Queryable Compression on Time-evolving Web and Social Networks with Streaming

Time-evolving web and social network graphs are modeled as a set of pages/individuals (nodes) and their arcs (links/relationships) that change over time. Due to their popularity, they have become increasingly massive in terms of their number of nodes, arcs, and lifetimes. However, these graphs are extremely sparse throughout their lifetimes. For example, it is estimated that Facebook has over a billion vertices, yet at any point in time, it has far less than 0.001% of all possible relationships. The space required to store these large sparse graphs may not fit in most main memories using underlying representations such as a series of adjacency matrices or adjacency lists. We propose building a compressed data structure that has a compressed binary tree corresponding to each row of each adjacency matrix of the time-evolving graph. We do not explicitly construct the adjacency matrix, and our algorithms take the time-evolving arc list representation as input for its construction. Our compressed structure allows for directed and undirected graphs, faster arc and neighborhood queries, as well as the ability for arcs and frames to be added and removed directly from the compressed structure (streaming operations). We use publicly available network data sets such as Flickr, Yahoo!, and Wikipedia in our experiments and show that our new technique performs as well or better than our benchmarks on all datasets in terms of compression size and other vital metrics.

Side Tributary Distribution of Quasi-Uniform Iterative Binary Tree Networks for River Networks

Self-similarity and plane-filling are intrinsic structure properties of natural river networks. Statistical data indicates that most natural river networks are Tokunaga trees. Researchers have explored to use iterative binary tree networks (IBTNs) to simulate natural river networks. However, the characteristics of natural rivers such as Tokunaga self-similarity and plane-filling cannot be easily guaranteed by the configuration of the IBTN. In this paper, the generator series and a quasi-uniform iteration rule are specified for the generation of nonstochastic quasi-uniform iterative binary tree networks (QU-IBTNs). First, we demonstrate that QU-IBTNs definitely satisfy self-similarity. Second, we show that the constraint for a QU-IBTN to be a Tokunaga tree is that the exterior links must be replaced in the generator series with a neighboring generator that is larger than the interior links during the iterative process. Moreover, two natural river networks are examined to reveal the inherent consistency with QU-IBTN at low Horton-Strahler orders.

Evaluation of teaching quality based on binary tree support vector machine

In order to solve the reliability of the evaluation results of teaching quality in universities and colleges, an improved model of teaching evaluation based on the Support vector machine was put forward. In this model, the evaluator does not need to give an evaluation result of the teacher’s teaching quality, but gives the score of each evaluation index, and then calls the Support vector machine, automatic classification of teachers’ teaching quality. The experiment proves that the improved algorithm can improve the teaching quality evaluation accuracy and the result is better.

A Combinatorial Bijection on di-sk Trees

A di-sk tree is a rooted binary tree whose nodes are labeled by $\oplus$ or $\ominus$, and no node has the same label as its right child. The di-sk trees are in natural bijection with separable permutations. We construct a combinatorial bijection on di-sk trees proving the two quintuples $(\mathrm{LMAX},\mathrm{LMIN},\mathrm{DESB},\mathsf{iar},\mathsf{comp})$ and $(\mathrm{LMAX},\mathrm{LMIN},\mathrm{DESB},\mathsf{comp},\mathsf{iar})$ have the same distribution over separable permutations. Here for a permutation $\pi$, $\mathrm{LMAX}(\pi)/\mathrm{LMIN}(\pi)$ is the set of values of the left-to-right maxima/minima of $\pi$ and $\mathrm{DESB}(\pi)$ is the set of descent bottoms of $\pi$, while $\mathsf{comp}(\pi)$ and $\mathsf{iar}(\pi)$ are respectively the number of components of $\pi$ and the length of initial ascending run of $\pi$. Interestingly, our bijection specializes to a bijection on $312$-avoiding permutations, which provides (up to the classical Knuth–Richards bijection) an alternative approach to a result of Rubey (2016) that asserts the two triples $(\mathrm{LMAX},\mathsf{iar},\mathsf{comp})$ and $(\mathrm{LMAX},\mathsf{comp},\mathsf{iar})$ are equidistributed on $321$-avoiding permutations. Rubey's result is a symmetric extension of an equidistribution due to Adin–Bagno–Roichman, which implies the class of $321$-avoiding permutations with a prescribed number of components is Schur positive. Some equidistribution results for various statistics concerning tree traversal are presented in the end.

Sandy Soil Liquefaction Prediction Based on Clustering-Binary Tree Neural Network Algorithm Model

The neural network algorithm is a small sample machine learning method built on the statistical learning theory and the lowest structural risk principle. Classical neural network algorithms mainly aim at solving two-classification problems, making it infeasible for multiclassification problems encountered in engineering practice. According to the main factors affecting sand liquefaction, a sand liquefaction discriminant model based on a clustering-binary tree multiclass neural network algorithm is established using the class distance idea in cluster analysis. The model can establish the nonlinear relationship between sand liquefaction and various influencing factors by learning limited samples. The research results show that the hierarchical structure based on the clustering-binary tree neural network algorithm is reasonable, and the sand liquefaction level can be categorized accurately.

Binary Tree Based Data Gathering Routing Scheme for Wireless Sensor Networks

Wireless sensor network (WSN) is an emerging area in networking since the era of 21 st century. The major benefits of WSN using sensor nodes make it affordable, scalable, economic and reliable. The limitations of sensor nodes are in terms of fixed and limited power supply, durability, storage and computational facilities which make energy as a vast challenge in deploying sensor nodes in order to prevent them from draining. This paper proposes a novel deployment scheme for connecting the sensor nodes in the form of a 4-sided virtual full binary tree structure. In the proposed scheme, data is expected to reach resource opulence Base Station (BS) via hops as equal to the height of the tree. Also, the stability of the network will increase by an average value of around 82.78% in the range of 49- 98% with existing scheme of the network lifetime with respect to different scenarios. The proposed scheme gives excellent results with a variable number of nodes and changing the size of deployment area of WSN.