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

Kritische Metalle: Wie die Schweizer Industrie vorsorgen kann

Im April 2016 organisierten der Entwicklungsfonds Seltene Metalle ESM, MatSearch Consulting Hofmann, die Empa sowie Life Cycle Consulting Althaus mit Unterstützung der SATW einen Workshop zum Thema «Daten-Netzwerk für kritische Rohstoffe». Der Terminus «kritische Rohstoffe» bezieht sich auf die von der Europäischen Union definierten Rohstoffe, hauptsächlich Metalle, die in Zukunft für den Wirtschaftsstandort dringend gebraucht werden, die aber aufgrund ihres Versorgungsrisikos ein Risiko für Europas Wirtschaft darstellen – zum Beispiel die Seltenen Erdelemente, aber auch Elemente wie Indium, Kobalt, Wolfram und viele andere. Workshop «Daten-Netzwerk kritische Rohstoffe» Teilnehmende aus Forschung, Industrie, mittelständischen Unternehmen, Verbänden und Politik diskutierten Möglichkeiten, wie die Schweiz auf drohende Versorgungsengpässe mit kritischen Rohstoffen reagieren kann. Moderierte Diskussionsgruppen befassten sich mit dem Einfluss kritischer Rohstoffe auf den Schweizer und den europäischen Markt. Sie identifizierten Hindernisse für eine adäquate Priorisierung des Themas in Unternehmen sowie relevante Akteure und besprachen Möglichkeiten, mehr Transparenz im Bereich kritischer Rohstoffe zu schaffen. Als grösste Herausforderung wurde nicht ein Mangel an Daten identifiziert, sondern ein unübersichtlicher Informationsfluss und fehlende Möglichkeiten für Firmen, sich individuell zu informieren sowie mangelndes Wissen über Strategien, wie mit Rohstoffknappheit umgegangen werden kann. Die grösste Herausforderung für die Schweiz und Europa besteht darin, das Bewusstsein für die Problematik der sicheren Verfügbarkeit kritischer Rohstoffe zu erhöhen. Die Kurzbroschüre bietet einen Überblick über das Thema mit speziellem Fokus auf die Schweiz