A Sharding Scheme Based on Graph Partitioning Algorithm for Public Blockchain

Blockchain technology,with its attributes of decentralization,immutability,and traceability,has emerged as a powerful catalyst for enhancing traditional industries in terms of optimizing business processes.However,transaction performance and scalability has become the main challenges hindering the widespread adoption of blockchain.Due to its inability to meet the demands of high-frequency trading,blockchain cannot be adopted in many scenarios.To improve the transaction capacity,researchers have proposed some on-chain scaling technologies,including lightning networks,directed acyclic graph technology,state channels,and shardingmechanisms,inwhich sharding emerges as a potential scaling technology.Nevertheless,excessive cross-shard transactions and uneven shard workloads prevent the sharding mechanism from achieving the expected aim.This paper proposes a graphbased sharding scheme for public blockchain to efficiently balance the transaction distribution.Bymitigating crossshard transactions and evening-out workloads among shards,the scheme reduces transaction confirmation latency and enhances the transaction capacity of the blockchain.Therefore,the scheme can achieve a high-frequency transaction as well as a better blockchain scalability.Experiments results show that the scheme effectively reduces the cross-shard transaction ratio to a range of 35%-56%and significantly decreases the transaction confirmation latency to 6 s in a blockchain with no more than 25 shards.

A Reduced-Order Modeling of Multi-Port RC Networks by Means of Graph Partitioning

A modified reduced-order method for RC networks which takes a division-and-conquest strategy is presented.The whole network is partitioned into a set of sub-networks at first,then each of them is reduced by Krylov subspace techniques,and finally all the reduced sub-networks are incorporated together.With some accuracy,this method can reduce the number of both nodes and components of the circuit comparing to the traditional methods which usually only offer a reduced net with less nodes.This can markedly accelerate the sparse-matrix-based simulators whose performance is dominated by the entity of the matrix or the number of components of the circuits.

Approximation Algorithms for Graph Partition into Bounded Independent Sets

The partition problem of a given graph into three independent sets of minimizing the maximum one is studied in this paper.This problem is NP-hard,even restricted to bipartite graphs.First,a simple 3/2-approximation algorithm for any 2-colorable graph is presented.An improved 7/5-approximation algorithm is then designed for a tree.The theoretical proof of the improved algorithm performance ratio is constructive,thus providing an explicit partition approach for each case according to the cardinality of two color classes.

Bipartite-Oriented Distributed Graph Partitioning for Big Learning

Many machine learning and data mining （MLDM] problems like recommendation, topic modeling, and medical diagnosis can be modeled as computing on bipartite graphs. However, inost distributed graph-parallel systems are oblivious to the unique characteristics in such graphs and existing online graph partitioning algorithms usually cause excessive repli- cation of vertices as well as significant pressure on network communication. This article identifies the challenges and oppor- tunities of partitioning bipartite graphs for distributed MLDM processing and proposes BiGraph, a set of bipartite-oriented graph partitioning algorithms. BiGraph leverages observations such as the skewed distribution of vertices, discriminated computation load and imbalanced data sizes between the two subsets of vertices to derive a set of optimal graph partition- ing algorithms that result in minimal vertex replication and network communication. BiGraph has been implemented on PowerGraph and is shown to have a performance boost up to 17.75X （from 1.16X） for four typical MLDM algorithnls, due to reducing up to 80% vertex replication, and up to 96% network traffic.

Fog Computing Dynamic Load Balancing Mechanism Based on Graph Repartitioning

Because of cloud computing's high degree of polymerization calculation mode, it can't give full play to the resources of the edge device such as computing, storage, etc. Fog computing can improve the resource utilization efficiency of the edge device, and solve the problem about service computing of the delay-sensitive applications. This paper researches on the framework of the fog computing, and adopts Cloud Atomization Technology to turn physical nodes in different levels into virtual machine nodes. On this basis, this paper uses the graph partitioning theory to build the fog computing's load balancing algorithm based on dynamic graph partitioning. The simulation results show that the framework of the fog computing after Cloud Atomization can build the system network flexibly, and dynamic load balancing mechanism can effectively configure system resources as well as reducing the consumption of node migration brought by system changes.

