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Federated learning (FL) is emerging as a sought-after distributed machine learning architecture, offering the advantage of model training without direct exposure of raw data. With advancements in network infrastructure, FL has been seamlessly integrated into edge computing. However, the limited resources on edge devices introduce security vulnerabilities to FL in the context. While blockchain technology promises to bolster security, practical deployment on resource-constrained edge devices remains a challenge. Moreover, the exploration of FL with multiple aggregators in edge computing is still new in the literature. Addressing these gaps, we introduce the Blockchain-empowered Heterogeneous Multi-Aggregator Federated Learning Architecture (BMA-FL). We design a novel light-weight Byzantine consensus mechanism, namely PBCM, to enable secure and fast model aggregation and synchronization in BMA-FL. We also dive into the heterogeneity problem in BMA-FL that the aggregators are associated with varied number of connected trainers with Non-IID data distributions and diverse training speed. We proposed a multi-agent deep reinforcement learning algorithm to help aggregators decide the best training strategies. The experiments on real-word datasets demonstrate the efficiency of BMA-FL to achieve better models faster than baselines, showing the efficacy of PBCM and proposed deep reinforcement learning algorithm.

In recent years, deep learning has revolutionized natural language processing (NLP) by enabling the development of models that can learn complex representations of language data, leading to significant improvements in performance across a wide range of NLP tasks. Deep learning models for NLP typically use large amounts of data to train deep neural networks, allowing them to learn the patterns and relationships in language data. This is in contrast to traditional NLP approaches, which rely on hand-engineered features and rules to perform NLP tasks. The ability of deep neural networks to learn hierarchical representations of language data, handle variable-length input sequences, and perform well on large datasets makes them well-suited for NLP applications. Driven by the exponential growth of textual data and the increasing demand for condensed, coherent, and informative summaries, text summarization has been a critical research area in the field of NLP. Applying deep learning to text summarization refers to the use of deep neural networks to perform text summarization tasks. In this survey, we begin with a review of fashionable text summarization tasks in recent years, including extractive, abstractive, multi-document, and so on. Next, we discuss most deep learning-based models and their experimental results on these tasks. The paper also covers datasets and data representation for summarization tasks. Finally, we delve into the opportunities and challenges associated with summarization tasks and their corresponding methodologies, aiming to inspire future research efforts to advance the field further. A goal of our survey is to explain how these methods differ in their requirements as understanding them is essential for choosing a technique suited for a specific setting.

Mobile Crowdsourcing (MCS) is a novel distributed computing paradigm that recruits skilled workers to perform location-dependent tasks. A number of mature incentive mechanisms have been proposed to address the worker recruitment problem in MCS systems. However, they all assume that there is a large enough worker pool and a sufficient number of users can be selected. This may be impossible in large-scale crowdsourcing environments. To address this challenge, we consider the MCS system defined on a location-aware social network provided by a social platform. In this system, we can recruit a small number of seed workers from the existing worker pool to spread the information of multiple tasks in the social network, thus attracting more users to perform tasks. In this paper, we propose a Multi-Task Diffusion Maximization (MT-DM) problem that aims to maximize the total utility of performing multiple crowdsourcing tasks under the budget. To accommodate multiple tasks diffusion over a social network, we create a multi-task diffusion model, and based on this model, we design an auction-based incentive mechanism, MT-DM-L. To deal with the high complexity of computing the multi-task diffusion, we adopt Multi-Task Reverse Reachable (MT-RR) sets to approximate the utility of information diffusion efficiently. Through both complete theoretical analysis and extensive simulations by using real-world datasets, we validate that our estimation for the spread of multi-task diffusion is accurate and the proposed mechanism achieves individual rationality, truthfulness, computational efficiency, and $(1-1/\sqrt{e}-\varepsilon)$ approximation with at least $1-\delta$ probability., Comment: 14 pages

In this paper, we study the non-monotone DR-submodular function maximization over integer lattice. Functions over integer lattice have been defined submodular property that is similar to submodularity of set functions. DR-submodular is a further extended submodular concept for functions over the integer lattice, which captures the diminishing return property. Such functions find many applications in machine learning, social networks, wireless networks, etc. The techniques for submodular set function maximization can be applied to DR-submodular function maximization, e.g., the double greedy algorithm has a $1/2$-approximation ratio, whose running time is $O(nB)$, where $n$ is the size of the ground set, $B$ is the integer bound of a coordinate. In our study, we design a $1/2$-approximate binary search double greedy algorithm, and we prove that its time complexity is $O(n\log B)$, which significantly improves the running time. Specifically, we consider its application to the profit maximization problem in social networks with a bipartite model, the goal of this problem is to maximize the net profit gained from a product promoting activity, which is the difference of the influence gain and the promoting cost. We prove that the objective function is DR-submodular over integer lattice. We apply binary search double greedy algorithm to this problem and verify the effectiveness.

