1,467 research outputs found
Potential Maximal Clique Algorithms for Perfect Phylogeny Problems
Kloks, Kratsch, and Spinrad showed how treewidth and minimum-fill, NP-hard
combinatorial optimization problems related to minimal triangulations, are
broken into subproblems by block subgraphs defined by minimal separators. These
ideas were expanded on by Bouchitt\'e and Todinca, who used potential maximal
cliques to solve these problems using a dynamic programming approach in time
polynomial in the number of minimal separators of a graph. It is known that
solutions to the perfect phylogeny problem, maximum compatibility problem, and
unique perfect phylogeny problem are characterized by minimal triangulations of
the partition intersection graph. In this paper, we show that techniques
similar to those proposed by Bouchitt\'e and Todinca can be used to solve the
perfect phylogeny problem with missing data, the two- state maximum
compatibility problem with missing data, and the unique perfect phylogeny
problem with missing data in time polynomial in the number of minimal
separators of the partition intersection graph
Improved Lower Bounds on the Compatibility of Multi-State Characters
We study a long standing conjecture on the necessary and sufficient
conditions for the compatibility of multi-state characters: There exists a
function such that, for any set of -state characters, is
compatible if and only if every subset of characters of is
compatible. We show that for every , there exists an incompatible set
of -state
characters such that every proper subset of is compatible. Thus, for every .
This improves the previous lower bound of given by Meacham (1983),
and generalizes the construction showing that given by Habib and
To (2011). We prove our result via a result on quartet compatibility that may
be of independent interest: For every integer , there exists an
incompatible set of
quartets over
labels such that every proper subset of is compatible. We contrast this
with a result on the compatibility of triplets: For every , if is
an incompatible set of more than triplets over labels, then some
proper subset of is incompatible. We show this upper bound is tight by
exhibiting, for every , a set of triplets over taxa such
that is incompatible, but every proper subset of is compatible
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Inference of single-cell phylogenies from lineage tracing data using Cassiopeia.
The pairing of CRISPR/Cas9-based gene editing with massively parallel single-cell readouts now enables large-scale lineage tracing. However, the rapid growth in complexity of data from these assays has outpaced our ability to accurately infer phylogenetic relationships. First, we introduce Cassiopeia-a suite of scalable maximum parsimony approaches for tree reconstruction. Second, we provide a simulation framework for evaluating algorithms and exploring lineage tracer design principles. Finally, we generate the most complex experimental lineage tracing dataset to date, 34,557 human cells continuously traced over 15 generations, and use it for benchmarking phylogenetic inference approaches. We show that Cassiopeia outperforms traditional methods by several metrics and under a wide variety of parameter regimes, and provide insight into the principles for the design of improved Cas9-enabled recorders. Together, these should broadly enable large-scale mammalian lineage tracing efforts. Cassiopeia and its benchmarking resources are publicly available at www.github.com/YosefLab/Cassiopeia
Constructing computer virus phylogenies
There has been much recent algorithmic work on the problem of reconstructing the evolutionary history of biological species. Computer virus specialists are interested in finding the evolutionary history of computer viruses - a virus is often written using code fragments from one or more other viruses, which are its immediate ancestors. A phylogeny for a collection of computer viruses is a directed acyclic graph whose nodes are the viruses and whose edges map ancestors to descendants and satisfy the property that each code fragment is "invented" only once. To provide a simple explanation for the data, we consider the problem of constructing such a phylogeny with a minimum number of edges. In general this optimization problem is NP-complete; some associated approximation problems are also hard, but others are easy. When tree solutions exist, they can be constructed and randomly sampled in polynomial time
Unique perfect phylogeny is NP-hard
We answer, in the affirmative, the following question proposed by Mike Steel
as a $100 challenge: "Is the following problem NP-hard? Given a ternary
phylogenetic X-tree T and a collection Q of quartet subtrees on X, is T the
only tree that displays Q ?
A Simple Characterization of the Minimal Obstruction Sets for Three-State Perfect Phylogenies
Lam, Gusfield, and Sridhar (2009) showed that a set of three-state characters
has a perfect phylogeny if and only if every subset of three characters has a
perfect phylogeny. They also gave a complete characterization of the sets of
three three-state characters that do not have a perfect phylogeny. However, it
is not clear from their characterization how to find a subset of three
characters that does not have a perfect phylogeny without testing all triples
of characters. In this note, we build upon their result by giving a simple
characterization of when a set of three-state characters does not have a
perfect phylogeny that can be inferred from testing all pairs of characters
The hardness of perfect phylogeny, feasible register assignment and other problems on thin colored graphs
AbstractIn this paper, we consider the complexity of a number of combinatorial problems; namely, Intervalizing Colored Graphs (DNA physical mapping), Triangulating Colored Graphs (perfect phylogeny), (Directed) (Modified) Colored Cutwidth, Feasible Register Assignment and Module Allocation for graphs of bounded pathwidth. Each of these problems has as a characteristic a uniform upper bound on the tree or path width of the graphs in “yes”-instances. For all of these problems with the exceptions of Feasible Register Assignment and Module Allocation, a vertex or edge coloring is given as part of the input. Our main results are that the parameterized variant of each of the considered problems is hard for the complexity classes W[t] for all t∈N. We also show that Intervalizing Colored Graphs, Triangulating Colored Graphs, and Colored Cutwidth are NP-Complete
A simple linear-time algorithm for finding path-decompositions of small width
We described a simple algorithm running in linear time for each fixed
constant , that either establishes that the pathwidth of a graph is
greater than , or finds a path-decomposition of of width at most
. This provides a simple proof of the result by Bodlaender that many
families of graphs of bounded pathwidth can be recognized in linear time.Comment: 9 page
Algorithms For Phylogeny Reconstruction In a New Mathematical Model
The evolutionary history of a set of species is represented by a tree called phylogenetic tree or phylogeny. Its structure depends on precise biological assumptions about the evolution of species. Problems related to phylogeny reconstruction (i.e., finding a tree representation of information regarding a set of items) are widely studied in computer science. Most of these problems have found to be NP-hard. Sometimes they can solved polynomially if appropriate restrictions on the structure of the tree are fixed. This paper summarizes the most recent problems and results in phylogeny reconstruction, and introduces an innovative tree model, called Phylogenetic Parsimonious Tree, which is justified by significant biological hypothesis. Using PPT two problems are studied: the existence and the reconstruction of a tree both when sequences of characters and partial order on interspecies distances are given. We rove complexity results that confirm the hardness of this class of problems
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