Reconciling a gene tree to a species tree under the duplication cost model
 Theor. Comput. Sci
, 2005
"... The general problem of reconciling the information from evolutionary trees representing the relationships between distinct gene families is of great importance in Bioinformatics and has been popularized among the Computer Science researchers in [7] (Ma, Li and Zhang, SIAM J. Comp. 2000) where the au ..."
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Cited by 21 (2 self)
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The general problem of reconciling the information from evolutionary trees representing the relationships between distinct gene families is of great importance in Bioinformatics and has been popularized among the Computer Science researchers in [7] (Ma, Li and Zhang, SIAM J. Comp. 2000) where the authors pose the intriguing question if a certain definition of minimum tree that reconciles a gene tree and a species tree is correct. We answer affirmatively to this question; moreover we show an efficient algorithm for computing such minimumleaf reconciliation trees and prove the uniqueness of such trees. We then tackle some different versions of the biological problem by showing that the exemplar problem, arising from the exemplar analysis of multigene genomes, is NPhard even when the number of copies of a given label is at most two. Finally we introduce two novel formulations for the problem of recombining evolutionary trees, extending the gene duplication problem studied in [7, 3, 8, 9, 6], and we give an exact algorithm (via dynamic programming) for one of these formulations. 1
Heuristics for the geneduplication problem: A θ(n) speedup for the local search
 RECOMB
, 2007
"... The geneduplication problem is to infer a species supertree from a collection of gene trees that are confounded by complex histories of gene duplications. This problem is NPhard and thus requires efficient and effective heuristics. Existing heuristics perform a stepwise search of the tree space, ..."
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Cited by 13 (7 self)
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The geneduplication problem is to infer a species supertree from a collection of gene trees that are confounded by complex histories of gene duplications. This problem is NPhard and thus requires efficient and effective heuristics. Existing heuristics perform a stepwise search of the tree space, where each step is guided by an exact solution to an instance of a local search problem. We show how this local search problem can be solved efficiently by reusing previously computed information. This improves the running time of the current solution by a factor of n, where n is the number of species in the resulting supertree solution, and makes the geneduplication problem more tractable for largescale phylogenetic analyses. We verify the exceptional performance of our solution in a comparison study using sets of large randomly generated gene trees. Furthermore, we demonstrate the utility of our solution by incorporating large genomic data sets from GenBank into a supertree analysis of plants.
Exact algorithms and applications for Treelike Weighted Set Cover
 JOURNAL OF DISCRETE ALGORITHMS
, 2006
"... We introduce an NPcomplete special case of the Weighted Set Cover problem and show its fixedparameter tractability with respect to the maximum subset size, a parameter that appears to be small in relevant applications. More precisely, in this practically relevant variant we require that the given ..."
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Cited by 12 (6 self)
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We introduce an NPcomplete special case of the Weighted Set Cover problem and show its fixedparameter tractability with respect to the maximum subset size, a parameter that appears to be small in relevant applications. More precisely, in this practically relevant variant we require that the given collection C of subsets of a some base set S should be “treelike.” That is, the subsets in C can be organized in a tree T such that every subset onetoone corresponds to a tree node and, for each element s of S, the nodes corresponding to the subsets containing s induce a subtree of T. This is equivalent to the problem of finding a minimum edge cover in an edgeweighted acyclic hypergraph. Our main result is an algorithm running in O(3 k ·mn) time where k denotes the maximum subset size, n: = S, and m: = C. The algorithm also implies a fixedparameter tractability result for the NPcomplete Multicut in Trees problem, complementing previous approximation results. Our results find applications in computational biology in phylogenomics and for saving memory in tree decomposition based graph algorithms.
Evolution of the chicken Tolllike receptor gene family: A story of
, 2008
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Tree decompositions of graphs: Saving memory in dynamic programming
 CTW 2004: CologneTwente Workshop on Graphs and Combinatorial Optimization, Villa Vigoni (CO
, 2004
"... We propose a simple and effective heuristic to save memory in dynamic programming on tree decompositions when solving graph optimization problems. The introduced “anchor technique ” is based on a treelike set covering problem. We substantiate our findings by experimental results. Our strategy has n ..."
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Cited by 10 (2 self)
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We propose a simple and effective heuristic to save memory in dynamic programming on tree decompositions when solving graph optimization problems. The introduced “anchor technique ” is based on a treelike set covering problem. We substantiate our findings by experimental results. Our strategy has negligible computational overhead concerning running time but achieves memory savings for nice tree decompositions and path decompositions between 60 % and 98%.
The GeneDuplication Problem: NearLinear Time Algorithms for NNI Based Local Searches
"... Abstract. The geneduplication problem is to infer a species supertree from a collection of gene trees that are confounded by complex histories of gene duplication events. This problem is NPcomplete and thus requires efficient and effective heuristics. Existing heuristics perform a stepwise search ..."
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Cited by 9 (1 self)
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Abstract. The geneduplication problem is to infer a species supertree from a collection of gene trees that are confounded by complex histories of gene duplication events. This problem is NPcomplete and thus requires efficient and effective heuristics. Existing heuristics perform a stepwise search of the tree space, where each step is guided by an exact solution to an instance of a local search problem. A classical local search problem is the NNI search problem, which is based on the nearest neighbor interchange operation. In this work we (i) provide a novel nearlinear time algorithm for the NNI search problem, (ii) introduce extensions that significantly enlarge the search space of the NNI search problem, and (iii) present algorithms for these extended versions that are asymptotically just as efficient as our algorithm for the NNI search problem. The substantially extended NNI search problem, along with the exceptional speedup achieved, make the geneduplication problem more tractable for largescale phylogenetic analyses. 1
Reconciling Gene Trees to a Species Tree
, 2003
"... In this paper we deal with the general problem of recombining the information from evolutionary trees representing the relationships between distinct gene families. First we solve a problem from [8] regarding the construction of a minimum reconciled tree by giving an e#cient algorithm. Then we s ..."
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Cited by 5 (0 self)
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In this paper we deal with the general problem of recombining the information from evolutionary trees representing the relationships between distinct gene families. First we solve a problem from [8] regarding the construction of a minimum reconciled tree by giving an e#cient algorithm. Then we show that the exemplar problem, arising from the exemplar analysis of multigene genomes [2], is NPhard even when the number of copies of a given label is at most two. Finally we introduce two novel formulations for the problem of recombining evolutionary trees, extending the notion of the gene duplication problem studied in [8, 11, 9, 10, 6], and we give an exact algorithm (via dynamic programming) for one of the formulations given.
An ω(n 2 /log n) speedup of tbr heuristics for the geneduplication problem
 IEEE/ACM Trans. Comput. Biol. and Bioinform
"... Abstract. The geneduplication problem is to infer a species supertree from gene trees that are confounded by complex histories of gene duplications. This problem is NPhard and thus requires efficient and effective heuristics. Existing heuristics perform a stepwise search of the tree space, where ..."
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Cited by 5 (2 self)
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Abstract. The geneduplication problem is to infer a species supertree from gene trees that are confounded by complex histories of gene duplications. This problem is NPhard and thus requires efficient and effective heuristics. Existing heuristics perform a stepwise search of the tree space, where each step is guided by an exact solution to an instance of a local search problem. We improve on the time complexity of the local search problem by a factor of n2 / log n, where n is the size of the resulting species supertree. Typically, several thousand instances of the local search problem are solved throughout a stepwise heuristic search. Hence, our improvement makes the geneduplication problem much more tractable for largescale phylogenetic analyses. 1