Influence Maximization (IM) is a classical combinatorial optimization problem, which can be widely used in mobile networks, social computing, and recommendation systems. It aims at selecting a small number of users such that maximizing the influence spread across the online social network. Because of its potential commercial and academic value, there are a lot of researchers focusing on studying the IM problem from different perspectives. The main challenge comes from the NP-hardness of the IM problem and \#P-hardness of estimating the influence spread, thus traditional algorithms for overcoming them can be categorized into two classes: heuristic algorithms and approximation algorithms. However, there is no theoretical guarantee for heuristic algorithms, and the theoretical design is close to the limit. Therefore, it is almost impossible to further optimize and improve their performance. With the rapid development of artificial intelligence, the technology based on Machine Learning (ML) has achieved remarkable achievements in many fields. In view of this, in recent years, a number of new methods have emerged to solve combinatorial optimization problems by using ML-based techniques. These methods have the advantages of fast solving speed and strong generalization ability to unknown graphs, which provide a brand-new direction for solving combinatorial optimization problems. Therefore, we abandon the traditional algorithms based on iterative search and review the recent development of ML-based methods, especially Deep Reinforcement Learning, to solve the IM problem and other variants in social networks. We focus on summarizing the relevant background knowledge, basic principles, common methods, and applied research. Finally, the challenges that need to be solved urgently in future IM research are pointed out., Comment: 45 pages

Aiming at selecting a small subset of nodes with maximum influence on networks, the Influence Maximization (IM) problem has been extensively studied. Since it is #P-hard to compute the influence spread given a seed set, the state-of-the-art methods, including heuristic and approximation algorithms, faced with great difficulties such as theoretical guarantee, time efficiency, generalization, etc. This makes it unable to adapt to large-scale networks and more complex applications. On the other side, with the latest achievements of Deep Reinforcement Learning (DRL) in artificial intelligence and other fields, lots of works have been focused on exploiting DRL to solve combinatorial optimization problems. Inspired by this, we propose a novel end-to-end DRL framework, ToupleGDD, to address the IM problem in this paper, which incorporates three coupled graph neural networks for network embedding and double deep Q-networks for parameters learning. Previous efforts to solve IM problem with DRL trained their models on subgraphs of the whole network, and then tested on the whole graph, which makes the performance of their models unstable among different networks. However, our model is trained on several small randomly generated graphs with a small budget, and tested on completely different networks under various large budgets, which can obtain results very close to IMM and better results than OPIM-C on several datasets, and shows strong generalization ability. Finally, we conduct a large number of experiments on synthetic and realistic datasets, and experimental results prove the effectiveness and superiority of our model., Comment: 13 pages, 7 figures

Influence Maximization (IM) is a famous topic in mobile networks and social computing, which aims at finding a small subset of users to maximize the influence spread through online information cascade. Recently, some careful researchers paid attention to diversity of information dissemination, especially community-aware diversity, and formulated the diversified IM problem. The diversity is ubiquitous in a lot of real-world applications, but they are all based on a given community structure. In social networks, we can form heterogeneous community structures for the same group of users according to different metrics. Therefore, how to quantify the diversity based on multiple community structures is an interesting question. In this paper, we propose the Composite Community-Aware Diversified IM (CC-DIM) problem, which aims at selecting a seed set to maximize the influence spread and the composite diversity over all possible community structures under consideration. To address the NP-hardness of CC-DIM problem, we adopt the technique of reverse influence sampling and design a random Generalized Reverse Reachable (G-RR) set to estimate the objective function. The composition of a random G-RR set is much more complex than the RR set used for the IM problem, which will lead to inefficiency of traditional sampling-based approximation algorithms. Because of this, we further propose a two-stage algorithm, Generalized HIST (G-HIST). It can not only return a $(1-1/e-\varepsilon)$ approximate solution with at least $(1-\delta)$ probability, but also improve the efficiency of sampling and ease the difficulty of searching by significantly reducing the average size of G-RR sets. Finally, we evaluate our G-HIST on real datasets against existing algorithms. The experimental results show the effectiveness of our proposed algorithm and its superiority over other baseline algorithms., Comment: 15 pages

