Hypergraphic LP Relaxations for Steiner Trees

We investigate hypergraphic LP relaxations for the Steiner tree problem, primarily the partition LP relaxation introduced by Koenemann et al. [Math. Programming, 2009]. Specifically, we are interested in proving upper bounds on the integrality gap of this LP, and studying its relation to other linear relaxations. Our results are the following. Structural results: We extend the technique of uncrossing, usually applied to families of sets, to families of partitions. As a consequence we show that any basic feasible solution to the partition LP formulation has sparse support. Although the number of variables could be exponential, the number of positive variables is at most the number of terminals. Relations with other relaxations: We show the equivalence of the partition LP relaxation with other known hypergraphic relaxations. We also show that these hypergraphic relaxations are equivalent to the well studied bidirected cut relaxation, if the instance is quasibipartite. Integrality gap upper bounds: We show an upper bound of sqrt(3) ~ 1.729 on the integrality gap of these hypergraph relaxations in general graphs. In the special case of uniformly quasibipartite instances, we show an improved upper bound of 73/60 ~ 1.216. By our equivalence theorem, the latter result implies an improved upper bound for the bidirected cut relaxation as well.Comment: Revised full version; a shorter version will appear at IPCO 2010

Binary Decision Diagrams: from Tree Compaction to Sampling

Any Boolean function corresponds with a complete full binary decision tree. This tree can in turn be represented in a maximally compact form as a direct acyclic graph where common subtrees are factored and shared, keeping only one copy of each unique subtree. This yields the celebrated and widely used structure called reduced ordered binary decision diagram (ROBDD). We propose to revisit the classical compaction process to give a new way of enumerating ROBDDs of a given size without considering fully expanded trees and the compaction step. Our method also provides an unranking procedure for the set of ROBDDs. As a by-product we get a random uniform and exhaustive sampler for ROBDDs for a given number of variables and size

OpenMS – An open-source software framework for mass spectrometry

<p>Abstract</p> <p>Background</p> <p>Mass spectrometry is an essential analytical technique for high-throughput analysis in proteomics and metabolomics. The development of new separation techniques, precise mass analyzers and experimental protocols is a very active field of research. This leads to more complex experimental setups yielding ever increasing amounts of data. Consequently, analysis of the data is currently often the bottleneck for experimental studies. Although software tools for many data analysis tasks are available today, they are often hard to combine with each other or not flexible enough to allow for rapid prototyping of a new analysis workflow.</p> <p>Results</p> <p>We present OpenMS, a software framework for rapid application development in mass spectrometry. OpenMS has been designed to be portable, easy-to-use and robust while offering a rich functionality ranging from basic data structures to sophisticated algorithms for data analysis. This has already been demonstrated in several studies.</p> <p>Conclusion</p> <p>OpenMS is available under the Lesser GNU Public License (LGPL) from the project website at <url>http://www.openms.de</url>.</p

LC-MSsim – a simulation software for liquid chromatography mass spectrometry data

<p>Abstract</p> <p>Background</p> <p>Mass Spectrometry coupled to Liquid Chromatography (LC-MS) is commonly used to analyze the protein content of biological samples in large scale studies. The data resulting from an LC-MS experiment is huge, highly complex and noisy. Accordingly, it has sparked new developments in Bioinformatics, especially in the fields of algorithm development, statistics and software engineering. In a quantitative label-free mass spectrometry experiment, crucial steps are the detection of peptide features in the mass spectra and the alignment of samples by correcting for shifts in retention time. At the moment, it is difficult to compare the plethora of algorithms for these tasks. So far, curated benchmark data exists only for peptide identification algorithms but no data that represents a ground truth for the evaluation of feature detection, alignment and filtering algorithms.</p> <p>Results</p> <p>We present <it>LC-MSsim</it>, a simulation software for LC-ESI-MS experiments. It simulates ESI spectra on the MS level. It reads a list of proteins from a FASTA file and digests the protein mixture using a user-defined enzyme. The software creates an LC-MS data set using a predictor for the retention time of the peptides and a model for peak shapes and elution profiles of the mass spectral peaks. Our software also offers the possibility to add contaminants, to change the background noise level and includes a model for the detectability of peptides in mass spectra. After the simulation, <it>LC-MSsim </it>writes the simulated data to mzData, a public XML format. The software also stores the positions (monoisotopic m/z and retention time) and ion counts of the simulated ions in separate files.</p> <p>Conclusion</p> <p><it>LC-MSsim </it>generates simulated LC-MS data sets and incorporates models for peak shapes and contaminations. Algorithm developers can match the results of feature detection and alignment algorithms against the simulated ion lists and meaningful error rates can be computed. We anticipate that <it>LC-MSsim </it>will be useful to the wider community to perform benchmark studies and comparisons between computational tools.</p