This work presents an energy-efficient NoC-based system for real-time multimedia applications employing approximate computing. The proposed video processing system, called SApp-NoC, is efficient in both energy and quality (QoS), employing a scalable NoC architecture composed of processing elements designed to accelerate the HEVC Fractional Motion Estimation (FME). Two solutions are proposed: HSApp-NoC (Heuristc-based SApp-NoC), and MLSApp-NoC (Machine Learning-based SApp-NoC). When compared to a precise solution processing 4K videos at 120 fps, HSApp-NoC and MLSApp-NoC reduce about 48.19% and 31.81% the energy consumption, at small quality reduction of 2.74% and 1.09%, respectively. Furthermore, a set of schedulability analysis is also proposed in order to guarantee the meeting of timing constraints at typical workload scenarios.
{"title":"Energy-Efficient NoC-Based Systems for Real-Time Multimedia Applications using Approximate Computing","authors":"Wagner Penny, D. Palomino, M. Porto, B. Zatt","doi":"10.5753/CTD.2021.15750","DOIUrl":"https://doi.org/10.5753/CTD.2021.15750","url":null,"abstract":"This work presents an energy-efficient NoC-based system for real-time multimedia applications employing approximate computing. The proposed video processing system, called SApp-NoC, is efficient in both energy and quality (QoS), employing a scalable NoC architecture composed of processing elements designed to accelerate the HEVC Fractional Motion Estimation (FME). Two solutions are proposed: HSApp-NoC (Heuristc-based SApp-NoC), and MLSApp-NoC (Machine Learning-based SApp-NoC). When compared to a precise solution processing 4K videos at 120 fps, HSApp-NoC and MLSApp-NoC reduce about 48.19% and 31.81% the energy consumption, at small quality reduction of 2.74% and 1.09%, respectively. Furthermore, a set of schedulability analysis is also proposed in order to guarantee the meeting of timing constraints at typical workload scenarios.","PeriodicalId":236085,"journal":{"name":"Anais do XXXIV Concurso de Teses e Dissertações da SBC (CTD-SBC 2021)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125847941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A multicore chip usually provides a shared memory abstraction implemented by a cache coherence protocol. On-chip coherence can scale gracefully as the number of cores grows, and it plays a major role for general purpose applications. Besides, multicore architectures are likely to relax constraints on store atomicity and on the ordering between loads and stores. As a result, the validation of shared memory faces two main challenges: the higher number of valid execution behaviors and the larger coherence protocol's state space. This dissertation faces those challenges and targets an important design automation phase: the (pre-silicon) functional verification of the shared memory subsystem of a multicore chip, whose behavior is specified by a memory consistency model (MCM). The main scientific contribution is a novel approach to the building of MCM checkers, along with technical contributions on random test generation and directed test generation. The contributions were reported by two papers in a premier IEEE/ACM conference and two articles in the most prestigious IEEE journal on Computer Aided Design of Integrated Circuits and Systems.
