The Median String Problem calls for finding a string that minimizes the average distance from a given set of strings. Under the Levenshtein (or edit) metric, the problem is NP-hard even for binary strings. We devised two novel integer linear programming models for this case and tested them against the only formulation we are aware of in the literature. Our numerical experiments attest to the efficacy of the proposed approach.

Abstract Point cloud registration is a fundamental problem in computer vision. The problem encompasses critical tasks such as feature estimation, correspondence matching, and transformation estimation. The point cloud registration problem can be cast as a quantile matching problem. We refined the quantile assignment algorithm by integrating prevalent feature descriptors and transformation estimation methods to enhance the correspondence between the source and target point clouds. We evaluated the performances of these descriptors and methods with our approach through controlled experiments on a dataset we constructed using well-known 3D models. This systematic investigation led us to identify the most suitable methods for complementing our approach. Subsequently, we devised a new end-to-end, coarse-to-fine pairwise point cloud registration framework. Finally, we tested our framework on indoor and outdoor benchmark datasets and compared our results with state-of-the-art point cloud registration methods.

MOTIVATION: Synthesizing genes to be expressed in other organisms is an essential tool in biotechnology. While the many-to-one mapping from codons to amino acids makes the genetic code degenerate, codon usage in a particular organism is not random either. This bias in codon use may have a remarkable effect on the level of gene expression. A number of measures have been developed to quantify a given codon sequence's strength to express a gene in a host organism. Codon optimization aims to find a codon sequence that will optimize one or more of these measures. Efficient computational approaches are needed since the possible number of codon sequences grows exponentially as the number of amino acids increases. RESULTS: We develop a unifying modeling approach for codon optimization. With our mathematical formulations based on graph/network representations of amino acid sequences, any combination of measures can be optimized in the same framework by finding a path satisfying additional limitations in an acyclic layered network. We tested our approach on bi-objectives commonly used in the literature, namely, Codon Pair Bias versus Codon Adaptation Index and Relative Codon Pair Bias versus Relative Codon Bias. However, our framework is general enough to handle any number of objectives concurrently with certain restrictions or preferences on the use of specific nucleotide sequences. We implemented our models using Python's Gurobi interface and showed the efficacy of our approach even for the largest proteins available. We also provided experimentation showing that highly expressed genes have objective values close to the optimized values in the bi-objective codon design problem. AVAILABILITY AND IMPLEMENTATION: http://alpersen.bilkent.edu.tr/NetworkCodon.zip. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The motivation behind this study is the essential need for survivability in the telecommunications networks. An optical signal should find its destination even if the network experiences an occasional fiber cut. We consider the design of a two-level survivable telecommunications network. Terminals compiling the access layer communicate through hubs forming the backbone layer. To hedge against single link failures in the network, we require the backbone subgraph to be two-edge connected and the terminal nodes to connect to the backbone layer in a dual-homed fashion, i.e., at two distinct hubs. The underlying design problem partitions a given set of nodes into hubs and terminals, chooses a set of connections between the hubs such that the resulting backbone network is two-edge connected, and for each terminal chooses two hubs to provide the dual-homing backbone access. All of these decisions are jointly made based on some cost considerations. We give alternative formulations using cut inequalities, compare these formulations, provide a polyhedral analysis of the small-sized formulation, describe valid inequalities, study the associated separation problems, and design variable fixing rules. All of these findings are then utilized in devising an efficient branch-and-cut algorithm to solve this network design problem.

Abstract The survivable hierarchical telecommunications network design problem consists of locating concentrators, assigning user nodes to concentrators, and linking concentrators in a reliable backbone network. In this article, we study this problem when the backbone is 2‐edge connected and when user nodes are linked to concentrators by a point‐to‐point access network. We formulate this problem as an integer linear program and present a facial study of the associated polytope. We describe valid inequalities and give sufficient conditions for these inequalities to be facet defining. We investigate the computational complexity of the corresponding separation problems. We propose some reduction operations to speed up the separation procedures. Finally, we devise a branch‐and‐cut algorithm based on these results and present the outcome of a computational study. © 2011 Wiley Periodicals, Inc. NETWORKS, 2012