Blockchain is an emerging decentralized data collection, sharing and storage technology, which have provided abundant transparent, secure, tamper-proof, secure and robust ledger services for various real-world use cases. Recent years have witnessed notable developments of blockchain technology itself as well as blockchain-adopting applications. Most existing surveys limit the scopes on several particular issues of blockchain or applications, which are hard to depict the general picture of current giant blockchain ecosystem. In this paper, we investigate recent advances of both blockchain technology and its most active research topics in real-world applications. We first review the recent developments of consensus mechanisms and storage mechanisms in general blockchain systems. Then extensive literature is conducted on blockchain enabled IoT, edge computing, federated learning and several emerging applications including healthcare, COVID-19 pandemic, social network and supply chain, where detailed specific research topics are discussed in each. Finally, we discuss the future directions, challenges and opportunities in both academia and industry.

The online social platforms, like Twitter, Facebook, LinkedIn and WeChat, have grown really fast in last decade and have been one of the most effective platforms for people to communicate and share information with each other. Due to the "word of mouth" effects, information usually can spread rapidly on these social media platforms. Therefore, it is important to study the mechanisms driving the information diffusion and quantify the consequence of information spread. A lot of efforts have been focused on this problem to help us better understand and achieve higher performance in viral marketing and advertising. On the other hand, the development of neural networks has blossomed in the last few years, leading to a large number of graph representation learning (GRL) models. Compared to traditional models, GRL methods are often shown to be more effective. In this paper, we present a comprehensive review for existing works using GRL methods for popularity prediction problem, and categorize related literatures into two big classes, according to their mainly used model and techniques: embedding-based methods and deep learning methods. Deep learning method is further classified into six small classes: convolutional neural networks, graph convolutional networks, graph attention networks, graph neural networks, recurrent neural networks, and reinforcement learning. We compare the performance of these different models and discuss their strengths and limitations. Finally, we outline the challenges and future chances for popularity prediction problem., Comment: 30 pages, 4 figures

Contact tracing has been proven an effective approach to control the virus spread in pandemics like COVID-19 pandemic. As an emerging powerful decentralized technique, blockchain has been explored to ensure data privacy and security in contact tracing processes. However, existing works are mostly high-level designs with no sufficient demonstration and treat blockchain as separate storage system assisting third-party central servers, ignoring the importance and capability of consensus mechanism and incentive mechanism. In this paper, we propose a light-weight and fully third-party free Blockchain-Driven Contact Tracing framework (BDCT) to bridge the gap. In the BDCT framework, RSA encryption based transaction verification method (RSA-TVM) is proposed to ensure contact tracing correctness, which can achieve more than 96\% contact cases recording accuracy even each person has 60\% probability of failing to verify the contact information. Reputation Corrected Delegated Proof of Stake (RC-DPoS) consensus mechanism is proposed together with the incentive mechanism, which can ensure timeliness of reporting contact cases and keep blockchain decentralized. A novel contact tracing simulation environment is created, which considers three different contact scenarios based on population density. The simulation results demonstrate the effectiveness, robustness and attack resistance of RSA-TVM and RC-DPoS in the proposed BDCT.

Online social networks have been one of the most effective platforms for marketing and advertising. Through "word of mouth" effects, information or product adoption could spread from some influential individuals to millions of users in social networks. Given a social network $G$ and a constant $k$, the influence maximization problem seeks for $k$ nodes in $G$ that can influence the largest number of nodes. This problem has found important applications, and a large amount of works have been devoted to identifying the few most influential users. But most of existing works only focus on the diffusion of a single idea or product in social networks. However, in reality, one company may produce multiple kinds of products and one user may also have multiple adoptions. Given multiple kinds of different products with different activation costs and profits, it is crucial for the company to distribute the limited budget among multiple products in order to achieve profit maximization. Profit Maximization with Multiple Adoptions (PM$^{2}$A) problem aims to seek for a seed set within the budget to maximize the overall profit. In this paper, a Randomized Modified Greedy (RMG) algorithm based on the Reverse Influence Sampling (RIS) technique is presented for the PM$^{2}$A problem, which could achieve a $(1-1/e-\varepsilon)$-approximate solution with high probability. Compared with the algorithm proposed in [16] that achieves a $\frac{1}{2}(1-1/e^{2})$-approximate solution, our algorithm provides a better performance ratio which is also the best performance ratio of the PM$^{2}$A problem. Comprehensive experiments on three real-world social networks are conducted, and the results demonstrate that our RMG algorithm outperforms the algorithm proposed in [16] and other heuristics in terms of profit maximization, and could better allocate the budget., Comment: 21 pages, 6 figures

