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Symmetry
Volume 9
Issue 6
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Symmetry, Volume 9, Issue 6 (June 2017) – 17 articles

Cover Story (view full-size image): The organocatalytic synthesis of enantiomerically-enriched (R)-modafinil, accomplished with the chiral bifunctional BINOL-phosphate was developed. In addition, the successful application of a dipeptide-based ligand in the biomimetic non-heme iron-catalyzed sulfoxidation towards (R)-modafinil is shown. The desired compound could be obtained in both cases via sulfoxidation using H2O2 as an environmentally friendly oxidant. View the paper
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249 KiB  
Article
Extension of the TODIM Method to Intuitionistic Linguistic Multiple Attribute Decision Making
by Shuwei Wang and Jia Liu
Symmetry 2017, 9(6), 95; https://doi.org/10.3390/sym9060095 - 21 Jun 2017
Cited by 34 | Viewed by 4387
Abstract
Practical decision situations are becoming increasingly complicated. It is common for a person to select or rank alternatives with respect to multiple attributes, and the TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) method, which is one of the [...] Read more.
Practical decision situations are becoming increasingly complicated. It is common for a person to select or rank alternatives with respect to multiple attributes, and the TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) method, which is one of the first multiple attribute decision making (MADM) methods based on prospect theory, has received more attention due to its great performance in considering the bounded rationality of decision makers (DMs). However, the classical TODIM method can only handle the MADM problems with crisp numbers. In this paper, considering that intuitionistic linguistic variables are convenient to describe uncertain or imprecise information, we propose the intuitionistic linguistic TODIM (IL-TODIM) method and intuitionistic uncertain linguistic TODIM (IUL-TODIM) method to solve uncertain MADM problems with IL and IUL variables, respectively. Additionally, a novel distance measure for IUL numbers is developed, based on which we can obtain the corresponding dominance degree of one alternative over another. Finally, examples are provided to show the validity of the proposed methods, and we also conduct a comparison of the results between the IL-TODIM method and the existing intuitionistic fuzzy MADM methods to illustrate the effectiveness of our proposed methods. Full article
4517 KiB  
Article
Cooperative Localization Algorithm for Multiple Mobile Robot System in Indoor Environment Based on Variance Component Estimation
by Qian Sun, Ming Diao, Ya Zhang and Yibing Li
Symmetry 2017, 9(6), 94; https://doi.org/10.3390/sym9060094 - 20 Jun 2017
Cited by 9 | Viewed by 3916
Abstract
The Multiple Mobile Robot (MMR) cooperative system is becoming a focus of study in various fields due to its advantages, such as high efficiency and good fault tolerance. However, the uncertainty and nonlinearity problems severely limit the cooperative localization accuracy of the MMR [...] Read more.
The Multiple Mobile Robot (MMR) cooperative system is becoming a focus of study in various fields due to its advantages, such as high efficiency and good fault tolerance. However, the uncertainty and nonlinearity problems severely limit the cooperative localization accuracy of the MMR system. Thus, to solve the problems mentioned above, this manuscript presents a cooperative localization algorithm for MMR systems based on Cubature Kalman Filter (CKF) and adaptive Variance Component Estimation (VCE) methods. In this novel algorithm, a nonlinear filter named CKF is used to enhance the cooperative localization accuracy and reduce the computational load. On the other hand, the adaptive VCE method is introduced to eliminate the effects of unknown system noise. Furthermore, the performance of the proposed algorithm is compared with that of the cooperative localization algorithm based on normal CKF by utilizing the real experiment data. In addition, the results demonstrate that the proposed algorithm outperforms the CKF cooperative localization algorithm both in accuracy and consistency. Full article
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7063 KiB  
Article
Image Enhancement for Surveillance Video of Coal Mining Face Based on Single-Scale Retinex Algorithm Combined with Bilateral Filtering
by Lei Si, Zhongbin Wang, Rongxin Xu, Chao Tan, Xinhua Liu, and Jing Xu
Symmetry 2017, 9(6), 93; https://doi.org/10.3390/sym9060093 - 19 Jun 2017
Cited by 21 | Viewed by 7083
Abstract
Surveillance videos of coal mining faces have close relation to the safety of coal miners and mining efficiency. However, surveillance videos are always disturbed by some severe conditions such as atomization, low illumination, glare, and so on. Therefore, this paper proposed a hybrid [...] Read more.
