Distributed Triangle Approximately Counting Algorithms in Simple Graph Stream

Recently, the counting algorithm of local topology structures, such as triangles, has been widely used in social network analysis, recommendation systems, user portraits and other fields. At present, the problem of counting global and local triangles in a graph stream has been widely studied, and numerous triangle counting steaming algorithms have emerged. To improve the throughput and scalability of streaming algorithms, many researches of distributed streaming algorithms on multiple machines are studied. In this article, we first propose a framework of distributed streaming algorithm based on the Master-Worker-Aggregator architecture. The two core parts of this framework are an edge distribution strategy, which plays a key role to affect the performance, including the communication overhead and workload balance, and aggregation method, which is critical to obtain the unbiased estimations of the global and local triangle counts in a graph stream. Then, we extend the state-of-the-art centralized algorithm TRIÈST into four distributed algorithms under our framework. Compared to their competitors, experimental results show that DVHT-i is excellent in accuracy and speed, performing better than the best existing distributed streaming algorithm. DEHT-b is the fastest algorithm and has the least communication overhead. What’s more, it almost achieves absolute workload balance.

Decomposition Strategies to Count Integer Solutions over Linear Constraints

Counting integer solutions of linear constraints has found interesting applications in various fields. It is equivalent to the problem of counting integer points inside a polytope. However, state-of-the-art algorithms for this problem become too slow for even a modest number of variables. In this paper, we propose new decomposition techniques which target both the elimination of variables as well as inequalities using structural properties of counting problems. Experiments on extensive benchmarks show that our algorithm improves the performance of state-of-the-art counting algorithms, while the overhead is usually negligible compared to the running time of integer counting.

Assessment of a claimed ultra-low frequency electromagnetic (ULFEM) earthquake precursor

Anomalous ultra-low frequency electromagnetic (ULFEM) pulses occurring before the M5.4 2007 and M4.0 2010 Alum Rock earthquakes have been claimed to increase in number days to weeks prior to each earthquake. We re-examine the previously reported ultra-low frequency (ULF: 0.01-10 Hz) magnetic data recorded at a QuakeFinder site located 9 km from the earthquake hypocenter, as well as data from a nearby Stanford-USGS site located 42 km from the hypocenter, to analyze the characteristics of the pulses and assess their origin. Using pulse definitions and pulse-counting algorithms analogous to those previously reported, we corroborate the increase in pulse counts before the 2007 Alum Rock earthquake at the QuakeFinder station, but we note that the number of pulses depends greatly on chosen temporal and amplitude detection thresholds. These thresholds are necessarily arbitrary because we lack a clear physical model or basis for their selection. We do not see the same increase in pulse counts before the 2010 Alum Rock earthquake at the QuakeFinder or Stanford-USGS station. In addition, when comparing specific pulses in the QuakeFinder data and Stanford-USGS data, we find that the majority of pulses do not match temporally, indicating the pulses are not from solar-driven ionospheric/magnetospheric disturbances or from atmospheric lightning, and lack a common origin. Notably, however, our assessment of the temporal distribution of pulse counts throughout the day shows pulse counts increase during peak human activity hours, strongly suggesting these pulses result from local cultural noise and are not tectonic in origin. The many unknowns about the character and even existence of precursory earthquake pulses means that otherwise standard numerical and statistical test cannot be applied. Yet here we show that exhaustive investigation of many different aspects of ULFEM signals can be used to properly characterize their origin.

Automatic Pest Counting from Pheromone Trap Images Using Deep Learning Object Detectors for Matsucoccus thunbergianae Monitoring

The black pine bast scale, M. thunbergianae, is a major insect pest of black pine and causes serious environmental and economic losses in forests. Therefore, it is essential to monitor the occurrence and population of M. thunbergianae, and a monitoring method using a pheromone trap is commonly employed. Because the counting of insects performed by humans in these pheromone traps is labor intensive and time consuming, this study proposes automated deep learning counting algorithms using pheromone trap images. The pheromone traps collected in the field were photographed in the laboratory, and the images were used for training, validation, and testing of the detection models. In addition, the image cropping method was applied for the successful detection of small objects in the image, considering the small size of M. thunbergianae in trap images. The detection and counting performance were evaluated and compared for a total of 16 models under eight model conditions and two cropping conditions, and a counting accuracy of 95% or more was shown in most models. This result shows that the artificial intelligence-based pest counting method proposed in this study is suitable for constant and accurate monitoring of insect pests.

Faster algorithms for counting subgraphs in sparse graphs

Given a k-node pattern graph H and an n-node host graph G, the subgraph counting problem asks to compute the number of copies of H in G. In this work we address the following question: can we count the copies of H faster if G is sparse? We answer in the affirmative by introducing a novel tree-like decomposition for directed acyclic graphs, inspired by the classic tree decomposition for undirected graphs. This decomposition gives a dynamic program for counting the homomorphisms of H in G by exploiting the degeneracy of G, which allows us to beat the state-of-the-art subgraph counting algorithms when G is sparse enough. For example, we can count the induced copies of any k-node pattern H in time $$2^{O(k^2)} O(n^{0.25k + 2} \log n)$$ 2 O ( k 2 ) O ( n 0.25 k + 2 log n ) if G has bounded degeneracy, and in time $$2^{O(k^2)} O(n^{0.625k + 2} \log n)$$ 2 O ( k 2 ) O ( n 0.625 k + 2 log n ) if G has bounded average degree. These bounds are instantiations of a more general result, parameterized by the degeneracy of G and the structure of H, which generalizes classic bounds on counting cliques and complete bipartite graphs. We also give lower bounds based on the Exponential Time Hypothesis, showing that our results are actually a characterization of the complexity of subgraph counting in bounded-degeneracy graphs.