In recent years, the blockchain-based Internet of Things (IoT) has been researched and applied widely, where each IoT device can act as a node in the blockchain. However, these lightweight nodes usually do not have enough computing power to complete the consensus or other computing-required tasks. Edge computing network gives a platform to provide computing power to IoT devices. A fundamental problem is how to allocate limited edge servers to IoT devices in a highly untrustworthy environment. In a fair competition environment, the allocation mechanism should be online, truthful, and privacy safe. To address these three challenges, we propose an online multi-item double auction (MIDA) mechanism, where IoT devices are buyers and edge servers are sellers. In order to achieve the truthfulness, the participants' private information is at risk of being exposed by inference attack, which may lead to malicious manipulation of the market by adversaries. Then, we improve our MIDA mechanism based on differential privacy to protect sensitive information from being leaked. It interferes with the auction results slightly but guarantees privacy protection with high confidence. Besides, we upgrade our privacy-preserving MIDA mechanism such that adapting to more complex and realistic scenarios. In the end, the effectiveness and correctness of algorithms are evaluated and verified by theoretical analysis and numerical simulations.

Recent years have seen various rumor diffusion models being assumed in detection of rumor source research of the online social network. Diffusion model is arguably considered as a very important and challengeable factor for source detection in networks but it is less studied. This paper provides an overview of three representative schemes of Independent Cascade-based, Epidemic-based, and Learning-based to model the patterns of rumor propagation as well as three major schemes of estimators for rumor sources since its inception a decade ago.

Electric Vehicles (EVs) are becoming more and more popular in our daily life, which replaces traditional fuel vehicles to reduce carbon emissions and protect the environment. EVs need to be charged, but the number of charging piles in a Charging Station (CS) is limited and charging is usually more time-consuming than fueling. According to this scenario, we propose a secure and efficient charging scheduling system based on a Directed Acyclic Graph (DAG)-blockchain and double auction mechanism. In a smart area, it attempts to assign EVs to the available CSs in the light of their submitted charging requests and status information. First, we design a lightweight charging scheduling framework that integrates DAG-blockchain and modern cryptography technology to ensure security and scalability during performing scheduling and completing tradings. In this process, a constrained multi-item double auction problem is formulated because of the limited charging resources in a CS, which motivates EVs and CSs in this area to participate in the market based on their preferences and statuses. Due to this constraint, our problem is more complicated and harder to achieve truthfulness as well as system efficiency compared to the existing double auction model. To adapt to it, we propose two algorithms, namely Truthful Mechanism for Charging (TMC) and Efficient Mechanism for Charging (EMC), to determine an assignment between EVs and CSs and pricing strategies. Then, both theoretical analysis and numerical simulations show the correctness and effectiveness of our proposed algorithms.

Attracted by the inherent security and privacy protection of the blockchain, incorporating blockchain into Internet of Things (IoT) has been widely studied in these years. However, the mining process requires high computational power, which prevents IoT devices from directly participating in blockchain construction. For this reason, edge computing service is introduced to help build the IoT blockchain, where IoT devices could purchase computational resources from the edge servers. In this paper, we consider the case that IoT devices also have other tasks that need the help of edge servers, such as data analysis and data storage. The profits they can get from these tasks is closely related to the amounts of resources they purchased from the edge servers. In this scenario, IoT devices will allocate their limited budgets to purchase different resources from different edge servers, such that their profits can be maximized. Moreover, edge servers will set "best" prices such that they can get the biggest benefits. Accordingly, there raise a pricing and budget allocation problem between edge servers and IoT devices. We model the interaction between edge servers and IoT devices as a multi-leader multi-follower Stackelberg game, whose objective is to reach the Stackelberg Equilibrium (SE). We prove the existence and uniqueness of the SE point, and design efficient algorithms to reach the SE point. In the end, we verify our model and algorithms by performing extensive simulations, and the results show the correctness and effectiveness of our designs., Comment: 11 pages, 6 figures

