Abstract The SM4 block cipher is a Chinese national standard and an ISO international standard. Since white-box cryptography has many real-life applications nowadays, a few white-box implementations of SM4 has been proposed, among which a type of constructions is dominated, which uses a linear or affine diagonal block encoding to protect the original three 32-bit branches entering a round function and uses its inverse as the input encoding to the S-box layer. In this paper, we analyse the security of this type of constructions against Lepoint et al.’s collision-based attack method. Our experiment under a small fraction of (encodings, round key) combinations shows that the rank of the concerned linear system is much less than the number of the involved unknowns, meaning these white-box SM4 implementations should resist Lepoint et al.’s method, but we leave it as an open problem whether there are such encodings that the rank of the corresponding linear system is slightly less than the number of the involved unknowns, in which scenario Lepoint et al.’s method may be used to recover a round key for the case with linear encodings and to remove most white-box operations until mainly some Boolean masks for the case with affine encodings.
{"title":"Cryptanalysis Of A Type Of White-Box Implementations Of The SM4 Block Cipher","authors":"Jiqiang Lu, Jingyu Li, Zexuan Chen, Yanan Li","doi":"10.1093/comjnl/bxad091","DOIUrl":"https://doi.org/10.1093/comjnl/bxad091","url":null,"abstract":"Abstract The SM4 block cipher is a Chinese national standard and an ISO international standard. Since white-box cryptography has many real-life applications nowadays, a few white-box implementations of SM4 has been proposed, among which a type of constructions is dominated, which uses a linear or affine diagonal block encoding to protect the original three 32-bit branches entering a round function and uses its inverse as the input encoding to the S-box layer. In this paper, we analyse the security of this type of constructions against Lepoint et al.’s collision-based attack method. Our experiment under a small fraction of (encodings, round key) combinations shows that the rank of the concerned linear system is much less than the number of the involved unknowns, meaning these white-box SM4 implementations should resist Lepoint et al.’s method, but we leave it as an open problem whether there are such encodings that the rank of the corresponding linear system is slightly less than the number of the involved unknowns, in which scenario Lepoint et al.’s method may be used to recover a round key for the case with linear encodings and to remove most white-box operations until mainly some Boolean masks for the case with affine encodings.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":"172 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135011338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Syed Irteza Hussain Jafri, Rozaida Ghazali, Irfan Javid, Yana Mazwin Mohmad Hassim, Mubashir Hayat Khan
Abstract Recommender systems are becoming more and more significant in today’s digital world and in the modern economy. They make a substantial contribution to company operations by offering tailored advice and decreasing overwhelm. Collaborative filtering, being popular in the domain of recommendation, is used to offer recommendations to attract the target audience based on the feedback of people with comparable interests. This method has some limitations, such as a cold-start issue, which makes the system less effective in anticipating unknown objects. We provide a hybrid deep-learning-based strategy centered on a method to enrich user and item profiles to address the cold-start issue in the recommendation process using a collaborative filtering approach. We employ pretrained deep learning models to produce rich user and item feature vectors that aid in the creation of useful suggestions and handling of user and item cold-start issues. The creation of more precise and tailored similarity matrices is made possible by adding metadata to the extracted features of the user and item. The results of the experiment demonstrate that in terms of precision and rate coverage, the proposed method performs better than the baseline techniques.
{"title":"A Hybrid Solution For The Cold Start Problem In Recommendation","authors":"Syed Irteza Hussain Jafri, Rozaida Ghazali, Irfan Javid, Yana Mazwin Mohmad Hassim, Mubashir Hayat Khan","doi":"10.1093/comjnl/bxad088","DOIUrl":"https://doi.org/10.1093/comjnl/bxad088","url":null,"abstract":"Abstract Recommender systems are becoming more and more significant in today’s digital world and in the modern economy. They make a substantial contribution to company operations by offering tailored advice and decreasing overwhelm. Collaborative filtering, being popular in the domain of recommendation, is used to offer recommendations to attract the target audience based on the feedback of people with comparable interests. This method has some limitations, such as a cold-start issue, which makes the system less effective in anticipating unknown objects. We provide a hybrid deep-learning-based strategy centered on a method to enrich user and item profiles to address the cold-start issue in the recommendation process using a collaborative filtering approach. We employ pretrained deep learning models to produce rich user and item feature vectors that aid in the creation of useful suggestions and handling of user and item cold-start issues. The creation of more precise and tailored similarity matrices is made possible by adding metadata to the extracted features of the user and item. The results of the experiment demonstrate that in terms of precision and rate coverage, the proposed method performs better than the baseline techniques.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135236050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The synchronous stream ciphers RCR-64 and RCR-32 designed by Sekar, Paul and Preneel are strengthened variants of the ciphers TPy and TPypy (designed by Biham and Seberry), respectively. The RCR ciphers have remained unbroken since they were published in 2007. In this paper, we present arguments that not only support the designers’ security claims but suggest, in general, that the ciphers are secure against several classes of cryptanalytic attacks. We find that the ciphers are best used with 256-bit keys and 384-bit IVs. We also suggest ways to protect software implementations of the RCR ciphers against (cache-)timing and processor flag attacks. Our performance evaluation suggests that the protected implementation of the RCR-64 encrypts long messages at speeds comparable to some of the fastest stream ciphers available today. Consequently, we find that the RCR ciphers may be well suited for PC-based applications in general and streaming audio / video applications in particular. This is the first paper to present a detailed study on the security and performance of the RCR ciphers.
