A note on the shortest common superstring of NGS reads

The Shortest Superstring Problem (SSP) consists, for a set of strings S = {s_1,...,s_n}, to find a minimum length string that contains all s_i, 1 <= i <= k, as substrings. This problem is proved to be NP-Complete and APX-hard. Guaranteed approximation algorithms have been proposed, the current best ratio being 2+11/23, which has been achieved following a long and difficult quest. However, SSP is highly used in practice on next generation sequencing (NGS) data, which plays an increasingly important role in sequencing. In this note, we show that the SSP approximation ratio can be improved on NGS reads by assuming specific characteristics of NGS data that are experimentally verified on a very large sampling set

On improving the approximation ratio of the r-shortest common superstring problem

The Shortest Common Superstring problem (SCS) consists, for a set of strings S = {s_1,...,s_n}, in finding a minimum length string that contains all s_i, 1<= i <= n, as substrings. While a 2+11/30 approximation ratio algorithm has recently been published, the general objective is now to break the conceptual lower bound barrier of 2. This paper is a step ahead in this direction. Here we focus on a particular instance of the SCS problem, meaning the r-SCS problem, which requires all input strings to be of the same length, r. Golonev et al. proved an approximation ratio which is better than the general one for r<= 6. Here we extend their approach and improve their approximation ratio, which is now better than the general one for r<= 7, and less than or equal to 2 up to r = 6

Intuitive Shape Modeling by Shading Design

Shading has a great impact to the human perception of 3D objects. Thus, in order to create or to deform a 3D object, it seems natural to manipulate its perceived shading. This paper presents a new solution for the software implementation of this idea. Our approach is based on the ability of a user to coarsely draw a shading, under different lighting directions. With this intuitive process, users can create or edit a height field (locally or globally), that will correspond to the drawn shading values. Moreover, we present the possibility to edit the shading intensity by means of a specular reflectance model

Coding cells of digital spaces: a framework to write generic digital topology algorithms

This paper proposes a concise coding of the cells of n-dimensional finite regular grids. It induces a simple, generic and efficient framework for implementing classical digital topology data structures and algorithms. Discrete subsets of multidimensional images (e.g. regions, digital surfaces, cubical cell complexes) have then a common and compact representation. Moreover, algorithms have a straightforward and efficient implementation, which is independent from the dimension or sizes of digital images. We illustrate that point with generic hypersurface boundary extraction algorithms by scanning or tracking. This framework has been implemented and basic operations as well as the presented applications have been benchmarked

Representing and Segmenting 2D Images by Means of Planar Maps with Discrete Embeddings: From Model to Applications.

International audienc

Reconstruction of lambertian surfaces by discrete equal height contours and regions propagation

This paper describes two new methods for the reconstruction of discrete surfaces from shading images. Both approaches are based on the reconstruction of a discrete surface by mixing photometric and geometric techniques. The processing of photometric informations is based on reflectance maps which are classic tools of shape from shading. The geometric features are extracted from the discrete surface and propagated along the surface. The propagation is based in one case on equal height discrete contour propagation and in the other case on region propagation. Both methods allow photometric stereo. Results of reconstruction from synthetic and real images are presented. 1