{"title":"Shared Memory Verification for Multicore Chip Designs","authors":"Marleson Graf, L. Santos","doi":"10.5753/CTD.2021.15760","DOIUrl":"https://doi.org/10.5753/CTD.2021.15760","url":null,"abstract":"A multicore chip usually provides a shared memory abstraction implemented by a cache coherence protocol. On-chip coherence can scale gracefully as the number of cores grows, and it plays a major role for general purpose applications. Besides, multicore architectures are likely to relax constraints on store atomicity and on the ordering between loads and stores. As a result, the validation of shared memory faces two main challenges: the higher number of valid execution behaviors and the larger coherence protocol's state space. This dissertation faces those challenges and targets an important design automation phase: the (pre-silicon) functional verification of the shared memory subsystem of a multicore chip, whose behavior is specified by a memory consistency model (MCM). The main scientific contribution is a novel approach to the building of MCM checkers, along with technical contributions on random test generation and directed test generation. The contributions were reported by two papers in a premier IEEE/ACM conference and two articles in the most prestigious IEEE journal on Computer Aided Design of Integrated Circuits and Systems.","PeriodicalId":236085,"journal":{"name":"Anais do XXXIV Concurso de Teses e Dissertações da SBC (CTD-SBC 2021)","volume":"105 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114573469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Digital platforms, including social media systems and messaging applications, have become a place for campaigns of misinformation that affect the credibility of the entire news ecosystem. The emergence of fake news in these environments has quickly evolved into a worldwide phenomenon, where the lack of scalable fact-checking strategies is especially worrisome. In this context, this thesis aim at investigating practical approaches for the automatic detection of fake news disseminated in digital platforms. Particularly, we explore new datasets and features for fake news detection to assess the prediction performance of current supervised machine learning approaches. We also propose an unbiased framework for quantifying the informativeness of features for fake news detection, and present an explanation of factors contributing to model decisions considering data from different scenarios. Finally, we propose and implement a new mechanism that accounts for the potential occurrence of fake news within the data, significantly reducing the number of content pieces journalists and fact-checkers have to go through before finding a fake story.
{"title":"Towards Automatic Fake News Detection in Digital Platforms: Properties, Limitations, and Applications","authors":"Julio C. S. Reis, Fabrício Benevenuto","doi":"10.5753/CTD.2021.15754","DOIUrl":"https://doi.org/10.5753/CTD.2021.15754","url":null,"abstract":"Digital platforms, including social media systems and messaging applications, have become a place for campaigns of misinformation that affect the credibility of the entire news ecosystem. The emergence of fake news in these environments has quickly evolved into a worldwide phenomenon, where the lack of scalable fact-checking strategies is especially worrisome. In this context, this thesis aim at investigating practical approaches for the automatic detection of fake news disseminated in digital platforms. Particularly, we explore new datasets and features for fake news detection to assess the prediction performance of current supervised machine learning approaches. We also propose an unbiased framework for quantifying the informativeness of features for fake news detection, and present an explanation of factors contributing to model decisions considering data from different scenarios. Finally, we propose and implement a new mechanism that accounts for the potential occurrence of fake news within the data, significantly reducing the number of content pieces journalists and fact-checkers have to go through before finding a fake story.","PeriodicalId":236085,"journal":{"name":"Anais do XXXIV Concurso de Teses e Dissertações da SBC (CTD-SBC 2021)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116280203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The balanced connected k-partition (BCPk) problem consists in partitioning a connected graph into connected subgraphs with similar weights. This problem arises in multiple practical applications, such as police patrolling, image processing, data base and operating systems. In this work, we address the BCPk using mathematical programming. We propose a compact formulation based on flows and a formulation based on separators. We introduce classes of valid inequalities and design polynomial-time separation routines. Moreover, to the best of our knowledge, we present the first polyhedral study for BCPk in the literature. Finally, we report on computational experiments showing that the proposed algorithms significantly outperform the state of the art for BCPk.