{"title":"Revisiting the Software-Efficient Stream Ciphers RCR-64 and RCR-32","authors":"Mabin Joseph, Gautham Sekar, R Balasubramanian","doi":"10.1093/comjnl/bxad084","DOIUrl":"https://doi.org/10.1093/comjnl/bxad084","url":null,"abstract":"Abstract The synchronous stream ciphers RCR-64 and RCR-32 designed by Sekar, Paul and Preneel are strengthened variants of the ciphers TPy and TPypy (designed by Biham and Seberry), respectively. The RCR ciphers have remained unbroken since they were published in 2007. In this paper, we present arguments that not only support the designers’ security claims but suggest, in general, that the ciphers are secure against several classes of cryptanalytic attacks. We find that the ciphers are best used with 256-bit keys and 384-bit IVs. We also suggest ways to protect software implementations of the RCR ciphers against (cache-)timing and processor flag attacks. Our performance evaluation suggests that the protected implementation of the RCR-64 encrypts long messages at speeds comparable to some of the fastest stream ciphers available today. Consequently, we find that the RCR ciphers may be well suited for PC-based applications in general and streaming audio / video applications in particular. This is the first paper to present a detailed study on the security and performance of the RCR ciphers.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135265441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Knowledge graph (KG) is introduced as side information into recommender systems, which can alleviate the sparsity and cold start problems in collaborative filtering. Existing studies mainly focus on modeling users’ historical behavior data and KG-based propagation. However, they have the limitation of ignoring noise information during recommendation. We consider that noise exists in two parts (i.e. KG and user-item interaction data). In this paper, we propose Knowledge-aware Dual-Channel Graph Neural Networks (KDGNN) to improve the recommendation performance by reducing the noise in the recommendation process. Specifically, (1) for the noise in KG, we design a personalized gating mechanism, namely dual-channel balancing mechanism, to block the propagation of redundant information in KG. (2) For the noise in user-item interaction data, we integrate personalized and knowledge-aware signals to capture user preferences fully and use personalized knowledge-aware attention to denoise user-item interaction data. Compared with existing KG-based methods, we aim to propose a knowledge-aware recommendation method from a new perspective of denoising. We perform performance analysis on three real-world datasets, and experiment results demonstrate that KDGNN achieves strongly competitive performance compared with several compelling state-of-the-art baselines.
{"title":"Knowledge-Aware Dual-Channel Graph Neural Networks For Denoising Recommendation","authors":"Hanwen Zhang, Li-e Wang, Zhigang Sun, Xianxian Li","doi":"10.1093/comjnl/bxad085","DOIUrl":"https://doi.org/10.1093/comjnl/bxad085","url":null,"abstract":"Abstract Knowledge graph (KG) is introduced as side information into recommender systems, which can alleviate the sparsity and cold start problems in collaborative filtering. Existing studies mainly focus on modeling users’ historical behavior data and KG-based propagation. However, they have the limitation of ignoring noise information during recommendation. We consider that noise exists in two parts (i.e. KG and user-item interaction data). In this paper, we propose Knowledge-aware Dual-Channel Graph Neural Networks (KDGNN) to improve the recommendation performance by reducing the noise in the recommendation process. Specifically, (1) for the noise in KG, we design a personalized gating mechanism, namely dual-channel balancing mechanism, to block the propagation of redundant information in KG. (2) For the noise in user-item interaction data, we integrate personalized and knowledge-aware signals to capture user preferences fully and use personalized knowledge-aware attention to denoise user-item interaction data. Compared with existing KG-based methods, we aim to propose a knowledge-aware recommendation method from a new perspective of denoising. We perform performance analysis on three real-world datasets, and experiment results demonstrate that KDGNN achieves strongly competitive performance compared with several compelling state-of-the-art baselines.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135444069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract While tensor accelerated compilers have proven effective in deploying deep neural networks (DNN) on general-purpose hardware, optimizing for FPGA remains challenging due to the complex DNN architectures and the heterogeneous, semi-open compute units. This paper introduces the Automatic Kernel Generation for DNN on CPU-FPGA (AKGF) framework for efficient deployment of DNN on heterogeneous CPU-FPGA platforms. AKGF generates an intermediate representation (IR) of the DNN using TVM’s Halide IR, annotates the operators of model layers in the IR to compute them on the corresponding hardware cores, and further optimizes the operator code for CPU and FPGA using ARM’s function library and the polyhedral model to enhance model inference speed and power consumption. The experimental tests conducted on a CPU-FPGA board validate the effectiveness of AKGF, demonstrating significant acceleration ratios (up to 6.7x) compared to state-of-the-art accelerators while achieving a 2x power optimization. AKGF effectively leverages the computational capabilities of both CPU and FPGA for high-performance deployment of DNN on CPU-FPGA platforms.