Graph partitioning algorithm for opportunistic routing in large-scale wireless network

Opportunistic routing takes advantage of the broadcast nature of wireless communications by forwarding data through a set of opportunistic paths instead of one ＇best＇ path in traditional routing. However, using the global scheduling opportunistic scheme like the existing opportunistic routing protocol （ExOR） would consume considerable transmission latency and energy in large-scale wireless topologies. In this article, a graph partitioning algorithm is proposed, namely, minimum cut with laplacians （MCL）, to divide the Ad-hoc network topology into subgraphs with minimized edge cuts across them. Then the existing opportunistic routing can be applied locally in each subgraph. In this way, forwarders in different subgraphs can transmit simultaneously, and each node only needs to maintain a local forwarder list instead of a global one. The simulations show that using MCL scheme in the opportunistic routing can reduce the end-to-end delay by about 49%, and increase the life time of the wireless node by about 39%.

Betweenness-based algorithm for a partition scale-free graph

Many real-world networks are found to be scale-free. However, graph partition technology, as a technology capable of parallel computing, performs poorly when scale-free graphs are provided. The reason for this is that traditional partitioning algorithms are designed for random networks and regular networks, rather than for scale-free networks. Multilevel graph-partitioning algorithms are currently considered to be the state of the art and are used extensively. In this paper, we analyse the reasons why traditional multilevel graph-partitioning algorithms perform poorly and present a new multilevel graph-partitioning paradigm, top down partitioning, which derives its name from the comparison with the traditional bottom-up partitioning. A new multilevel partitioning algorithm, named betweenness-based partitioning algorithm, is also presented as an implementation of top-down partitioning paradigm. An experimental evaluation of seven different real-world scale-free networks shows that the betweenness-based partitioning algorithm significantly outperforms the existing state-of-the-art approaches.

Parallel hydrodynamic finite element model with an N-Best refining partition scheme

We enhance a robust parallel finite element model for coasts and estuaries cases with the use of N-Best refinement algorithms,in multilevel partitioning scheme.Graph partitioning is an important step to construct the parallel model,in which computation speed is a big concern.The partitioning strategy includes the division of the research domain into several semi-equal-sized sub-domains,minimizing the sum weight of edges between different sub-domains.Multilevel schemes for graph partitioning are divided into three phases:coarsening,partitioning,and uncoarsening.In the uncoarsening phase,many refinement algorithms have been proposed previously,such as KL,Greedy,and Boundary refinements.In this study,we propose an N-Best refinement algorithm and show its advantages in our case study of Xiamen Bay.Compared with original partitioning algorithm in previous models,the N-Best algorithm can speed up the computation by 1.9 times,and the simulation results are in a good match with the in-situ data.

Mathematical Models for a Social Partitioning Problem

In this paper we develop modeling techniques for a social partitioning problem. Different social interaction regulations are imposed during pandemics to prevent the spread of diseases. We suggest partitioning a set of company employees as an effective way to curb the spread, and use integer programming techniques to model it. The goal of the model is to maximize the number of direct interactions between employees who are essential for company’s work subject to the constraint that all employees should be partitioned into components of no more than a certain size implied by the regulations. Then we further develop the basic model to take into account different restrictions and provisions. We also give heuristics for solving the problem. Our computational results include sensitivity analysis on some of the models and analysis of the heuristic performance.

Memoryless cooperative graph search based on the simulated annealing algorithm

We have studied the problem of reaching a globally optimal segment for a graph-like environment with a single or a group of autonomous mobile agents. Firstly, two efficient simulated-annealing-like algorithms are given for a single agent to solve the problem in a partially known environment and an unknown environment, respectively. It shows that under both proposed control strategies, the agent will eventually converge to a globally optimal segment with probability 1. Secondly, we use multi-agent searching to simultaneously reduce the computation complexity and accelerate convergence based on the algorithms we have given for a single agent. By exploiting graph partition, a gossip-consensus method based scheme is presented to update the key parameter--radius of the graph, ensuring that the agents spend much less time finding a globally optimal segment.