Surveillance videos of coal mining faces have close relation to the safety of coal miners and mining efficiency. However, surveillance videos are always disturbed by some severe conditions such as atomization, low illumination, glare, and so on. Therefore, this paper proposed a hybrid algorithm (SSR-BF) based on the integration of single-scale Retinex (SSR) and bilateral filtering (BF) to enhance the image quality of surveillance videos. BF was coupled with SSR to reduce the noises and perfect the edge information in the image. The schematic diagram and pseudocode of SSR-BF was designed, and the parameters were set rationally to ensure the enhancement effects through some simulations. Finally, some comparisons with other methods were carried out, and the simulation results demonstrated that the proposed algorithm was superior to others and could be applied to image enhancement for poormonochrome images, especially the surveillance video of a coal mining face. Full article
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10416 KiB  
Article
High-Capacity Data-Hiding Scheme on Synthesized Pitches Using Amplitude Enhancement—A New Vision of Non-Blind Audio Steganography
by Hung-Jr. Shiu, Bor-Shing Lin, Chia-Wei Cheng, Chien-Hung Huang and Chin-Laung Lei
Symmetry 2017, 9(6), 92; https://doi.org/10.3390/sym9060092 - 17 Jun 2017
Cited by 9 | Viewed by 4707
Abstract
This work proposes a new and non-blind steganographic scheme for synthesized pitches. Synthesized music is popularly used to demonstrate early versions of compositions conveniently and at low-cost. They can also be utilized to pass secrets or obtain digital rights. The method consists of [...] Read more.
This work proposes a new and non-blind steganographic scheme for synthesized pitches. Synthesized music is popularly used to demonstrate early versions of compositions conveniently and at low-cost. They can also be utilized to pass secrets or obtain digital rights. The method consists of two procedures, of which the first is the realistic simulation of synthesized pitches using a computer and the second is the hiding of secrets during the generated simulated pitches. The first part of this paper reviews attempts to discover the fundamental patterns of synthesized pitches and to develop a strategy for generating approximate pitches using a computer. The component frequencies are used to generate a pitch in which to hide secrets. Legal receivers receive the referenced composition and frequencies, enabling them to generate the synthesized pitches according to the main frequencies of the referenced composition. Finally, the generated and received pitches are compared to identify the secret bits. As more frequencies are used to hide secret bits, more secret bits can be embedded in the synthesized pitches. The use of more frequencies makes synthesized pitches more realistic compared to real ones. The performance of the proposed method is also compared with that of competing methods and under common attacks. Full article
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2492 KiB  
Article
Performance Enhancement of Indoor Pedestrian Positioning with Two-Order Bayesian Estimation Based on EKF and PF
by Tao Jiang, Xianfeng Yang and Xufei Cui
Symmetry 2017, 9(6), 91; https://doi.org/10.3390/sym9060091 - 16 Jun 2017
Cited by 2 | Viewed by 3860
Abstract
To improve the accuracy of indoor pedestrian positioning, an indoor pedestrian positioning system with two-order Bayesian estimation based on Extended Kalman Filter (EKF) and Particle Filter (PF) is proposed in this paper. The presented system combines a foot-mounted inertial sensor, a Wi-Fi propagation [...] Read more.
To improve the accuracy of indoor pedestrian positioning, an indoor pedestrian positioning system with two-order Bayesian estimation based on Extended Kalman Filter (EKF) and Particle Filter (PF) is proposed in this paper. The presented system combines a foot-mounted inertial sensor, a Wi-Fi propagation model and building structure to make good use of these information resources. There are two updates in this system in order to limit the accumulative errors of inertial sensors. In the first update, the inertial navigation system (INS) is the main system in the calculation of pedestrian positioning, and Zero-velocity update (ZUPT) is introduced as the reference to correct the accumulative errors of INS based on EKF. To further limit the accumulative errors of inertial sensors, the estimated results obtained from the first update, including horizontal position information, are introduced as the observations based on PF in the second update; Pedestrian Dead Reckoning (PDR) is the main system in the calculation of pedestrian positioning, and the weight of particles is determined by the Wi-Fi propagation model, building structure information and output of the first update. The results show that the accuracy of positioning is effectively increased. Full article
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222 KiB  
Article
Coincidences of the Concave Integral and the Pan-Integral
by Yao Ouyang, Jun Li and Radko Mesiar
Symmetry 2017, 9(6), 90; https://doi.org/10.3390/sym9060090 - 16 Jun 2017
Cited by 18 | Viewed by 3540
Abstract
In this note, we discuss when the concave integral coincides with the pan- integral with respect to the standard arithmetic operations + and ·. The subadditivity of the underlying monotone measure is one sufficient condition for this equality. We show also another sufficient [...] Read more.