{"title":"AKGF: Automatic Kernel Generation for DNN on CPU-FPGA","authors":"Dong Dong, Hongxu Jiang, Boyu Diao","doi":"10.1093/comjnl/bxad086","DOIUrl":"https://doi.org/10.1093/comjnl/bxad086","url":null,"abstract":"Abstract While tensor accelerated compilers have proven effective in deploying deep neural networks (DNN) on general-purpose hardware, optimizing for FPGA remains challenging due to the complex DNN architectures and the heterogeneous, semi-open compute units. This paper introduces the Automatic Kernel Generation for DNN on CPU-FPGA (AKGF) framework for efficient deployment of DNN on heterogeneous CPU-FPGA platforms. AKGF generates an intermediate representation (IR) of the DNN using TVM’s Halide IR, annotates the operators of model layers in the IR to compute them on the corresponding hardware cores, and further optimizes the operator code for CPU and FPGA using ARM’s function library and the polyhedral model to enhance model inference speed and power consumption. The experimental tests conducted on a CPU-FPGA board validate the effectiveness of AKGF, demonstrating significant acceleration ratios (up to 6.7x) compared to state-of-the-art accelerators while achieving a 2x power optimization. AKGF effectively leverages the computational capabilities of both CPU and FPGA for high-performance deployment of DNN on CPU-FPGA platforms.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135444351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dongchao Ma, Dongmei Wang, Xiaofu Huang, Yuekun Hu, Li Ma
Abstract The high energy density of solar energy gives wireless sensor networks advantages in outdoor monitoring applications. However, long-term stable monitoring is challenging due to frequent weather changes, shading by buildings and trees, etc. The existing research usually uses two technologies to solve the above problems: (1) the energy prediction algorithm, and (2) the energy-aware routing strategy. However, in an actual deployment, frequent weather changes can significantly reduce the accuracy of the existing prediction algorithms. When using the algorithms as the support for energy-aware routing, the network lifetime is less than ideal. The existing routing strategies are in need of further improvement. Because of its lack of environmental adaptability, nodes consume energy quickly and have a high mortality rate. Therefore, aiming at the long-term stability of solar wireless sensor networks, this paper proposes a prediction algorithm based on classification and recurrent neural networks, and integrates the shadow judgement method from our previous research to correct the predicted values. Furthermore, we propose a routing optimization model that can flexibly adjust the target according to the solar intensity. The experimental results show that the prediction and routing scheduling algorithm can significantly improve the energy prediction accuracy (30–50%) and prolong the network lifetime (10–42%) in outdoor small sensor scenarios.
