Rearranging cars of an incoming train in a hump yard is a widely discussed topic.We focus on the train marshalling problem where the incoming cars of a train are distributed to a certain number of sorting tracks.When pulled out again to build the outgoing train, cars sharing the same destination should appear consecutively.The goal is to minimize the number of sorting tracks.We suggest a graph-theoretic approach for this N P-complete problem.The idea is to partition an associated directed graph into what we call pseudochains of minimum length.We describe a greedy-type heuristic to solve the partitioning problem which, on random instances, performs better than the known heuristics for the train marshalling problem.

In the freight car dispatching problem, empty freight cars have to be assigned to known demands respecting a given time horizon and certain constraints. The goal is to minimize the resulting transportation costs. One of the constraints is that customers can specify the type of cars they want. It is possible, however, that cars of certain types can be substituted by other cars, either in a 1‐to‐1 fashion or at different exchange rates. We show that these substitutions make the dispatching problem hard to solve and hard to approximate. We model the dispatching problem as an integral generalized transportation problem on a bipartite graph. Using rounding techniques, the LP‐relaxation can be transformed to a transportation schedule violating some of the constraints slightly. Under an additional assumption on the cost function, we fix this violation and derive a 4‐approximation of the problem. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 66(1), 33–39 2015

MOTIVATION: DNA microarrays allow the simultaneous measurement of thousands of gene expression levels in any given patient sample. Gene expression data have been shown to correlate with survival in several cancers, however, analysis of the data is difficult, since typically at most a few hundred patients are available, resulting in severely underdetermined regression or classification models. Several approaches exist to classify patients in different risk classes, however, relatively little has been done with respect to the prediction of actual survival times. We introduce CASPAR, a novel method to predict true survival times for the individual patient based on microarray measurements. CASPAR is based on a multivariate Cox regression model that is embedded in a Bayesian framework. A hierarchical prior distribution on the regression parameters is specifically designed to deal with high dimensionality (large number of genes) and low sample size settings, that are typical for microarray measurements. This enables CASPAR to automatically select small, most informative subsets of genes for prediction. RESULTS: Validity of the method is demonstrated on two publicly available datasets on diffuse large B-cell lymphoma (DLBCL) and on adenocarcinoma of the lung. The method successfully identifies long and short survivors, with high sensitivity and specificity. We compare our method with two alternative methods from the literature, demonstrating superior results of our approach. In addition, we show that CASPAR can further refine predictions made using clinical scoring systems such as the International Prognostic Index (IPI) for DLBCL and clinical staging for lung cancer, thus providing an additional tool for the clinician. An analysis of the genes identified confirms previously published results, and furthermore, new candidate genes correlated with survival are identified.

MOTIVATION: In a wide range of experimental techniques in biology, there is a need for an efficient method to calculate the melting temperature of pairings of two single DNA strands. Avoiding cross-hybridization when choosing primers for the polymerase chain reaction or selecting probes for large-scale DNA assays are examples where the exact determination of melting temperatures is important. Beyond being exact, the method has to be efficient, as these techniques often require the simultaneous calculation of melting temperatures of up to millions of possible pairings. The problem is to simultaneously determine the most stable alignment of two sequences, including potential loops and bulges, and calculate the corresponding melting temperature. RESULTS: As the melting temperature can be expressed as a fraction in terms of enthalpy and entropy differences of the corresponding annealing reaction, we propose to use a fractional programming algorithm, the Dinkelbach algorithm, to solve the problem. To calculate the required differences of enthalpy and entropy, the Nearest Neighbor model is applied. Using this model, the substeps of the Dinkelbach algorithm in our problem setting turn out to be calculations of alignments which optimize an additive score function. Thus, the usual dynamic programming techniques can be applied. The result is an efficient algorithm to determine melting temperatures of two DNA strands, suitable for large-scale applications such as primer or probe design. AVAILABILITY: The software is available for academic purposes from the authors. A web interface is provided at http://www.zaik.uni-koeln.de/bioinformatik/fptm.html