In this note, we discuss when the concave integral coincides with the pan- integral with respect to the standard arithmetic operations + and ·. The subadditivity of the underlying monotone measure is one sufficient condition for this equality. We show also another sufficient condition, which, in the case of finite spaces, is necessary, too. Full article
749 KiB  
Article
Towards Secure Data Retrieval for Multi-Tenant Architecture Using Attribute-Based Key Word Search
by Hanshu Hong, Yunhao Xia and Zhixin Sun
Symmetry 2017, 9(6), 89; https://doi.org/10.3390/sym9060089 - 16 Jun 2017
Cited by 2 | Viewed by 3537
Abstract
Searchable encryption mechanism and attribute-based encryption (ABE) are two effective tools for providing fine-grained data access control in the cloud. Researchers have also taken their advantages to present searchable encryption schemes based on ABE and have achieved significant results. However, most of the [...] Read more.
Searchable encryption mechanism and attribute-based encryption (ABE) are two effective tools for providing fine-grained data access control in the cloud. Researchers have also taken their advantages to present searchable encryption schemes based on ABE and have achieved significant results. However, most of the existing key word search schemes based on ABE lack the properties of key exposure protection and highly efficient key updating when key leakage happens. To better tackle these problems, we present a key insulated attribute-based data retrieval scheme with key word search (KI-ABDR-KS) for multi-tenant architecture. In our scheme, a data owner can make a self-centric access policy of the encrypted data. Only when the possessing attributes match with the policy can a receiver generate a valid trapdoor and search the ciphertext. The proposed KI-ABDR-KS also provides full security protection when key exposure happens, which can minimize the damage brought by key exposure. Furthermore, the system public parameters remain unchanged during the process of key updating; this will reduce the considerable overheads brought by parameters synchronization. Finally, our KI-ABDR-KS is proven to be secure under chosen-keyword attack and achieves better efficiency compared to existing works. Full article
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2258 KiB  
Article
Synthesis of (R)-Modafinil via Organocatalyzed and Non-Heme Iron-Catalyzed Sulfoxidation Using H2O2 as an Environmentally Benign Oxidant
by Felix E. Held, Kerstin A. Stingl and Svetlana B. Tsogoeva
Symmetry 2017, 9(6), 88; https://doi.org/10.3390/sym9060088 - 16 Jun 2017
Cited by 6 | Viewed by 6960
Abstract
The first organocatalyzed sulfoxidation reaction towards enantioenriched (R)-modafinil (Armodafinil®), a drug against narcolepsy, is reported here. A series of chiral organocatalysts, e.g., different chiral BINOL-phosphates, or a fructose-derived N-substituted oxazolidinone ketone (Shi catalyst) were applied for the sulfoxidation [...] Read more.
The first organocatalyzed sulfoxidation reaction towards enantioenriched (R)-modafinil (Armodafinil®), a drug against narcolepsy, is reported here. A series of chiral organocatalysts, e.g., different chiral BINOL-phosphates, or a fructose-derived N-substituted oxazolidinone ketone (Shi catalyst) were applied for the sulfoxidation reaction with environmentally friendly H2O2 as a convenient oxygen transferring agent. Furthermore, the potential of a biomimetic catalytic system consisting of FeCl3 and a dipeptide-based chiral ligand was demonstrated, which constitutes the most successful asymmetric non-heme iron-catalyzed synthesis of (R)-modafinil so far. Full article
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1126 KiB  
Article
Discrete Optimization with Fuzzy Constraints
by Primož Jelušič and Bojan Žlender
Symmetry 2017, 9(6), 87; https://doi.org/10.3390/sym9060087 - 16 Jun 2017
Cited by 10 | Viewed by 5765
Abstract
The primary benefit of fuzzy systems theory is to approximate system behavior where analytic functions or numerical relations do not exist. In this paper, heuristic fuzzy rules were used with the intention of improving the performance of optimization models, introducing experiential rules acquired [...] Read more.