Bitcoin, as one of the most popular cryptocurrency, is recently attracting much attention of investors. Bitcoin price prediction task is consequently a rising academic topic for providing valuable insights and suggestions. Existing bitcoin prediction works mostly base on trivial feature engineering, that manually designs features or factors from multiple areas, including Bticoin Blockchain information, finance and social media sentiments. The feature engineering not only requires much human effort, but the effectiveness of the intuitively designed features can not be guaranteed. In this paper, we aim to mining the abundant patterns encoded in bitcoin transactions, and propose k-order transaction graph to reveal patterns under different scope. We propose the transaction graph based feature to automatically encode the patterns. A novel prediction method is proposed to accept the features and make price prediction, which can take advantage from particular patterns from different history period. The results of comparison experiments demonstrate that the proposed method outperforms the most recent state-of-art methods.

The real-time traffic monitoring is a fundamental mission in a smart city to understand traffic conditions and avoid dangerous incidents. In this paper, we propose a reliable and efficient traffic monitoring system that integrates blockchain and the Internet of vehicles technologies effectively. It can crowdsource its tasks of traffic information collection to vehicles that run on the road instead of installing cameras in every corner. First, we design a lightweight blockchain-based information trading framework to model the interactions between traffic administration and vehicles. It guarantees reliability, efficiency, and security during executing trading. Second, we define the utility functions for the entities in this system and come up with a budgeted auction mechanism that motivates vehicles to undertake the collection tasks actively. In our algorithm, it not only ensures that the total payment to the selected vehicles does not exceed a given budget, but also maintains the truthfulness of auction process that avoids some vehicles to offer unreal bids for getting greater utilities. Finally, we conduct a group of numerical simulations to evaluate the reliability of our trading framework and performance of our algorithms, whose results demonstrate their correctness and efficiency perfectly., Comment: in IEEE Transactions on Reliability

Influence maximization (IM) is a representative and classic problem that has been studied extensively before. The most important application derived from the IM problem is viral marketing. Take us as a promoter, we want to get benefits from the influence diffusion in a given social network, where each influenced (activated) user is associated with a benefit. However, there is often competing information initiated by our rivals diffusing in the same social network at the same time. Consider such a scenario, a user is influenced by both my information and my rivals' information. Here, the benefit from this user should be weakened to certain degree. How to quantify the degree of weakening? Based on that, we propose an overall evaluations on benefits of influence (OEBI) problem. We prove the objective function of the OEBI problem is not monotone, not submodular, and not supermodular. Fortunately, we can decompose this objective function into the difference of two submodular functions and adopt a modular-modular procedure to approximate it with a data-dependent approximation guarantee. Because of the difficulty to compute the exact objective value, we design a group of unbiased estimators by exploiting the idea of reverse influence sampling, which can improve time efficiency significantly without losing its approximation ratio. Finally, numerical experiments on real datasets verified the effectiveness of our approaches regardless of performance and efficiency.

With the development of intelligent vehicles, security and reliability communication between vehicles has become a key problem to be solved in Internet of vehicles(IoVs). Blockchain is considered as a feasible solution due to its advantages of decentralization, unforgeability and collective maintenance. However, the computing power of nodes in IoVs is limited, while the consensus mechanism of blockchain requires that the miners in the system have strong computing power for mining calculation. It consequently cannot satisfy the requirements, which is the challenges for the application of blockchain in IoVs. In fact, the application of blockchain in IoVs can be implemented by employing edge computing. The key entity of edge computing is the edge servers(ESs). Roadside nodes(RSUs) can be deployed as ESs of edge computing in IoVs. We have studied the ES deployment scheme for covering more vehicle nodes in IoVs, and propose a randomized algorithm to calculate approximation solutions. Finally, we simulated the performance of the proposed scheme and compared it with other deployment schemes.

