63 research outputs found
Gerbil: A Fast and Memory-Efficient -mer Counter with GPU-Support
A basic task in bioinformatics is the counting of -mers in genome strings.
The -mer counting problem is to build a histogram of all substrings of
length in a given genome sequence. We present the open source -mer
counting software Gerbil that has been designed for the efficient counting of
-mers for . Given the technology trend towards long reads of
next-generation sequencers, support for large becomes increasingly
important. While existing -mer counting tools suffer from excessive memory
resource consumption or degrading performance for large , Gerbil is able to
efficiently support large without much loss of performance. Our software
implements a two-disk approach. In the first step, DNA reads are loaded from
disk and distributed to temporary files that are stored at a working disk. In a
second step, the temporary files are read again, split into -mers and
counted via a hash table approach. In addition, Gerbil can optionally use GPUs
to accelerate the counting step. For large , we outperform state-of-the-art
open source -mer counting tools for large genome data sets.Comment: A short version of this paper will appear in the proceedings of WABI
201
Hardness and Approximation of Octilinear Steiner Trees
Given a point set K of terminals in the plane, the octilinear Steiner tree problem is to find a shortest tree that interconnects all terminals and edges run either in horizontal, vertical, or 45° diagonal direction. This problem is fundamental for the novel octilinear routing paradigm in VLSI design, the so-called X-architecture. As the related rectilinear and the Euclidian Steiner tree problem are well-known to be NP-hard, the same was widely believed for the octilinear Steiner tree problem but left open for quite some time. In this paper, we prove the NP-completeness of the decision version of the octilinear Steiner tree problem. We also show how to reduce the octilinear Steiner tree problem to the Steiner tree problem in graphs of polynomial size with the following approximation guarantee. We construct a graph of size O(n^2/epsilon^2) which contains a (1+epsilon)-approximation of a minimum octilinear Steiner tree for every epsilon > 0 and n = |K|. Hence, we can apply any k-approximation algorithm for the Steiner tree problem in graphs (the currently best known bound is k=1.55) and achieve an (k+epsilon)-approximation bound for the octilinear Steiner tree problem. This approximation guarantee also holds for the more difficult case where the Steiner tree has to avoid blockages (obstacles bounded by octilinear polygons)
Shortest paths in linear time on minor-closed graph classes, with an application to Steiner tree approximation
AbstractWe generalize the linear-time shortest-paths algorithm for planar graphs with nonnegative edge-weights of Henzinger et al. (1994) to work for any proper minor-closed class of graphs. We argue that their algorithm can not be adapted by standard methods to all proper minor-closed classes. By using recent deep results in graph minor theory, we show how to construct an appropriate recursive division in linear time for any graph excluding a fixed minor and how to transform the graph and its division afterwards, so that it has maximum degree three. Based on such a division, the original framework of Henzinger et al. can be applied. Afterwards, we show that using this algorithm, one can implement Mehlhorn’s (1988) 2-approximation algorithm for the Steiner tree problem in linear time on these graph classes
Route Planning in Transportation Networks
We survey recent advances in algorithms for route planning in transportation
networks. For road networks, we show that one can compute driving directions in
milliseconds or less even at continental scale. A variety of techniques provide
different trade-offs between preprocessing effort, space requirements, and
query time. Some algorithms can answer queries in a fraction of a microsecond,
while others can deal efficiently with real-time traffic. Journey planning on
public transportation systems, although conceptually similar, is a
significantly harder problem due to its inherent time-dependent and
multicriteria nature. Although exact algorithms are fast enough for interactive
queries on metropolitan transit systems, dealing with continent-sized instances
requires simplifications or heavy preprocessing. The multimodal route planning
problem, which seeks journeys combining schedule-based transportation (buses,
trains) with unrestricted modes (walking, driving), is even harder, relying on
approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4,
previously published by Microsoft Research. This work was mostly done while
the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at
Microsoft Research Silicon Valle
High Quality Quadrilateral Surface Meshing Without Template Restrictions: A New Approach Based on Network Flow Techniques
We investigate the following mesh refinement problem: Given a mesh of polygons in three-dimensional space, find a decomposition into strictly convex quadrilaterals such that the resulting mesh is conforming and satisfies prescribed local density constraints. We show that this problem can efficiently be solved by a reduction to a minimum cost bidirected flow problem, if the mesh does not contain branching edges, that is, edges incident to more than two polygons. This approach handles optimization criteria such as density, angles and regularity, too. For meshes with branchings, the problem is feasible if and only if a certain system of linear equations over GF(2) has a solution. To enhance the mesh quality for meshes with branchings, we introduce a two-stage approach which first decomposes the whole mesh into components without branchings, and then uses minimum cost bidirected flows on the components in a second phase. We report on our computational results which indicate that..
- …