Algorithm Engineering for fundamental Sorting and Graph Problems

Fundamental Algorithms build a basis knowledge for every computer science undergraduate or a professional programmer. It is a set of basic techniques one can find in any (good) coursebook on algorithms and data structures. In this thesis we try to close the gap between theoretically worst-case optimal classical algorithms and the real-world circumstances one face under the assumptions imposed by the data size, limited main memory or available parallelism

NOISE SHAPING IN SAR ADC

The successive approximation register (SAR) analog-to-digital converter (ADC) is currently the most popular type of ADC architecture, owing to its power efficiency. They are also used in multichannel systems, where power efficiency is of high importance because of the large number of simultaneously working channels. However, the SAR ADC architecture is not the most area efficient. In SAR ADCs, the binary weighted capacitive digital-to-analog converter (DAC) is used, which means that one additional bit of resolution costs double the increase of area. Oversampling and noise shaping are methods that allow an increase in resolution without an increase of area. In this paper we present the new SAR ADC architectures with a noise shaping. A first-order noise transfer function (NTF) with zero located nearly at one can be achieved. We propose two modifications of the architecture: with zero-only NTF and with the NTF with additional pole. The additional pole theoretically increases the efficiency of noise shaping to further 3 dB. The architectures were applied to the design of SAR ADCs in a 65 nm complementary metal-oxide semiconductor (CMOS) with OSR equal to 10. A 6-bit capacitive DAC was used. The proposed  architectures  provide nearly 4 additional bits in ENOB. The equalent input bandwitdth is equal to 200 kHz with the sampling rate equal to 4 MS/s

Distribution and dynamic of Castor fiber (Castoridae, Mammalia) population in forest-steppe rivers: a case of the State Nature Reserve Privolzhskaya Lesostep', Penza region, European Russia

The work presents the first results of annual monitoring of a beaver population on the territory of Ostrovtsovskaya Lesostep' (State Nature Reserve Privolzhskaya Lesostep', Penza region). In 2014–2017 all water-courses and water-bodies, including the River Khoper, River Selimutka, River Yuzhnaya and several oxbows of the Khoper were investigated twice a year for assessing the beaver abundance using the method of settlements capacity. The mean density of dams was 7.7 dams/km of watercourse, the maximum was on the River Yuzhnaya – 10.8 dams/km, and the minimum was on the River Selimutka – 5.5 dams/km. During the study period 10 to 13 beaver settlements were observed, the total abundance of beavers tends to decrease (from 42 to 30 animals). The present density of beavers and a lack of food resources limit a further increase of the species abundance

Inducing Suffix and LCP Arrays in External Memory

We consider full text index construction in external memory (EM). Our first contribution is an inducing algorithm for suffix arrays in external memory, which utilizes an efficient EM priority queue and runs in sorting complexity. Practical tests show that this algorithm outperforms the previous best EM suffix sorter [Dementiev et al., JEA 2008] by a factor of about two in time and I/O-volume. Our second contribution is to augment the first algorithm to also construct the array of longest common prefixes (LCPs). This yields the first EM construction algorithm for LCP arrays. The overhead in time and I/O volume for this extended algorithm over plain suffix array construction is roughly two. Our algorithms scale far beyond problem sizes previously considered in the literature (text size of 80 GiB using only 4 GiB of RAM in our experiments).

A Polynomial Time Randomized Parallel Approximation Algorithm for Finding Heavy Planar Subgraphs

We provide an approximation algorithm for the Maximum Weight Planar Subgraph problem, the NP-hard problem of finding a heaviest planar subgraph in an edge-weighted graph G. In the general case our algorithm has performance ratio at least 1/3 + 1/72 matching the best algorithm known so far, though in several special cases we prove stronger results. In particular, we obtain performance ratio 2/3 (instead of 7/12) for the NP-hard Maximum Weight Outerplanar Subgraph problem meeting the performance ratio of the best algorithm for the unweighted case. When the maximum weight planar subgraph is one of several special types of Hamiltonian graphs, we show performance ratios at least 2/5 and 4/9 (instead of 1/3 + 1/72), and 1/2 (instead of 4/9) for the unweighted case

Design and Implementation of a Practical I/O-efficient Shortest Paths Algorithm

We report on initial experimental results for a practical I/O-efficient Single-Source Shortest-Paths (SSSP) algorithm on general undirected sparse graphs where the ratio between the largest and the smallest edge weight is reasonably bounded (for example integer weights in {1,...,2 32}) and the realistic assumption holds that main memory is big enough to keep one bit per vertex. While our implementation only guarantees average-case efficiency, i.e., assuming randomly chosen edge-weights, it turns out that its performance on real-world instances with non-random edge weights is actually even better than on the respective inputs with random weights. Furthermore, compared to the currently best implementation for external-memory BFS [6], which in a sense constitutes a lower bound for SSSP, the running time of our approach always stayed within a factor of five, for the most difficult graph classes the difference was even less than a factor of two. We are not aware of any previous I/O-efficient implementation for the classic general SSSP in a (semi) external setting: in two recent projects [10, 23], Kumar/Schwabe-like SSSP approaches on graphs of at most 6 million vertices have been tested, forcing the authors to artificially restrict the main memory size, M, to rather unrealistic 4 to 16 MBytes in order not to leave the semi-external setting or produce huge running times for larger graphs: for random graphs of 2 20 vertices, the best previous approach needed over six hours. In contrast, for a similar ratio of input size vs. M, but on a 128 times larger and even sparser random graph, our approach was less than seven times slower, a relative gain of nearly 20. On a real-world 24 million node street graph, our implementation was over 40 times faster. Even larger gains of over 500 can be estimated for ran

Improved external memory BFS implementations

ALEXNEX07/ ANACO04: Workshop on Algorithm Engineering & Experiments, 6 January 2007, Astor Crowne Plaza, New Orleans, LouisianaBreadth first search (BPS) traversal on massive graphs in external memory was considered non-viable until recently, because of the large number of I/Os it incurs. Ajwani et al. [3] showed that the randomized variant of the o(n) I/O algorithm of Mehlhorn and Meyer [24] (MM.BFS) can compute the BPS level decomposition for large graphs (around a billion edges) in a few hours for small diameter graphs and a few days for large diameter graphs. We improve upon their implementation of this algorithm by reducing the overhead associated with each BPS level, thereby improving the results for large diameter graphs which are more difficult for BPS traversal in external memory. Also, we present the implementation of the deterministic variant of MM.BFS and show that in most cases, it outperforms the randomized variant. The running time for BPS traversal is further improved with a heuristic that preserves the worst case guarantees of MM_BFS, Together, they reduce the time for BFS on large diameter graphs from days shown in [3] to hours. In particular, on line graphs with random layout on disks, our implementation of the deterministic variant of MM_BFS with the proposed heuristic is more than 75 times faster than the previous best result for the randomized variant of MM.BFS in [3]