Mining in the blockchain requires high computing power to solve the hash puzzle for example proof-of-work puzzle. It takes high cost to achieve the calculation of this problem in devices of IOT, especially the mobile devices of IOT. It consequently restricts the application of blockchain in mobile environment. However, edge computing can be utilized to solve the problem for insufficient computing power of mobile devices in IOT. Edge servers can recruit many mobile devices to contribute computing power together to mining and share the reward of mining with these recruited mobile devices. In this paper, we propose an incentivizing mechanism based on edge computing for mobile blockchain. We design a two-stage Stackelberg Game to jointly optimize the reward of edge servers and recruited mobile devices. The edge server as the leader sets the expected fee for the recruited mobile devices in Stage I. The mobile device as a follower provides its computing power to mine according to the expected fee in Stage. It proves that this game can obtain a uniqueness Nash Equilibrium solution under the same or different expected fee. In the simulation experiment, we obtain a result curve of the profit for the edge server with the different ratio between the computing power from the edge server and mobile devices. In addition, the proposed scheme has been compared with the MDG scheme for the profit of the edge server. The experimental results show that the profit of the proposed scheme is more than that of the MDG scheme under the same total computing power.

Online social network has been one of the most important platforms for viral marketing. Most of existing researches about diffusion of adoptions of new products on networks are about one diffusion. That is, only one piece of information about the product is spread on the network. However, in fact, one product may have multiple features and the information about different features may spread independently in social network. When a user would like to purchase the product, he would consider all of the features of the product comprehensively not just consider one. Based on this, we propose a novel problem, multi-feature budgeted profit maximization (MBPM) problem, which first considers budgeted profit maximization under multiple features propagation of one product. Given a social network with each node having an activation cost and a profit, MBPM problem seeks for a seed set with expected cost no more than the budget to make the total expected profit as large as possible. We consider MBPM problem under the adaptive setting, where seeds are chosen iteratively and next seed is selected according to current diffusion results. We study adaptive MBPM problem under two models, oracle model and noise model. The oracle model assumes conditional expected marginal profit of any node could be obtained in O(1) time and a (1-1/e) expected approximation policy is proposed. Under the noise model, we estimate conditional expected marginal profit of a node by modifying the EPIC algorithm and propose an efficient policy, which could return a (1-exp({\epsilon}-1)) expected approximation ratio. Several experiments are conducted on six realistic datasets to compare our proposed policies with their corresponding non-adaptive algorithms and some heuristic adaptive policies. Experimental results show efficiencies and superiorities of our policies., Comment: 12 pages, 6 figures

Influence maximization problem attempts to find a small subset of nodes that makes the expected influence spread maximized, which has been researched intensively before. They all assumed that each user in the seed set we select is activated successfully and then spread the influence. However, in the real scenario, not all users in the seed set are willing to be an influencer. Based on that, we consider each user associated with a probability with which we can activate her as a seed, and we can attempt to activate her many times. In this paper, we study the adaptive influence maximization with multiple activations (Adaptive-IMMA) problem, where we select a node in each iteration, observe whether she accepts to be a seed, if yes, wait to observe the influence diffusion process; If no, we can attempt to activate her again with a higher cost or select another node as a seed. We model the multiple activations mathematically and define it on the domain of integer lattice. We propose a new concept, adaptive dr-submodularity, and show our Adaptive-IMMA is the problem that maximizing an adaptive monotone and dr-submodular function under the expected knapsack constraint. Adaptive dr-submodular maximization problem is never covered by any existing studies. Thus, we summarize its properties and study its approximability comprehensively, which is a non-trivial generalization of existing analysis about adaptive submodularity. Besides, to overcome the difficulty to estimate the expected influence spread, we combine our adaptive greedy policy with sampling techniques without losing the approximation ratio but reducing the time complexity. Finally, we conduct experiments on several real datasets to evaluate the effectiveness and efficiency of our proposed policies.

With the development of smart cities, not only are all corners of the city connected to each other, but also connected from city to city. They form a large distributed network together, which can facilitate the integration of distributed energy station (DES) and corresponding smart aggregators. Nevertheless, because of potential security and privacy protection arisen from trustless energies trading, how to make such energies trading goes smoothly is a tricky challenge. In this paper, we propose a blockchain-based multiple energies trading (B-MET) system for secure and efficient energies trading by executing a smart contract we design. Because energies trading requires the blockchain in B-MET system to have high throughput and low latency, we design a new byzantine-based consensus mechanism (BCM) based on node's credit to improve efficiency for the consortium blockchain under the B-MET system. Then, we take combined heat and power (CHP) system as a typical example that provides distributed energies. We quantify their utilities, and model the interactions between aggregators and DESs in a smart city by a novel multi-leader multi-follower Stackelberg game. It is analyzed and solved by reaching Nash equilibrium between aggregators, which reflects the competition between aggregators to purchase energies from DESs. In the end, we conduct plenty of numerical simulations to evaluate and verify our proposed model and algorithms, which demonstrate their correctness and efficiency completely.