{"title":"The Balanced Connected k-Partition Problem: Polyhedra and Algorithms","authors":"M. J. Ota, F. Miyazawa, Phablo F. S. Moura","doi":"10.5753/CTD.2021.15763","DOIUrl":"https://doi.org/10.5753/CTD.2021.15763","url":null,"abstract":"The balanced connected k-partition (BCPk) problem consists in partitioning a connected graph into connected subgraphs with similar weights. This problem arises in multiple practical applications, such as police patrolling, image processing, data base and operating systems. In this work, we address the BCPk using mathematical programming. We propose a compact formulation based on flows and a formulation based on separators. We introduce classes of valid inequalities and design polynomial-time separation routines. Moreover, to the best of our knowledge, we present the first polyhedral study for BCPk in the literature. Finally, we report on computational experiments showing that the proposed algorithms significantly outperform the state of the art for BCPk.","PeriodicalId":236085,"journal":{"name":"Anais do XXXIV Concurso de Teses e Dissertações da SBC (CTD-SBC 2021)","volume":"14 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128963691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
João Pedro Moreira Ferreira, Renato Martins, E. R. Nascimento
Learning to move naturally from music, i.e., to dance, is one of the most complex motions humans often perform effortlessly. Existing techniques of automatic dance generation with classical CNN and RNN models undergo training and variability issues due to the non-Euclidean geometry of the motion manifold. We design a novel method based on GCNs to tackle the problem of automatic dance generation from audio. Our method uses an adversarial learning scheme conditioned on the input music audios to create natural motions. The results demonstrate that the proposed GCN model outperforms the state-of-the-art in different experiments. Visual results of the motion generation and explanation can be visualized through the link: http://youtu.be/fGDK6UkKzvA
{"title":"Synthesizing Realistic Human Dance Motions Conditioned by Musical Data using Graph Convolutional Networks","authors":"João Pedro Moreira Ferreira, Renato Martins, E. R. Nascimento","doi":"10.5753/CTD.2021.15762","DOIUrl":"https://doi.org/10.5753/CTD.2021.15762","url":null,"abstract":"Learning to move naturally from music, i.e., to dance, is one of the most complex motions humans often perform effortlessly. Existing techniques of automatic dance generation with classical CNN and RNN models undergo training and variability issues due to the non-Euclidean geometry of the motion manifold. We design a novel method based on GCNs to tackle the problem of automatic dance generation from audio. Our method uses an adversarial learning scheme conditioned on the input music audios to create natural motions. The results demonstrate that the proposed GCN model outperforms the state-of-the-art in different experiments. Visual results of the motion generation and explanation can be visualized through the link: http://youtu.be/fGDK6UkKzvA","PeriodicalId":236085,"journal":{"name":"Anais do XXXIV Concurso de Teses e Dissertações da SBC (CTD-SBC 2021)","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131914265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Heterogeneous systems employing CPUs and GPUs are becoming increasingly popular in large-scale data centers and cloud environments. In these platforms, sharing a GPU across different applications is an important feature to improve hardware utilization and system throughput. However, under scenarios where GPUs are competitively shared, some challenges arise. The decision on the simultaneous execution of different kernels is made by the hardware and depends on the kernels resource requirements. Besides that, it is very difficult to understand all the hardware variables involved in the simultaneous execution decisions, in order to describe a formal allocation method. In this work, we studied the impact that kernel resource requirements have in concurrent execution and used machine learning (ML) techniques to infer the interference caused by the concurrent execution, and to classify the slowdown that results from this interference. The ML techniques were analyzed over the GPU benchmark suites, Rodinia, Parboil and SHOC. Our results showed that, from the features selected in the analysis, the number of blocks per grid, number of threads per block, and number of registers are the resource consumption features that most affect the performance of the concurrent execution.
{"title":"Concurrency and Interference Analysis of Kernels on GPUs","authors":"Pablo Carvalho, Lúcia M. A. Drummond, C. Bentes","doi":"10.5753/CTD.2021.15757","DOIUrl":"https://doi.org/10.5753/CTD.2021.15757","url":null,"abstract":"Heterogeneous systems employing CPUs and GPUs are becoming increasingly popular in large-scale data centers and cloud environments. In these platforms, sharing a GPU across different applications is an important feature to improve hardware utilization and system throughput. However, under scenarios where GPUs are competitively shared, some challenges arise. The decision on the simultaneous execution of different kernels is made by the hardware and depends on the kernels resource requirements. Besides that, it is very difficult to understand all the hardware variables involved in the simultaneous execution decisions, in order to describe a formal allocation method. In this work, we studied the impact that kernel resource requirements have in concurrent execution and used machine learning (ML) techniques to infer the interference caused by the concurrent execution, and to classify the slowdown that results from this interference. The ML techniques were analyzed over the GPU benchmark suites, Rodinia, Parboil and SHOC. Our results showed that, from the features selected in the analysis, the number of blocks per grid, number of threads per block, and number of registers are the resource consumption features that most affect the performance of the concurrent execution.","PeriodicalId":236085,"journal":{"name":"Anais do XXXIV Concurso de Teses e Dissertações da SBC (CTD-SBC 2021)","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125458224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work makes contributions that reach central problems in connection with data dependencies. The first problem regards the discovery of dependencies of high expressive power. We introduce an efficient algorithm for the discovery of denial constraints: a type of dependency that has enough expressive power to generalize other important types of dependencies and to express complex business rules. The second problem concerns the application of dependencies for improving data consistency. We present a modification for traditional dependency discovery approaches that enables the dependency discovery algorithms to return reliable results even if they run on data containing some inconsistent records. Also, we present a system for detecting violations of dependencies efficiently. Our extensive experimental evaluation shows that our system is up to three orders-of-magnitude faster than state-of-the-art solutions, especially for larger datasets and massive numbers of dependency violations. The last contribution in this work regards the application of dependencies in query optimization. We present a system for the automatic discovery and selection of functional dependencies. Our experimental evaluation shows that our system selects relevant functional dependencies that help reducing the overall query response time for various types of query workloads.
