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"Sudoku"
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Mathematics of a Sudo-Kurve
We investigate a type of a Sudoku variant called Sudo-Kurve, which allows bent rows and columns, and develop a new, yet equivalent, variant we call a Sudo-Cube. We examine the total number of distinct solution grids for this type with or without symmetry. We study other mathematical aspects of this puzzle along with the minimum number of clues needed and the number of ways to place individual symbols.
Journal Article
Exact Method for Generating Strategy-Solvable Sudoku Clues
A Sudoku puzzle often has a regular pattern in the arrangement of initial digits and it is typically made solvable with known solving techniques called strategies. In this paper, we consider the problem of generating such Sudoku instances. We introduce a rigorous framework to discuss solvability for Sudoku instances with respect to strategies. This allows us to handle not only known strategies but also general strategies under a few reasonable assumptions. We propose an exact method for determining Sudoku clues for a given set of clue positions that is solvable with a given set of strategies. This is the first exact method except for a trivial brute-force search. Besides the clue generation, we present an application of our method to the problem of determining the minimum number of strategy-solvable Sudoku clues. We conduct experiments to evaluate our method, varying the position and the number of clues at random. Our method terminates within 1 min for many grids. However, as the number of clues gets closer to 20, the running time rapidly increases and exceeds the time limit set to 600 s. We also evaluate our method for several instances with 17 clue positions taken from known minimum Sudokus to see the efficiency for deciding unsolvability.
Journal Article
An Efficient Data-Hiding Scheme Based on Multidimensional Mini-SuDoKu
The massive Internet of Things (IoT) connecting various types of intelligent sensors for goods tracking in logistics, environmental monitoring and smart grid management is a crucial future ICT. High-end security and low power consumption are major requirements in scaling up the IoT. In this research, we propose an efficient data-hiding scheme to deal with the security problems and power saving issues of multimedia communication among IoT devises. Data hiding is the practice of hiding secret data into cover images in order to conceal and prevent secret data from being intercepted by malicious attackers. One of the established research streams of data-hiding methods is based on reference matrices (RM). In this study, we propose an efficient data-hiding scheme based on multidimensional mini-SuDoKu RM. The proposed RM possesses high complexity and can effectively improve the security of data hiding. In addition, this study also defines a range locator function which can significantly improve the embedding efficiency of multidimensional RM. Experimental results show that our data-hiding scheme can not only obtain better image quality, but also achieve higher embedding capacity than other related schemes.
Journal Article
Character table sudokus
It is a fun game to complete a partial character table of a finite group. We show that one can reconstruct a missing row or column from a given table. The proof relies on deep properties of fully ramified characters. Moreover, we extend a classification of groups with a “large” character degree started by Snyder and continued by Durfee and Jensen.
Journal Article
Disperse Partial Shading Effect of Photovoltaic Array by Means of the Modified Complementary SuDoKu Puzzle Topology
This paper presents a novel modified Complementary SuDoKu puzzle (MC-SDKP) topology for the static reconfiguration of photovoltaic (PV) arrays. It was developed with the aim of enhancing the power output of a PV array which is exposed to partially shaded conditions (PSCs). To disperse patterns of both center shading and corner shading, the MC-SDKP technique modified and combined the Optimal SDKP and the Complementary SDKP (C-SDKP) topologies. An 8 × 8 PV array configured with the MC-SDKP topology was exposed to nine different shading patterns, and its performance was compared with that of the other four topologies. The results of the performance evaluation confirmed that, when configured according to the MC-SDKP, the PV array produced the highest average power output among all five topologies, with a 15.07% higher output on average than the total-cross tied. The PV array with the MC-SDKP topology also exhibited the lowest average power loss (1.34%). This study clearly established the effectiveness of the MC-SDKP topology at mitigating the effects of both center and corner shading. The advantages of the MC-SDKP reconfiguration technique are: an increase in extracted power, a reduction in current mismatch losses, an improvement in shade dispersion under conditions of center shading, and good scalability.
Journal Article