{"title":"KEFSAR: A Solar-Aware Routing Strategy For Rechargeable IoT Based On High-Accuracy Prediction","authors":"Dongchao Ma, Dongmei Wang, Xiaofu Huang, Yuekun Hu, Li Ma","doi":"10.1093/comjnl/bxad074","DOIUrl":"https://doi.org/10.1093/comjnl/bxad074","url":null,"abstract":"Abstract The high energy density of solar energy gives wireless sensor networks advantages in outdoor monitoring applications. However, long-term stable monitoring is challenging due to frequent weather changes, shading by buildings and trees, etc. The existing research usually uses two technologies to solve the above problems: (1) the energy prediction algorithm, and (2) the energy-aware routing strategy. However, in an actual deployment, frequent weather changes can significantly reduce the accuracy of the existing prediction algorithms. When using the algorithms as the support for energy-aware routing, the network lifetime is less than ideal. The existing routing strategies are in need of further improvement. Because of its lack of environmental adaptability, nodes consume energy quickly and have a high mortality rate. Therefore, aiming at the long-term stability of solar wireless sensor networks, this paper proposes a prediction algorithm based on classification and recurrent neural networks, and integrates the shadow judgement method from our previous research to correct the predicted values. Furthermore, we propose a routing optimization model that can flexibly adjust the target according to the solar intensity. The experimental results show that the prediction and routing scheduling algorithm can significantly improve the energy prediction accuracy (30–50%) and prolong the network lifetime (10–42%) in outdoor small sensor scenarios.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134919155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Fault-tolerant performance of a network is the prerequisite and guarantee for the normal operation of a network, which is often characterized by connectivity. Let $H$ denote a connected subgraph of $G$ and $H^{*}$ denote the union of the set of all connected subgraphs of $H$ and the set of the trivial graph. Super $H$-connectivity (resp. super $H^{*}$-connectivity) satisfies the conditions of both super connectivity and $H$-structure connectivity (resp. $H$-substructure connectivity). These two kinds of new connectivity provide a new metric to measure the fault-tolerance of the network, that is, the super structure fault-tolerance. The generalized hypercube $G(m_{r}, m_{r-1},..., m_{1})$ is a universal topology of interconnection networks that contains other commonly used topologies and it has been applied in many data center networks because of its excellent qualities. In this paper, we research the super structure fault-tolerance of $G(m_{r}, m_{r-1},..., m_{1})$ by studying super $H$-connectivity $kappa ^{prime}(G|H)$ and super $H^{*}$-connectivity $kappa ^{prime}(G|H^{*})$ for $Hin {K_{1,M}, C_{3}, C_{4}, K_{4}}$.
{"title":"Super Structure Fault-Tolerance Assessment of the Generalized Hypercube","authors":"Chang Shu, Yan Wang, Jianxi Fan, Guijuan Wang","doi":"10.1093/comjnl/bxad072","DOIUrl":"https://doi.org/10.1093/comjnl/bxad072","url":null,"abstract":"Abstract Fault-tolerant performance of a network is the prerequisite and guarantee for the normal operation of a network, which is often characterized by connectivity. Let $H$ denote a connected subgraph of $G$ and $H^{*}$ denote the union of the set of all connected subgraphs of $H$ and the set of the trivial graph. Super $H$-connectivity (resp. super $H^{*}$-connectivity) satisfies the conditions of both super connectivity and $H$-structure connectivity (resp. $H$-substructure connectivity). These two kinds of new connectivity provide a new metric to measure the fault-tolerance of the network, that is, the super structure fault-tolerance. The generalized hypercube $G(m_{r}, m_{r-1},..., m_{1})$ is a universal topology of interconnection networks that contains other commonly used topologies and it has been applied in many data center networks because of its excellent qualities. In this paper, we research the super structure fault-tolerance of $G(m_{r}, m_{r-1},..., m_{1})$ by studying super $H$-connectivity $kappa ^{prime}(G|H)$ and super $H^{*}$-connectivity $kappa ^{prime}(G|H^{*})$ for $Hin {K_{1,M}, C_{3}, C_{4}, K_{4}}$.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":"359 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134919156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The low transaction capacity, high transaction cost and long-term privacy concerns of the current Ethereum platform are notorious. Developers are seeking alternative blockchain platforms to migrate their blockchain-based applications to reduce their applications’ use-cost and improve their applications’ user experience. The Hyperledger Fabric (HLF) platform with resiliency, flexibility, scalability and confidentiality is preferred for developers to migrate their Ethereum blockchain-based applications. However, it is laborious for developers to migrate blockchain-based applications from the Ethereum platform to the HLF platform. In this paper, we first propose a complete and secure migration solution to ease the migration process. The main idea of our solution is to design a toolbox to help developers automatically eliminate the adverse effects that the differences between Ethereum and HLF may bring to the migrated application. Developers with the toolbox can migrate the application with little time and minimal modification. It is theoretically proved that the migrated application with the toolbox is secure. Besides, a prototype of the toolbox is implemented. The extensive experiments demonstrate that the time for the migration process is acceptable, and the toolbox has little impact on the migrated application’s performance.