{"title":"Discovery and Application of Data Dependencies","authors":"Eduardo H. M. Pena, E. Almeida","doi":"10.5753/CTD.2021.15749","DOIUrl":"https://doi.org/10.5753/CTD.2021.15749","url":null,"abstract":"This work makes contributions that reach central problems in connection with data dependencies. The first problem regards the discovery of dependencies of high expressive power. We introduce an efficient algorithm for the discovery of denial constraints: a type of dependency that has enough expressive power to generalize other important types of dependencies and to express complex business rules. The second problem concerns the application of dependencies for improving data consistency. We present a modification for traditional dependency discovery approaches that enables the dependency discovery algorithms to return reliable results even if they run on data containing some inconsistent records. Also, we present a system for detecting violations of dependencies efficiently. Our extensive experimental evaluation shows that our system is up to three orders-of-magnitude faster than state-of-the-art solutions, especially for larger datasets and massive numbers of dependency violations. The last contribution in this work regards the application of dependencies in query optimization. We present a system for the automatic discovery and selection of functional dependencies. Our experimental evaluation shows that our system selects relevant functional dependencies that help reducing the overall query response time for various types of query workloads.","PeriodicalId":236085,"journal":{"name":"Anais do XXXIV Concurso de Teses e Dissertações da SBC (CTD-SBC 2021)","volume":"265 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126052724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alexander Razborov (1985) developed the approximation method to obtain lower bounds on the size of monotone circuits deciding if a graph contains a clique. Given a "small" circuit, this technique consists in finding a monotone Boolean function which approximates the circuit in a distribution of interest, but makes computation errors in that same distribution. To prove that such a function is indeed a good approximation, Razborov used the sunflower lemma of ErdH{o}s and Rado (1960). This technique was improved by Alon and Boppana (1987) to show lower bounds for a larger class of monotone computational problems. In that same work, the authors also improved the result of Razborov for the clique problem, using a relaxed variant of sunflowers. More recently, Rossman (2010) developed another variant of sunflowers, now called "robust sunflowers", to obtain lower bounds for the clique problem in random graphs. In the following years, the concept of robust sunflowers found applications in many areas of computational complexity, such as DNF sparsification, randomness extractors and lifting theorems. Even more recent was the breakthrough result of Alweiss, Lovett, Wu and Zhang (2020), which improved Rossman's bound on the size of hypergraphs without robust sunflowers. This result was employed to obtain a significant progress on the sunflower conjecture. In this work, we will show how the recent progress in sunflower theorems can be applied to improve monotone circuit lower bounds. In particular, we will show the best monotone circuit lower bound obtained up to now, breaking a 20-year old record of Harnik and Raz (2000). We will also improve the lower bound of Alon and Boppana for the clique function in a slightly more restricted range of clique sizes. Our exposition is self-contained. These results were obtained in a collaboration with Benjamin Rossman and Mrinal Kumar.