MOTIVATION: Pathway Hunter Tool (PHT), is a fast, robust and user-friendly tool to analyse the shortest paths in metabolic pathways. The user can perform shortest path analysis for one or more organisms or can build virtual organisms (networks) using enzymes. Using PHT, the user can also calculate the average shortest path (Jungnickel, 2002 Graphs, Network and Algorithm. Springer-Verlag, Berlin), average alternate path and the top 10 hubs in the metabolic network. The comparative study of metabolic connectivity and observing the cross talk between metabolic pathways among various sequenced genomes is possible. RESULTS: A new algorithm for finding the biochemically valid connectivity between metabolites in a metabolic network was developed and implemented. A predefined manual assignment of side metabolites (like ATP, ADP, water, CO(2) etc.) and main metabolites is not necessary as the new concept uses chemical structure information (global and local similarity) between metabolites for identification of the shortest path.

metabolic pathway alignmentload pointchoke pointdrug targetpathway analysisconserved pathwaysalternate pathsshortest path

MOTIVATION: It is widely believed that for two proteins Aand Ba sequence identity above some threshold implies structural similarity due to a common evolutionary ancestor. Since this is only a sufficient, but not a necessary condition for structural similarity, the question remains what other criteria can be used to identify remote homologues. Transitivity refers to the concept of deducing a structural similarity between proteins A and C from the existence of a third protein B, such that A and B as well as B and C are homologues, as ascertained if the sequence identity between A and B as well as that between B and C is above the aforementioned threshold. It is not fully understood if transitivity always holds and whether transitivity can be extended ad infinitum. RESULTS: We developed a graph-based clustering approach, where transitivity plays a crucial role. We determined all pair-wise similarities for the sequences in the SwissProt database using the Smith-Waterman local alignment algorithm. This data was transformed into a directed graph, where protein sequences constitute vertices. A directed edge was drawn from vertex A to vertex B if the sequences A and B showed similarity, scaled with respect to the self-similarity of A, above a fixed threshold. Transitivity was important in the clustering process, as intermediate sequences were used, limited though by the requirement of having directed paths in both directions between proteins linked over such sequences. The length dependency-implied by the self-similarity-of the scaling of the alignment scores appears to be an effective criterion to avoid clustering errors due to multi-domain proteins. To deal with the resulting large graphs we have developed an efficient library. Methods include the novel graph-based clustering algorithm capable of handling multi-domain proteins and cluster comparison algorithms. Structural Classification of Proteins (SCOP) was used as an evaluation data set for our method, yielding a 24% improvement over pair-wise comparisons in terms of detecting remote homologues. AVAILABILITY: The software is available to academic users on request from the authors. CONTACT: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]. SUPPLEMENTARY INFORMATION: http://www.zaik.uni-koeln.de/~schliep/ProtClust.html.

Linial and Saks [2] have shown that $O(\log N)$ evaluations of an order preserving map $f:p \to \mathbb{R}$ are necessary and sufficient to determine whether $\alpha \in f(P)$, where N is the number of ideals of N and $\alpha \in \mathbb{R}$ is a given real number. In this paper, we investigate the problem of how to perform the evaluations so that Linial and Saks’ bound is guaranteed, and solve the problem for the classes of interval and series-parallel orders and hence, in particular, for rooted trees. We observe that the greedy-type binary search algorithm, which is optimal for chains, already need not be optimal for general rooted trees. We furthermore discuss the computational complexity of the general search problem and obtain results indicating that the general problem might be hard.

Construction of classes of ordered sets are given for which the setup minimization problem can be solved by an efficient algorithm. Those constructions generalize series-parallel connections. Special classes of ordered sets are exhibited for which the greedy algorithm yields an optimal linear extension. In particular, it is shown that the class of N-free ordered sets is both defect optimal and strongly greedy.