Profit maximization (PM) is to select a subset of users as seeds for viral marketing in online social networks, which balances between the cost and the profit from influence spread. We extend PM to that under the general marketing strategy, and form continuous profit maximization (CPM-MS) problem, whose domain is on integer lattices. The objective function of our CPM-MS is dr-submodular, but non-monotone. It is a typical case of unconstrained dr-submodular maximization (UDSM) problem, and take it as a starting point, we study UDSM systematically in this paper, which is very different from those existing researcher. First, we introduce the lattice-based double greedy algorithm, which can obtain a constant approximation guarantee. However, there is a strict and unrealistic condition that requiring the objective value is non-negative on the whole domain, or else no theoretical bounds. Thus, we propose a technique, called lattice-based iterative pruning. It can shrink the search space effectively, thereby greatly increasing the possibility of satisfying the non-negative objective function on this smaller domain without losing approximation ratio. Then, to overcome the difficulty to estimate the objective value of CPM-MS, we adopt reverse sampling strategies, and combine it with lattice-based double greedy, including pruning, without losing its performance but reducing its running time. The entire process can be considered as a general framework to solve the UDSM problem, especially for applying to social networks. Finally, we conduct experiments on several real datasets to evaluate the effectiveness and efficiency of our proposed algorithms., Comment: in IEEE Transactions on Computational Social Systems

Revenue maximization (RM) is one of the most important problems on online social networks (OSNs), which attempts to find a small subset of users in OSNs that makes the expected revenue maximized. It has been researched intensively before. However, most of exsiting literatures were based on non-adaptive seeding strategy and on simple information diffusion model, such as IC/LT-model. It considered the single influenced user as a measurement unit to quantify the revenue. Until Collaborate Game model appeared, it considered activity as a basic object to compute the revenue. An activity initiated by a user can only influence those users whose distance are within k-hop from the initiator. Based on that, we adopt adaptive seed strategy and formulate the Revenue Maximization under the Size Budget (RMSB) problem. If taking into account the product's promotion, we extend RMSB to the Revenue Maximization under the Community Budget (RMCB) problem, where the influence can be distributed over the whole network. The objective function of RMSB and RMCB is adatpive monotone and not adaptive submodular, but in some special cases, it is adaptive submodular. We study the RMSB and RMCB problem under both the speical submodular cases and general non-submodular cases, and propose RMSBSolver and RMCBSolver to solve them with strong theoretical guarantees, respectively. Especially, we give a data-dependent approximation ratio for RMSB problem under the general non-submodular cases. Finally, we evaluate our proposed algorithms by conducting experiments on real datasets, and show the effectiveness and accuracy of our solutions.

Activity maximization is a task of seeking a small subset of users in a given social network that makes the expected total activity benefit maximized. This is a generalization of many real applications. In this paper, we extend activity maximization problem to that under the general marketing strategy $\vec{x}$, which is a $d$-dimensional vector from a lattice space and has probability $h_u(\vec{x})$ to activate a node $u$ as a seed. Based on that, we propose the continuous activity maximization (CAM) problem, where the domain is continuous and the seed set we select conforms to a certain probability distribution. It is a new topic to study the problem about information diffusion under the lattice constraint, thus, we address the problem systematically here. First, we analyze the hardness of CAM and how to compute the objective function of CAM accurately and effectively. We prove this objective function is monotone, but not DR-submodular and not DR-supermodular. Then, we develop a monotone and DR-submodular lower bound and upper bound of CAM, and apply sampling techniques to design three unbiased estimators for CAM, its lower bound and upper bound. Next, adapted from IMM algorithm and sandwich approximation framework, we obtain a data-dependent approximation ratio. This process can be considered as a general method to solve those maximization problem on lattice but not DR-submodular. Last, we conduct experiments on three real-world datasets to evaluate the correctness and effectiveness of our proposed algorithms., Comment: in IEEE Transactions on Network Science and Engineering