The primary benefit of fuzzy systems theory is to approximate system behavior where analytic functions or numerical relations do not exist. In this paper, heuristic fuzzy rules were used with the intention of improving the performance of optimization models, introducing experiential rules acquired from experts and utilizing recommendations. The aim of this paper was to define soft constraints using an adaptive network-based fuzzy inference system (ANFIS). This newly-developed soft constraint was applied to discrete optimization for obtaining optimal solutions. Even though the computational model is based on advanced computational technologies including fuzzy logic, neural networks and discrete optimization, it can be used to solve real-world problems of great interest for design engineers. The proposed computational model was used to find the minimum weight solutions for simply-supported laterally-restrained beams. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making)
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6356 KiB  
Article
Focus Assessment Method of Gaze Tracking Camera Based on ε-Support Vector Regression
by Duc Thien Luong, Jeon Seong Kang, Phong Ha Nguyen, Min Beom Lee and Kang Ryoung Park
Symmetry 2017, 9(6), 86; https://doi.org/10.3390/sym9060086 - 14 Jun 2017
Cited by 1 | Viewed by 4577
Abstract
In order to capture an eye image of high quality in a gaze-tracking camera, an auto-focusing mechanism is used, which requires accurate focus assessment. Although there has been previous research on focus assessment in the spatial or wavelet domains, there are few previous [...] Read more.
In order to capture an eye image of high quality in a gaze-tracking camera, an auto-focusing mechanism is used, which requires accurate focus assessment. Although there has been previous research on focus assessment in the spatial or wavelet domains, there are few previous studies that combine all of the methods of spatial and wavelet domains. Since all of the previous focus assessments in the spatial or wavelet domain methods have disadvantages, such as being affected by illumination variation, etc., we propose a new focus assessment method by combining the spatial and wavelet domain methods for the gaze-tracking camera. This research is novel in the following three ways, in comparison with the previous methods. First, the proposed focus assessment method combines the advantages of spatial and wavelet domain methods by using ε-support vector regression (SVR) with a symmetrical Gaussian radial basis function (RBF) kernel. In order to prevent the focus score from being affected by a change in image brightness, both linear and nonlinear normalizations are adopted in the focus score calculation. Second, based on the camera optics, we mathematically prove the reason for the increase in the focus score in the case of daytime images or a brighter illuminator compared to nighttime images or a darker illuminator. Third, we propose a new criterion to compare the accuracies of the focus measurement methods. This criterion is based on the ratio of relative overlapping amount (standard deviation of focus score) between two adjacent positions along the Z-axis to the entire range of focus score variety between these two points. Experimental results showed that the proposed method outperforms other methods. Full article
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9819 KiB  
Article
Symmetry and Structure in the POT Family of Proton Coupled Peptide Transporters
by Simon Newstead
Symmetry 2017, 9(6), 85; https://doi.org/10.3390/sym9060085 - 14 Jun 2017
Cited by 2 | Viewed by 6934
Abstract
The POT family of proton coupled oligopeptide transporters belong to the Major Facilitator Superfamily of secondary active transporters and are found widely distributed in bacterial, plant, fungal and animal genomes. POT transporters use the inwardly directed proton electrochemical gradient to drive the concentrative [...] Read more.
The POT family of proton coupled oligopeptide transporters belong to the Major Facilitator Superfamily of secondary active transporters and are found widely distributed in bacterial, plant, fungal and animal genomes. POT transporters use the inwardly directed proton electrochemical gradient to drive the concentrative uptake of di- and tri-peptides across the cell membrane for metabolic assimilation. Mammalian members of the family, PepT1 and PepT2, are responsible for the uptake and retention of dietary protein in the human body, and due to their promiscuity in ligand recognition, play important roles in the pharmacokinetics of drug transport. Recent crystal structures of bacterial and plant members have revealed the overall architecture for this protein family and provided a framework for understanding proton coupled transport within the POT family. An interesting outcome from these studies has been the discovery of symmetrically equivalent structural and functional sites. This review will highlight both the symmetry and asymmetry in structure and function within the POT family and discuss the implications of these considerations in understanding transport and regulation. Full article
(This article belongs to the Special Issue Symmetry in Structural Biology)
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643 KiB  
Article
Early- and Late-Light Embryonic Stimulation Modulates Similarly Chicks’ Ability to Filter out Distractors
by Cinzia Chiandetti, Bastien S. Lemaire, Elisabetta Versace and Giorgio Vallortigara
Symmetry 2017, 9(6), 84; https://doi.org/10.3390/sym9060084 - 8 Jun 2017
Cited by 16 | Viewed by 5209
Abstract
Chicks (Gallus gallus) learned to run from a starting box to a target located at the end of a runway. At test, colourful and bright distractors were placed just outside the starting box. Dark incubated chicks (maintained in darkness from fertilization [...] Read more.