Alexander Razborov(1985)发展了一种近似方法来获得判定图中是否包含团的单调回路大小的下界。给定一个“小”电路，该技术包括找到一个单调布尔函数，该函数在感兴趣的分布中近似电路，但在同一分布中产生计算误差。为了证明这样的函数确实是一个很好的近似，Razborov使用了ErdH{o}s和Rado(1960)的向日葵引理。Alon和Boppana(1987)改进了这种技术，以显示更大类单调计算问题的下界。在同一篇文章中，作者还改进了Razborov关于团问题的结果，使用了向日葵的松弛变体。最近，Rossman(2010)开发了向日葵的另一种变体，现在称为“鲁棒向日葵”，以获得随机图中团问题的下界。在接下来的几年里，鲁棒向日葵的概念在计算复杂性的许多领域得到了应用，比如DNF稀疏化、随机提取器和提升定理。更近的是Alweiss, Lovett, Wu和Zhang(2020)的突破性成果，他们改进了Rossman关于无鲁棒向日葵超图大小的界。利用这一结果，向日葵猜想取得了重大进展。在这项工作中，我们将展示如何将葵花定理的最新进展应用于改进单调电路的下界。特别是，我们将展示迄今为止获得的最佳单调电路下界，打破了Harnik和Raz(2000) 20年来的记录。我们还将在稍微受限的团大小范围内改进团函数的Alon和Boppana的下界。我们的论述是独立的。这些结果是与Benjamin Rossman和Mrinal Kumar合作获得的。
{"title":"Sunflower Theorems in Monotone Circuit Complexity","authors":"B. P. Cavalar, Y. Kohayakawa","doi":"10.5753/CTD.2021.15761","DOIUrl":"https://doi.org/10.5753/CTD.2021.15761","url":null,"abstract":"Alexander Razborov (1985) developed the approximation method to obtain lower bounds on the size of monotone circuits deciding if a graph contains a clique. Given a \"small\" circuit, this technique consists in finding a monotone Boolean function which approximates the circuit in a distribution of interest, but makes computation errors in that same distribution. To prove that such a function is indeed a good approximation, Razborov used the sunflower lemma of ErdH{o}s and Rado (1960). This technique was improved by Alon and Boppana (1987) to show lower bounds for a larger class of monotone computational problems. In that same work, the authors also improved the result of Razborov for the clique problem, using a relaxed variant of sunflowers. More recently, Rossman (2010) developed another variant of sunflowers, now called \"robust sunflowers\", to obtain lower bounds for the clique problem in random graphs. In the following years, the concept of robust sunflowers found applications in many areas of computational complexity, such as DNF sparsification, randomness extractors and lifting theorems. Even more recent was the breakthrough result of Alweiss, Lovett, Wu and Zhang (2020), which improved Rossman's bound on the size of hypergraphs without robust sunflowers. This result was employed to obtain a significant progress on the sunflower conjecture. In this work, we will show how the recent progress in sunflower theorems can be applied to improve monotone circuit lower bounds. In particular, we will show the best monotone circuit lower bound obtained up to now, breaking a 20-year old record of Harnik and Raz (2000). We will also improve the lower bound of Alon and Boppana for the clique function in a slightly more restricted range of clique sizes. Our exposition is self-contained. These results were obtained in a collaboration with Benjamin Rossman and Mrinal Kumar.","PeriodicalId":236085,"journal":{"name":"Anais do XXXIV Concurso de Teses e Dissertações da SBC (CTD-SBC 2021)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122636073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. G. Andrade, F. Marquezino, Daniel R. Figueiredo
Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the relationship between quantum and random walks has been recently discussed in specific scenarios, this work establishes a formal equivalence between the two processes on arbitrary finite graphs and general conditions for shift and coin operators. It requires empowering random walks with time heterogeneity, where the transition probability of the walker is non-uniform and time dependent. The equivalence is obtained by equating the probability of measuring the quantum walk on a given node of the graph and the probability that the random walk is at that same node, for all nodes and time steps. The first result establishes procedure for a stochastic matrix sequence to induce a random walk that yields the exact same vertex probability distribution sequence of any given quantum walk, including the scenario with multiple interfering walkers. The second result establishes a similar procedure in the opposite direction. Given any random walk, a time-dependent quantum walk with the exact same vertex probability distribution is constructed. Interestingly, the matrices constructed by the first procedure allows for a different simulation approach for quantum walks where node samples respect neighbor locality and convergence is guaranteed by the law of large numbers, enabling efficient (polynomial-time) sampling of quantum graph trajectories. Furthermore, the complexity of constructing this sequence of matrices is discussed in the general case.