{"title":"A Toolbox for Migrating the Blockchain-Based Application From Ethereum to Hyperledger Fabric","authors":"Zhonghao Zhai, Subin Shen, Yanqin Mao","doi":"10.1093/comjnl/bxad061","DOIUrl":"https://doi.org/10.1093/comjnl/bxad061","url":null,"abstract":"Abstract The low transaction capacity, high transaction cost and long-term privacy concerns of the current Ethereum platform are notorious. Developers are seeking alternative blockchain platforms to migrate their blockchain-based applications to reduce their applications’ use-cost and improve their applications’ user experience. The Hyperledger Fabric (HLF) platform with resiliency, flexibility, scalability and confidentiality is preferred for developers to migrate their Ethereum blockchain-based applications. However, it is laborious for developers to migrate blockchain-based applications from the Ethereum platform to the HLF platform. In this paper, we first propose a complete and secure migration solution to ease the migration process. The main idea of our solution is to design a toolbox to help developers automatically eliminate the adverse effects that the differences between Ethereum and HLF may bring to the migrated application. Developers with the toolbox can migrate the application with little time and minimal modification. It is theoretically proved that the migrated application with the toolbox is secure. Besides, a prototype of the toolbox is implemented. The extensive experiments demonstrate that the time for the migration process is acceptable, and the toolbox has little impact on the migrated application’s performance.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135525799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Correction to: Metaheuristic-Enabled Artificial Neural Network Framework For Multimodal Biometric Recognition With Local Fusion Visual Features","authors":"","doi":"10.1093/comjnl/bxad064","DOIUrl":"https://doi.org/10.1093/comjnl/bxad064","url":null,"abstract":"","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136041498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Patrizio Angelini, Giordano Da Lozzo, Henry Förster, Thomas Schneck
Abstract The $2$-layer drawing model is a well-established paradigm to visualize bipartite graphs where vertices of the two parts lie on two horizontal lines and edges lie between these lines. Several beyond-planar graph classes have been studied under this model. Surprisingly, however, the fundamental class of $k$-planar graphs has been considered only for $k=1$ in this context. We provide several contributions that address this gap in the literature. First, we show tight density bounds for the classes of $2$-layer $k$-planar graphs with $kin {2,3,4,5}$. Based on these results, we provide a Crossing Lemma for $2$-layer $k$-planar graphs, which then implies a general density bound for $2$-layer $k$-planar graphs. We prove this bound to be almost optimal with a corresponding lower bound construction. Finally, we study relationships between $k$-planarity and $h$-quasiplanarity in the $2$-layer model and show that $2$-layer $k$-planar graphs have pathwidth at most $k+1$ while there are also $2$-layer $k$-planar graphs with pathwidth at least $(k+3)/2$.
$2$层绘图模型是一种成熟的二部图可视化范例，其中两个部分的顶点位于两条水平线上，边缘位于两条水平线之间。在此模型下，研究了几种超越平面的图类。然而，令人惊讶的是，在这种情况下，k -平面图的基本类只在k=1时才被考虑。我们提供了几个贡献，以解决这一差距的文献。首先，我们展示了$k in {2,3,4,5}$的$2$-层$k$-平面图类的紧密密度界。基于这些结果，我们提供了一个2层k图的交叉引理，从而暗示了2层k图的一般密度界。我们用相应的下界构造证明了这个界是几乎最优的。最后，我们研究了$k$-平面性和$h$-拟平面性在$2$层模型中的关系，并证明$2$层$k$-平面图的路径宽度最多为$k+1$，同时也存在$2$层$k$-平面图的路径宽度至少为$(k+3)/2$。
{"title":"2-Layer <i>k</i>-Planar Graphs Density, Crossing Lemma, Relationships And Pathwidth","authors":"Patrizio Angelini, Giordano Da Lozzo, Henry Förster, Thomas Schneck","doi":"10.1093/comjnl/bxad038","DOIUrl":"https://doi.org/10.1093/comjnl/bxad038","url":null,"abstract":"Abstract The $2$-layer drawing model is a well-established paradigm to visualize bipartite graphs where vertices of the two parts lie on two horizontal lines and edges lie between these lines. Several beyond-planar graph classes have been studied under this model. Surprisingly, however, the fundamental class of $k$-planar graphs has been considered only for $k=1$ in this context. We provide several contributions that address this gap in the literature. First, we show tight density bounds for the classes of $2$-layer $k$-planar graphs with $kin {2,3,4,5}$. Based on these results, we provide a Crossing Lemma for $2$-layer $k$-planar graphs, which then implies a general density bound for $2$-layer $k$-planar graphs. We prove this bound to be almost optimal with a corresponding lower bound construction. Finally, we study relationships between $k$-planarity and $h$-quasiplanarity in the $2$-layer model and show that $2$-layer $k$-planar graphs have pathwidth at most $k+1$ while there are also $2$-layer $k$-planar graphs with pathwidth at least $(k+3)/2$.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135463997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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