A Knowledge Graph based Software Engineering Curriculum Design Method

New theories,methodologies,and technologies have been continuously invented and widely applied in modern software development,along with many new tools and best practices that are of remarkable significance in the software industry.In Software Engineering(SE)programs of universities,it is quite difficult for their curricula to chase after the fast-evolving technology trend.As a consequence,there have been significant challenges in designing an evolvable SE curriculum.In this paper,we present a knowledge graph based curriculum design method for SE programs.Knowledge Points(KPs)are organized into a multi-layer and multi-dimensionally annotated knowledge graph called SEKG,and five principles are applied to partition the SEKG into a set of inter-related courses.Metrics for evaluating the quality of an SE curriculum are briefly discussed.This method can not only help design a systematic curriculum from existing software engineering KPs but also facilitate curriculum evolution to adapt to technology trends.

K_(1,7)与P_(6)的强积图的任意可分性

设G=(V,E)是n个顶点的简单图。序列λ=(λ_(1),λ_(2),·,λ_(p))满足λ_(1)+λ_(2)+·+λ_(p)=n,则序列λ被称为是可允许的序列。如果图G的顶点集V的一个划分(V_(1),V_(2),·,V_(p))满足|V_(i)|=λ_(i),i=1,2,·,p,且G[V_(i)]是连通的,则这个可允许的序列λ被称为是可表示的,并且称图G是λ-可分的。记K1,t是最大度为t的星,K1,t■Pn为星与路的强积图,图K1,7■P6是(1,λ_(2),·,λ_(p))-可分的。

Color image segmentation using mean shift and improved ant clustering

To improve the segmentation quality and efficiency of color image,a novel approach which combines the advantages of the mean shift(MS) segmentation and improved ant clustering method is proposed.The regions which can preserve the discontinuity characteristics of an image are segmented by MS algorithm,and then they are represented by a graph in which every region is represented by a node.In order to solve the graph partition problem,an improved ant clustering algorithm,called similarity carrying ant model(SCAM-ant),is proposed,in which a new similarity calculation method is given.Using SCAM-ant,the maximum number of items that each ant can carry will increase,the clustering time will be effectively reduced,and globally optimized clustering can also be realized.Because the graph is not based on the pixels of original image but on the segmentation result of MS algorithm,the computational complexity is greatly reduced.Experiments show that the proposed method can realize color image segmentation efficiently,and compared with the conventional methods based on the image pixels,it improves the image segmentation quality and the anti-interference ability.

Domain Decomposition for Wavelet Single Layer on Geometries with Patches

We focus on the single layer formulation which provides an integral equation of the first kind that is very badly conditioned. The condition number of the unpreconditioned system increases exponentially with the multiscale levels. A remedy utilizing overlapping domain decompositions applied to the Boundary Element Method by means of wavelets is examined. The width of the overlapping of the subdomains plays an important role in the estimation of the eigenvalues as well as the condition number of the additive domain decomposition operator. We examine the convergence analysis of the domain decomposition method which depends on the wavelet levels and on the size of the subdomain overlaps. Our theoretical results related to the additive Schwarz method are corroborated by numerical outputs.

New Network Immunization Strategy ~tter than the EGP Strategy

This paper aims at designing a better net-work i,,imozatopm strategy to fight against the Sus- ceptible-Infected-Susceptible （SIS） type epidemic spreading in networks. Previous work used the nurrber of drops in the spectral radius of the net-work for evaluation and guiding the design of im-munization strategies. Instead, we propose using the infected node number in the steady state of SIS spreading as the appropriate metric. We use the metric to point out the limitations of the Equal Graph Partitioning （EGP） strategy and the ＂max-△λ＂ strategy, which are two representative network inmmnization strategies, and then identify the criti-cal role of epidemic spreading parameters in the e-valuation and design of network immuzization strat- egies. Based on all of these, we design a new immuzization strategy. Simulation results show that our strategy performs consistently better than the EGP strategy. In many cases, it uses only 50% less re-sources to achieve the same immuzization effect.