{"title":"Characterizing the Relationship Between Unitary Quantum Walks and Non-Homogeneous Random Walks","authors":"M. G. Andrade, F. Marquezino, Daniel R. Figueiredo","doi":"10.5753/CTD.2021.15756","DOIUrl":"https://doi.org/10.5753/CTD.2021.15756","url":null,"abstract":"Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the relationship between quantum and random walks has been recently discussed in specific scenarios, this work establishes a formal equivalence between the two processes on arbitrary finite graphs and general conditions for shift and coin operators. It requires empowering random walks with time heterogeneity, where the transition probability of the walker is non-uniform and time dependent. The equivalence is obtained by equating the probability of measuring the quantum walk on a given node of the graph and the probability that the random walk is at that same node, for all nodes and time steps. The first result establishes procedure for a stochastic matrix sequence to induce a random walk that yields the exact same vertex probability distribution sequence of any given quantum walk, including the scenario with multiple interfering walkers. The second result establishes a similar procedure in the opposite direction. Given any random walk, a time-dependent quantum walk with the exact same vertex probability distribution is constructed. Interestingly, the matrices constructed by the first procedure allows for a different simulation approach for quantum walks where node samples respect neighbor locality and convergence is guaranteed by the law of large numbers, enabling efficient (polynomial-time) sampling of quantum graph trajectories. Furthermore, the complexity of constructing this sequence of matrices is discussed in the general case.","PeriodicalId":236085,"journal":{"name":"Anais do XXXIV Concurso de Teses e Dissertações da SBC (CTD-SBC 2021)","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114821144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An EPG graph G is an edge-intersection graph of paths on a grid. In this thesis, we analyze structural characterizations and complexity aspects regarding EPG graphs. Our main focus is on the class of B1-EPG graphs whose intersection model satisfies well-known the Helly property, called Helly-B1-EPG. We show that the problem of recognizing Helly-B1-EPG graphs is NP-complete. Besides, other intersection graph classes such as VPG, EPT, and VPT were also studied. We completely solve the problem of determining the Helly and strong Helly numbers of Bk-EPG graphs and Bk-VPG graphs for each non-negative integer k. Finally, we show that every Chordal B1-EPG graph is at the intersection of VPT and EPT.
{"title":"On the Helly Property of Some Intersection Graphs","authors":"T. Santos, J. Szwarcfiter, U. Souza, C. Bornstein","doi":"10.5753/CTD.2021.15752","DOIUrl":"https://doi.org/10.5753/CTD.2021.15752","url":null,"abstract":"An EPG graph G is an edge-intersection graph of paths on a grid. In this thesis, we analyze structural characterizations and complexity aspects regarding EPG graphs. Our main focus is on the class of B1-EPG graphs whose intersection model satisfies well-known the Helly property, called Helly-B1-EPG. We show that the problem of recognizing Helly-B1-EPG graphs is NP-complete. Besides, other intersection graph classes such as VPG, EPT, and VPT were also studied. We completely solve the problem of determining the Helly and strong Helly numbers of Bk-EPG graphs and Bk-VPG graphs for each non-negative integer k. Finally, we show that every Chordal B1-EPG graph is at the intersection of VPT and EPT.","PeriodicalId":236085,"journal":{"name":"Anais do XXXIV Concurso de Teses e Dissertações da SBC (CTD-SBC 2021)","volume":"283 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124523060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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