105 research outputs found
A Random Walk Approach to Broadcasting on Random Recursive Trees
In the broadcasting problem on trees, a -message originating in an
unknown node is passed along the tree with a certain error probability . The
goal is to estimate the original message without knowing the order in which the
nodes were informed. A variation of the problem is considering this
broadcasting process on a randomly growing tree, which Addario-Berry et al.
have investigated for uniform and linear preferential attachment recursive
trees. We extend their studies of the majority estimator to the entire group of
very simple increasing trees as well as shape exchangeable trees using the
connection to inhomogeneous random walks and other stochastic processes with
memory effects such as P\'olya Urns
Compositional Algorithms on Compositional Data: Deciding Sheaves on Presheaves
Algorithmicists are well-aware that fast dynamic programming algorithms are
very often the correct choice when computing on compositional (or even
recursive) graphs. Here we initiate the study of how to generalize this
folklore intuition to mathematical structures writ large. We achieve this
horizontal generality by adopting a categorial perspective which allows us to
show that: (1) structured decompositions (a recent, abstract generalization of
many graph decompositions) define Grothendieck topologies on categories of data
(adhesive categories) and that (2) any computational problem which can be
represented as a sheaf with respect to these topologies can be decided in
linear time on classes of inputs which admit decompositions of bounded width
and whose decomposition shapes have bounded feedback vertex number. This
immediately leads to algorithms on objects of any C-set category; these include
-- to name but a few examples -- structures such as: symmetric graphs, directed
graphs, directed multigraphs, hypergraphs, directed hypergraphs, databases,
simplicial complexes, circular port graphs and half-edge graphs.
Thus we initiate the bridging of tools from sheaf theory, structural graph
theory and parameterized complexity theory; we believe this to be a very
fruitful approach for a general, algebraic theory of dynamic programming
algorithms. Finally we pair our theoretical results with concrete
implementations of our main algorithmic contribution in the AlgebraicJulia
ecosystem.Comment: Revised and simplified notation and improved exposition. The
companion code can be found here:
https://github.com/AlgebraicJulia/StructuredDecompositions.j
An efficient graph algorithm for dominance constraints
Dominance constraints are logical descriptions of trees that are widely used in computational linguistics. Their general satisfiability problem is known to be NP-complete. Here we identify normal dominance constraints and present an efficient graph algorithm for testing their satisfiablity in deterministic polynomial time. Previously, no polynomial time algorithm was known
SCIL - Symbolic Constraints in Integer Linear Programming
We describe SCIL. SCIL introduces symbolic constraints into branch-and-cut-and-price algorithms for integer linear programs. Symbolic constraints are known from constraint programming and contribute significantly to the expressive power, ease of use, and efficiency of constraint programs
Efficient Interpretation of Tandem Mass Tags in Top-Down Proteomics
Mass spectrometry is the major analytical tool for the identification and quantification of proteins in biological samples. In so-called top-down proteomics, separation and mass spectrometric analysis is performed at the level of intact proteins, without preparatory digestion steps. It has been shown that the tandem mass tag (TMT) labeling technology, which is often used for quantification based on digested proteins (bottom-up studies), can be applied in top-down proteomics as well. This, however, leads to a complex interpretation problem, where we need to annotate measured peaks with their respective generating protein, the number of charges, and the a priori unknown
number of TMT-groups attached to this protein.
In this work, we give an algorithm for the efficient enumeration of all valid
annotations that fulfill available experimental constraints. Applying the
algorithm to real-world data, we show that the annotation problem can indeed
be efficiently solved. However, our experiments also demonstrate that reliable
annotation in complex mixtures requires at least partial sequence information
and high mass accuracy and resolution to go beyond the proof-of-concept stage
Scheduling shared continuous resources on many-cores
© 2017 Springer Science+Business Media New York We consider the problem of scheduling a number of jobs on m identical processors sharing a continuously divisible resource. Each job j comes with a resource requirement [InlineEquation not available: see fulltext.]. The job can be processed at full speed if granted its full resource requirement. If receiving only an x-portion of (Formula presented.), it is processed at an x-fraction of the full speed. Our goal is to find a resource assignment that minimizes the makespan (i.e., the latest completion time). Variants of such problems, relating the resource assignment of jobs to their processing speeds, have been studied under the term discrete–continuous scheduling. Known results are either very pessimistic or heuristic in nature. In this article, we suggest and analyze a slightly simplified model. It focuses on the assignment of shared continuous resources to the processors. The job assignment to processors and the ordering of the jobs have already been fixed. It is shown that, even for unit size jobs, finding an optimal solution is NP-hard if the number of processors is part of the input. Positive results for unit size jobs include a polynomial-time algorithm for any constant number of processors. Since the running time is infeasible for practical purposes, we also provide more efficient algorithm variants: an optimal algorithm for two processors and a [InlineEquation not available: see fulltext.] -approximation algorithm for m processors
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