Worst-case errors of linear algorithms for identification in H

We present two new linear algorithms for the single source shortest paths problem. The worst case running time of the first algorithm is O(m + C log C), where m is the number of edges of the input network and C is the ratio of the largest and the smallest edge weight. The pseudo-polynomial character of the time dependence can be overcome by the fact that Dijkstra's kind of shortest paths algorithms can be implemented "from the middle", when the shortest paths to the source are known in advance for a subset of the network vertices. This allows the processing of a subset of the edges with the proposed algorithm and processing of the rest of the edges with any Dijkstra's kind algorithm afterwards. Partial implementation of the algorithm enabled the construction of a second, highly efficient and simple linear algorithm. The proposed algorithm is efficient for all classes of networks and extremely efficient for networks with small C. The decision which classes of networks are most suitable for the proposed approach can be made based on simple parameters. Experimental efficiency analysis shows that this approach significantly reduces total computing time.

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Worst-case asymptotic properties of linear algorithms for H/sub ∞/ identification

Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304) ◽

10.1109/cdc.1999.833400 ◽

2003 ◽

Author(s):

Jie Chen ◽

Guoxiang Gu

Keyword(s):

Asymptotic Properties ◽

Worst Case ◽

Linear Algorithms

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Bit-parallel sequence-to-graph alignment

10.1101/323063 ◽

2018 ◽

Cited By ~ 4

Author(s):

Mikko Rautiainen ◽

Veli Mäkinen ◽

Tobias Marschall

Keyword(s):

Variant Calling ◽

Global Alignment ◽

Alignment Algorithm ◽

Exact Matching ◽

Worst Case ◽

De Bruijn Graphs ◽

Graph Alignment ◽

Linear Sequence ◽

String Graphs ◽

Linear Algorithms

Graphs are commonly used to represent sets of sequences. Either edges or nodes can be labeled by sequences, so that each path in the graph spells a concatenated sequence. Examples include graphs to represent genome assemblies, such as string graphs and de Bruijn graphs, and graphs to represent a pan-genome and hence the genetic variation present in a population. Being able to align sequencing reads to such graphs is a key step for many analyses and its applications include genome assembly, read error correction, and variant calling with respect to a variation graph. Here, we generalize two linear sequence-to-sequence algorithms to graphs: the Shift-And algorithm for exact matching and Myers’ bitvector algorithm for semi-global alignment. These linear algorithms are both based on processing w sequence characters with a constant number of operations, where w is the word size of the machine (commonly 64), and achieve a speedup of w over naive algorithms. Our bitvector-based graph alignment algorithm reaches a worst case runtime of for acyclic graphs and O(V + mE log w) for arbitrary cyclic graphs. We apply it to four different types of graphs and observe a speedup between 3.1-fold and 10.1-fold compared to previous algorithms.

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Linear algorithms for worst case identification in ℋ/sup ∞/ with applications to flexible structures

Proceedings of 1994 American Control Conference - ACC '94 ◽

10.1109/acc.1994.751705 ◽

2005 ◽

Author(s):

Guoxiang Gu ◽

Cheng-Chih Chu ◽

Gisoon Kim

Keyword(s):

Flexible Structures ◽

Worst Case ◽

Case Identification ◽

Linear Algorithms

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Mosaic Mapping: A Means of Tiling Images to Shorten Acquisition Speed for Lower - Magnification SEM Images and Wavelength Dispersive Spectrometers (WDS) X-Ray Maps

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100164659 ◽

1996 ◽

Vol 54 ◽

pp. 438-439

Author(s):

J.D. Geller ◽

C.R. Herrington

Keyword(s):

Limiting Factors ◽

X Rays ◽

Angular Range ◽

Acceptance Angle ◽

Sem Images ◽

Worst Case ◽

X Ray ◽

Focusing Distance ◽

Layered Crystals ◽

Working Distance

The minimum magnification for which an image can be acquired is determined by the design and implementation of the electron optical column and the scanning and display electronics. It is also a function of the working distance and, possibly, the accelerating voltage. For secondary and backscattered electron images there are usually no other limiting factors. However, for x-ray maps there are further considerations. The energy-dispersive x-ray spectrometers (EDS) have a much larger solid angle of detection that for WDS. They also do not suffer from Bragg’s Law focusing effects which limit the angular range and focusing distance from the diffracting crystal. In practical terms EDS maps can be acquired at the lowest magnification of the SEM, assuming the collimator does not cutoff the x-ray signal. For WDS the focusing properties of the crystal limits the angular range of acceptance of the incident x-radiation. The range is dependent upon the 2d spacing of the crystal, with the acceptance angle increasing with 2d spacing. The natural line width of the x-ray also plays a role. For the metal layered crystals used to diffract soft x-rays, such as Be - O, the minimum magnification is approximately 100X. In the worst case, for the LEF crystal which diffracts Ti - Zn, ˜1000X is the minimum.

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