Chicks (Gallus gallus) learned to run from a starting box to a target located at the end of a runway. At test, colourful and bright distractors were placed just outside the starting box. Dark incubated chicks (maintained in darkness from fertilization to hatching) stopped significantly more often, assessing more the left-side distractor than chicks hatched after late (for 42 h during the last three days before hatching) or early (for 42 h after fertilization) exposure to light. The results show that early embryonic light stimulation can modulate this particular behavioural lateralization comparably to the late application of it, though via a different route. Full article
(This article belongs to the Special Issue Brain Asymmetry of Structure and/or Function)
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945 KiB  
Article
Rice Leaf Lateral Asymmetry in the Relationship between SPAD and Area-Based Nitrogen Concentration
by Shen Yuan, Travis Luc Goron, Liying Huang, Lilian Wu and Fei Wang
Symmetry 2017, 9(6), 83; https://doi.org/10.3390/sym9060083 - 2 Jun 2017
Cited by 4 | Viewed by 5310
Abstract
Rice leaves display lateral asymmetry around the midrib, and the narrow side exhibits higher leaf area-based nitrogen concentration (Na) and soil plant analysis development (SPAD) values than the wider side. However, the difference in the relationship between the SPAD of each side and [...] Read more.
Rice leaves display lateral asymmetry around the midrib, and the narrow side exhibits higher leaf area-based nitrogen concentration (Na) and soil plant analysis development (SPAD) values than the wider side. However, the difference in the relationship between the SPAD of each side and Na of the corresponding lateral half, and the optimal position along the leaf blade for SPAD measurements are not known. In this study, the relationship between SPAD and Na of both sides of the top three leaves was determined with 17 rice varieties grown over three growing seasons in two locations. The relationship between SPAD and Na displayed leaf lateral asymmetry, in which the wide side reflected a higher coefficient of determination than the narrow side. The ability to estimate Na of the whole leaf was slightly improved by averaging SPAD values across the leaf sides and measured points for the top two leaves. Apparently, it was more accurate and easier to measure SPAD readings on the wide side than the narrow side of rice leaf blade with respect to estimating plant N status. Due to the relatively poor relationship of the upper leaf, and the structural limit for SPAD measurements of the base, this study suggests that the most suitable and representative position for SPAD meter measurement on the leaf blade of rice is the lower-middle part from the leaf apex on the wide side. Full article
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395 KiB  
Article
Some Single-Valued Neutrosophic Dombi Weighted Aggregation Operators for Multiple Attribute Decision-Making
by Jiqian Chen and Jun Ye
Symmetry 2017, 9(6), 82; https://doi.org/10.3390/sym9060082 - 2 Jun 2017
Cited by 144 | Viewed by 6173
Abstract
The Dombi operations of T-norm and T-conorm introduced by Dombi can have the advantage of good flexibility with the operational parameter. In existing studies, however, the Dombi operations have so far not yet been used for neutrosophic sets. To propose new aggregation operators [...] Read more.
The Dombi operations of T-norm and T-conorm introduced by Dombi can have the advantage of good flexibility with the operational parameter. In existing studies, however, the Dombi operations have so far not yet been used for neutrosophic sets. To propose new aggregation operators for neutrosophic sets by the extension of the Dombi operations, this paper firstly presents the Dombi operations of single-valued neutrosophic numbers (SVNNs) based on the operations of the Dombi T-norm and T-conorm, and then proposes the single-valued neutrosophic Dombi weighted arithmetic average (SVNDWAA) operator and the single-valued neutrosophic Dombi weighted geometric average (SVNDWGA) operator to deal with the aggregation of SVNNs and investigates their properties. Because the SVNDWAA and SVNDWGA operators have the advantage of good flexibility with the operational parameter, we develop a multiple attribute decision-making (MADM) method based on the SVNWAA or SVNWGA operator under a SVNN environment. Finally, an illustrative example about the selection problem of investment alternatives is given to demonstrate the application and feasibility of the developed approach. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making)
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2176 KiB  
Article
Enhanced Quality of Service of Cell-Edge User by Extending Modified Largest Weighted Delay First Algorithm in LTE Networks
by Hasibur Rashid Chayon, Kaharudin Bin Dimyati, Harikrishnan Ramiah and Ahmed Wasif Reza
Symmetry 2017, 9(6), 81; https://doi.org/10.3390/sym9060081 - 31 May 2017
Cited by 12 | Viewed by 5741
Abstract
Long Term Evolution (LTE) is the prominent technology in Fourth Generation (4G) communication standards, which provides higher throughput and better Quality of Service (QoS) to all users. However, users in the cell-edge area are receiving comparatively low QoS due to the distance from [...] Read more.
