TY  - JOUR
A1  - Klemz, Boris
A1  - Rote, Günter
T1  - Linear-Time Algorithms for Maximum-Weight Induced Matchings and Minimum Chain Covers in Convex Bipartite Graphs
JF  - Algorithmica
N2  - A bipartite graph G=(U,V,E) is convex if the vertices in V can be linearly ordered such that for each vertex u∈U, the neighbors of u are consecutive in the ordering of V. An induced matching H of G is a matching for which no edge of E connects endpoints of two different edges of H. We show that in a convex bipartite graph with n vertices and m weighted edges, an induced matching of maximum total weight can be computed in O(n+m) time. An unweighted convex bipartite graph has a representation of size O(n) that records for each vertex u∈U the first and last neighbor in the ordering of V. Given such a compact representation, we compute an induced matching of maximum cardinality in O(n) time. In convex bipartite graphs, maximum-cardinality induced matchings are dual to minimum chain covers. A chain cover is a covering of the edge set by chain subgraphs, that is, subgraphs that do not contain induced matchings of more than one edge. Given a compact representation, we compute a representation of a minimum chain cover in O(n) time. If no compact representation is given, the cover can be computed in O(n+m) time. All of our algorithms achieve optimal linear running time for the respective problem and model, and they improve and generalize the previous results in several ways: The best algorithms for the unweighted problem versions had a running time of O(n\(^{2}\)) (Brandstädt et al. in Theor. Comput. Sci. 381(1–3):260–265, 2007. https://doi.org/10.1016/j.tcs.2007.04.006). The weighted case has not been considered before.
KW  - dynamic programming
KW  - graph algorithm
KW  - induced matching
KW  - chain cover
KW  - convex bipartite graph
KW  - certifying algorithm
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-267876
SN  - 1432-0541
VL  - 84
IS  - 4
ER  - 
TY  - JOUR
A1  - Bischler, Thorsten
A1  - Kopf, Matthias
A1  - Voss, Bjoern
T1  - Transcript mapping based on dRNA-seq data
JF  - BMC Bioinformatics
N2  - Background: RNA-seq and its variant differential RNA-seq (dRNA-seq) are today routine methods for transcriptome analysis in bacteria. While expression profiling and transcriptional start site prediction are standard tasks today, the problem of identifying transcriptional units in a genome-wide fashion is still not solved for prokaryotic systems. 
Results: We present RNASEG, an algorithm for the prediction of transcriptional units based on dRNA-seq data. A key feature of the algorithm is that, based on the data, it distinguishes between transcribed and un-transcribed genomic segments. Furthermore, the program provides many different predictions in a single run, which can be used to infer the significance of transcriptional units in a consensus procedure. We show the performance of our method based on a well-studied dRNA-seq data set for Helicobacter pylori. 
Conclusions: With our algorithm it is possible to identify operons and 5'- and 3'-UTRs in an automated fashion. This alleviates the need for labour intensive manual inspection and enables large-scale studies in the area of comparative transcriptomics.
KW  - transcriptional start site
KW  - dynamic programming
KW  - RNA-seq
KW  - differential
KW  - segmentation
KW  - transcriptional uni
KW  - transcriptome
KW  - reveals
KW  - model
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-116663
SN  - 1471-2105
VL  - 15
IS  - 122
ER  -