Optimal Data Placement and Replication Approach for SIoT with Edge

Social networks(SNs)are sources with extreme number of users around the world who are all sharing data like images,audio,and video to their friends using IoT devices.This concept is the so-called Social Internet of Things(SIot).The evolving nature of edge-cloud computing has enabled storage of a large volume of data from various sources,and this task demands an efficient storage procedure.For this kind of large volume of data storage,the usage of data replication using edge with geo-distributed cloud service area is suited to fulfill the user’s expectations with low latency.The major issue is the way to store the data and replicate these large data items optimally and allocate the request from the data center efficiently.For efficient storage of these data,we use edge server,which is part of the cloud server,in this study.Thus,the data are distributed and stored with quick access,which will reduce the latency with response.The proposed data placement approach learns with machine learning(ML)algorithm called radial basis kernel function assisted with support vector machine(RBF-SVM)to classify the data center for storing the user and friend’s data from the SIoT devices.These learning algorithms will be used to predict the workload of the data stored in the data center as either edge or cloud depending on the existing time slots.The data placement with dynamic nature is also optimized using the proposed dynamic graph partitioning(GP)method to meet the individual user’s demand of low latency with minimum costs.This way will keep the SIoT data placement efficient and effective over time.Accordingly,this proposed data placement and replication approach introduces three kinds of innovations compared with the existing data placement approach.(i)Rather than storing the user data in a single cloud,this study uses the edge server closest to the SIoT devices for faster access with reduced response time.(ii)The classification algorithm called RBF-SVM is used to find storage for user for reducing data replication.(iii)Dynamic GP is introduced for data placement with reduced latency and minimum cost to fulfil the dynamic nature of the SN.The simulation result of this approach obtains reduced latency of 130 ms and minimum cost compared with those of the existing data placement approaches.Therefore,our proposed data placement with ML-based learning on edge provides promising results in terms of efficiency,effectiveness,and performance with reduced latency and minimum cost.

A new multi-level algorithm for balanced partition problem on large scale directed graphs

Graph partition is a classical combinatorial optimization and graph theory problem,and it has a lot of applications,such as scientific computing,VLSI design and clustering etc.In this paper,we study the partition problem on large scale directed graphs under a new objective function,a new instance of graph partition problem.We firstly propose the modeling of this problem,then design an algorithm based on multi-level strategy and recursive partition method,and finally do a lot of simulation experiments.The experimental results verify the stability of our algorithm and show that our algorithm has the same good performance as METIS.In addition,our algorithm is better than METIS on unbalanced ratio.

An Incremental Partitioning Graph Similarity Search Based on Tree Structure Index

Graph similarity search is a common operation of graph database,and graph editing distance constraint is the most common similarity measure to solve graph similarity search problem.However,accurate calculation of graph editing distance is proved to be NP hard,and the filter and verification framework are adopted in current method.In this paper,a dictionary tree based clustering index structure is proposed to reduce the cost of candidate graph,and is verified in the filtering stage.An efficient incremental partition algorithm was designed.By calculating the distance between query graph and candidate graph partition,the filtering effect was further enhanced.Experiments on real large graph datasets show that the performance of this algorithm is significantly better than that of the existing algorithms.

似星树与路的乘积图的任意可分性

设似星树S=S(a 1,a 2,…,a t,b 1,b 2,…,b s),其中a i(1≤i≤t)是奇数,bj(1≤j≤s)是偶数.首先,讨论似星树S与路Pl的乘积图S■P l在t和s不同取值下是否为任意可分图,并用图不含完美匹配的方法和反证法给出其不是任意可分图的充分条件;其次,分析图S■P l的Hamilton性,并用似星树的任意可分性给出图为任意可分图的充分条件.结果表明,当t=1且s≤2时,图S■P l是任意可分图;当t≥2或t=0,或者t=1,s≥3,b 1=b 2=…=b s,t+s≥l+2时,图S■P l均不是任意可分图.

广义太阳图与路的笛卡儿积图的任意可分性

给定n个顶点的图G.如果对于n的满足∑_(i=1)^(k)n_(i)=n的任意一个正整数序列τ=(n_(1),n_(2),···,n_(k)),都存在顶点集V(G)的划分(V_(1),V_(2),···,V_(k))满足|V_(i)|=n_(i),并且Vi导出的子图G[V_(i)]是连通的,其中1≤i≤k,则称图G是任意可分图(简称为AP).我们用S^(**)=S(n;k_(1),k_(2),···,k_(n))来表示一类广义太阳图.本文主要讨论图类S^(**)□Pm的任意可分性.