Long Term Evolution (LTE) is the prominent technology in Fourth Generation (4G) communication standards, which provides higher throughput and better Quality of Service (QoS) to all users. However, users in the cell-edge area are receiving comparatively low QoS due to the distance from eNodeB (eNB) and bad channel conditions. The Conventional Modified Largest Weighted Delay First (MLWDF) algorithm is unable to resolve this issue, as it does not consider the location of the user. This paper proposes an extended MLWDF (EMLWDF) downlink scheduling algorithm to provide better services to the cell-edge user as well as to the cell-center user. The proposed algorithm divides the eNB cell area into inner and outer regions. It includes the distance of the user from attached eNB, received Signal to Interference plus Noise Ratio (SINR) and error probability into the original algorithm. The simulated results are compared with other well-known algorithms and the comparison shows that the proposed algorithm enhances overall 56.23% of cell-edge user throughput and significantly improves the average user throughput, fairness index, and spectral efficiency. Full article
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260 KiB  
Article
Multiple Attribute Decision-Making Method Using Correlation Coefficients of Normal Neutrosophic Sets
by Jun Ye
Symmetry 2017, 9(6), 80; https://doi.org/10.3390/sym9060080 - 26 May 2017
Cited by 29 | Viewed by 4022
Abstract
The normal distribution is a usual one of various distributions in the real world. A normal neutrosophic set (NNS) is composed of both a normal fuzzy number and a neutrosophic number, which a significant tool for describing the incompleteness, indeterminacy, and inconsistency of [...] Read more.
The normal distribution is a usual one of various distributions in the real world. A normal neutrosophic set (NNS) is composed of both a normal fuzzy number and a neutrosophic number, which a significant tool for describing the incompleteness, indeterminacy, and inconsistency of the decision-making information. In this paper, we propose two correlation coefficients between NNSs based on the score functions of normal neutrosophic numbers (NNNs) (basic elements in NNSs) and investigate their properties. Then, we develop a multiple attribute decision-making (MADM) method with NNSs under normal neutrosophic environments, where, by correlation coefficient values between each alternative (each evaluated NNS) and the ideal alternative (the ideal NNS), the ranking order of alternatives and the best one are given in the normal neutrosophic decision-making process. Finally, an illustrative example about the selection problem of investment alternatives is provided to demonstrate the application and feasibility of the developed decision-making method. Compared to the existing MADM approaches based on aggregation operators of NNNs, the proposed MADM method based on the correlation coefficients of NNSs shows the advantage of its simple decision-making process. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making)
273 KiB  
Communication
Path Embeddings with Prescribed Edge in the Balanced Hypercube Network
by Dan Chen, Zhongzhou Lu, Zebang Shen, Gaofeng Zhang, Chong Chen and Qingguo Zhou
Symmetry 2017, 9(6), 79; https://doi.org/10.3390/sym9060079 - 26 May 2017
Cited by 2 | Viewed by 4209
Abstract
The balanced hypercube network, which is a novel interconnection network for parallel computation and data processing, is a newly-invented variant of the hypercube. The particular feature of the balanced hypercube is that each processor has its own backup processor and they are connected [...] Read more.
The balanced hypercube network, which is a novel interconnection network for parallel computation and data processing, is a newly-invented variant of the hypercube. The particular feature of the balanced hypercube is that each processor has its own backup processor and they are connected to the same neighbors. A Hamiltonian bipartite graph with bipartition V 0 ∪ V 1 x ∈ V 0 y ∈ V 1 . It is known that each edge is on a Hamiltonian cycle of the balanced hypercube. In this paper, we prove that, for an arbitrary edge e in the balanced hypercube, there exists a Hamiltonian path between any two vertices x and y in different partite sets passing through e with e ≠ x y . This result improves some known results. Full article
(This article belongs to the Special Issue Symmetry in Complex Networks II)
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