Community partition is an important problem in many areas such as biology network, social network. The objective of this problem is to analyse the relationships among data via the network topology. In this paper, we consider the community partition problem under IC model in social networks. We formulate the problem as a combinatorial optimization problem which aims at partitioning a given social network into disjoint M communities. The objective is to maximize the sum of influence propagation of a social network through maximizing it within each community. The existing work shows the influence maximization for community partition problem (IMCPP) to be NP hard. We first prove that the objective function of IMCPP under IC model is neither submodular nor supermodular. Then both supermodular upper bound and submodular lower bound are constructed and proved so that the sandwich framework can be applied. A continuous greedy algorithm and a discrete implementation are designed for upper bound and lower bound problems and the algorithm for both of the two problems gets a 1-1/e approximation ratio. We also devise a simply greedy to solve the original objective function and apply the sandwich approximation framework to it to guarantee a data dependent approximation factor. Finally, our algorithms are evaluated on two real data sets, which clearly verifies the effectiveness of our method in community partition problem, as well as the advantage of our method against the other methods., Comment: 32 pages. arXiv admin note: text overlap with arXiv:2002.08554

The world-changing blockchain technique provides a novel method to establish a secure, trusted and decentralized system for solving the security and personal privacy problems in Industrial Internet of Things (IIoT) applications. The mining process in blockchain requires miners to solve a proof-of-work puzzle, which requires high computational power. However, the lightweight IIoT devices cannot directly participate in the mining process due to the limitation of power and computational resources. The edge computing service makes it possible for IIoT applications to build a blockchain network, in which IIoT devices purchase computational resources from edge servers and thus can offload their computational tasks. The amount of computational resource purchased by IIoT devices depends on how many profits they can get in the mining process, and will directly affect the security of the blockchain network. In this paper, we investigate the incentive mechanism for the blockchain platform to attract IIoT devices to purchase more computational power from edge servers to participate in the mining process, thereby building a more secure blockchain network. We model the interaction between the blockchain platform and IIoT devices as a two-stage Stackelberg game, where the blockchain platform act as the leader, and IIoT devices act as followers. We analyze the existence and uniqueness of the Stackelberg equilibrium, and propose an efficient algorithm to compute the Stackelberg equilibrium point. Furthermore, we evaluate the performance of our algorithm through extensive simulations, and analyze the strategies of blockchain platform and IIoT devices under different situations.

The combined cooling, heating and power (CCHP) system is a typical distributed, electricity-gas integrated energy scheme in a community. First, it generates electricity by use of gas, and then exploits the waste heat to supply community with heat and cooling. In this paper, we consider a smart city consisting of a number of communities (CCHPs) and an agent of power grid (APG), where CCHPs can sell energy to the APG according to its bid. To study all utilities of entities in such a city from energy trading, a noncooperative Stackelberg game between APG and CCHPs is formulated. Here, the APG gives a bid for buying the energy from CCHPs, then CCHPs respond to the APG with their optimal energy supply that maximizing their utilities according to this bid. We show that the maximum profit to the APG and utilities to the CCHPs can be obtained at the Stackelberg equilibrium, which is guaranteed to exist and unique. Because the complete information about energy supply of each CCHP is unknown to the APG in advance, we propose a distributed algorithm that is able to find the point of equilibrium through a limited number of iterations. Taking privacy protection and transaction security into consideration, we design a blockchain-enabled energy management system. This system is composed of Internet of Energy (IoE) sub-system and blockchain sub-system, where the information interactions as well as energy transactions between APG and CCHPs can be carried out effectively and safely. Finally, security analysis and numerical simulations show the effectiveness and accuracy of our proposed mechanism., Comment: in IEEE Internet of Things Journal

Community partition is of great importance in social networks because of the rapid increasing network scale, data and applications. We consider the community partition problem under LT model in social networks, which is a combinatorial optimization problem that divides the social network to disjoint $m$ communities. Our goal is to maximize the sum of influence propagation through maximizing it within each community. As the influence propagation function of community partition problem is supermodular under LT model, we use the method of Lov{$\acute{a}$}sz Extension to relax the target influence function and transfer our goal to maximize the relaxed function over a matroid polytope. Next, we propose a continuous greedy algorithm using the properties of the relaxed function to solve our problem, which needs to be discretized in concrete implementation. Then, random rounding technique is used to convert the fractional solution to integer solution. We present a theoretical analysis with $1-1/e$ approximation ratio for the proposed algorithms. Extensive experiments are conducted to evaluate the performance of the proposed continuous greedy algorithms on real-world online social networks datasets and the results demonstrate that continuous community partition method can improve influence spread and accuracy of the community partition effectively., Comment: arXiv admin note: text overlap with arXiv:2003.10439