Comparative analysis of box-covering algorithms for fractal networks

Research on fractal networks is a dynamically growing field of network science. A central issue is to analyze the fractality with the so-called box-covering method. As this problem is known to be NP-hard, a plethora of approximating algorithms have been proposed throughout the years. This study aims to establish a unified framework for comparing approximating box-covering algorithms by collecting, implementing, and evaluating these methods in various aspects including running time and approximation ability. This work might also serve as a reference for both researchers and practitioners, allowing fast selection from a rich collection of box-covering algorithms with a publicly available codebase.

Size effect characteristics of structural surfaces by improved projective covering method

Accurate characteristic of structural surfaces roughness at the relevant scale is very important to understand mechanical properties of rock mass discontinuities. So, a systematic investigation has been carried out to understand the effect of scale on the structural surface roughness by fractal dimension method. Firstly, considering the shortcoming of the projective covering method (PCM), we improved this method based on stochastic approach. Secondly, to investigate the size effect of the structural surface roughness, we selected six sampling windows, respectively, from the central and four corners part of structural planes (2 m × 2 m). The sampling windows range from 62.5 mm × 62.5 mm to 2000 mm × 2000 mm. And then, we calculated fractal parameters of the different size surfaces using improved projective covering method (IPCM) at the same resolution. Thirdly, we discussed a new method of determining reasonable size of structural surfaces by the parameter $$\Delta D_{\max }^{SD}$$ Δ D max SD . This parameter is difference of the maximum fractal dimension of the same size structural surface in different regions. The results show that: (1) The size effect of structure surfaces is different with different morphological surface. Generally, as the size increases, the roughness of structure surfaces increases and then decreases. There is positive size effect in small scale and negative size effect in large scale. (2) For a given structural surface, when the same size surfaces are selected from different locations of the structural planes, and the size effect characteristics are also different. (3) As the size of structure surfaces increases, the parameter $$\Delta D_{\max }^{SD}$$ Δ D max SD gradually decreases and tends to almost constant. The result of this study is a useful supplement to the comprehensive understanding of the size effect of structural surfaces roughness.

Outside-in box covering method and information dimension of Sierpinski networks

Self-similarity is a significant property for complex networks. Box coverage method and dimension calculation are vital tools to study the characteristic of complex networks. In this paper, we propose an outside-in (OSI) box covering method for the Sierpinski networks, and it is attested that this coverage algorithm is superior to CBB algorithm. In addition, we deduce the optimal box recurrence formula of weighted and unweighted networks theoretically, and the result is the same as that of the algorithm value. We also obtain the information dimension of weighted network, which verifies the validity and feasibility of our method.

OPTIMIZATION ASSIGNMENT OF WESTERN PATROL UNIT (KRI) ELEMENT IN SEA SECURITY OPERATIONS IN RIAU ISLANDS WATER AREAS USING SET COVERING MODEL

The territorial waters of Riau Islands are one of the locations with a high level of vulnerability to violations in thesea in Indonesia, because this region is directly adjacent to neighboring countries and is an international tradeand shipping route. One of the roles of the Indonesian Navy is to maintain the security of national jurisdictions,including in the territorial waters of Riau Islands, which are then realized in Operation Sea Security, where theimplementation still has several constraints, namely budget constraints, technical capabilities, number of ships,limited information, and limitations supporting facilities, so that the implementation of Marine SecurityOperations is not optimal. The main reason is the placement of patrol boats during operations is not wellorganized. With these problems, a study was conducted using the set covering method to get the most optimallocation for patrol boat placement with as few ships as possible but still be able to reach the entire waters of theRiau Islands and minimize operational costs. In this study a discrete approach was taken, namely thedetermination of the critical points, which numbered 37 vulnerable points. All these points must be affordable bythe ship on duty.Keywords: Set Covering, Location Selection, Marine Security Operations, Riau Islands Waters Region