Balanced Partitioning Research Articles

DRONE: An Efficient Distributed Subgraph-Centric Framework for Processing Large-Scale Power-law Graphs

Nowadays, the ever-increasing volume of graph-structured data such as social networks, graph databases and knowledge graphs requires to be processed efficiently and scalably. These natural graphs commonly found in the real world have highly skewed power-law degree distribution and are called power-law graphs. The subgraph-centric programming model is a promising approach applied in many state-of-the-art distributed graph computing frameworks. However, the performance of subgraph-centric frameworks is limited when processing large-scale power-law graphs. When deployed to the subgraph-centric framework, existing graph partitioning algorithms are not suitable for power-law graphs. In this paper, we present a novel distributed graph computing framework, DRONE (Distributed gRaph cOmputiNg Engine), which leverages the subgraph-centric model and the vertex-cut graph partitioning strategy. DRONE also supports the fault tolerance mechanism to accommodate the increasing scale of machines with negligible overhead (6.48% on average). We further study the execution workflow of DRONE and propose an efficient and balanced graph partition algorithm (EBV) for DRONE. Experiments show that DRONE reduces the running time on real-world graphs by 25.6%, on average, compared to the state-of-the-art distributed graph computing frameworks. In addition, the EBV graph partition algorithm reduces the replication factor by at least 21.8% than other self-based partition algorithms. Our results indicate that DRONE has excellent potential in processing large-scale power-law graphs.

Efficient Knowledge Graph Embedding Training Framework with Multiple GPUs

When training a large-scale knowledge graph embedding (KGE) model with multiple graphics processing units (GPUs), the partition-based method is necessary for parallel training. However, existing partition-based training methods suffer from low GPU utilization and high input/output (10) overhead between the memory and disk. For a high 10 overhead between the disk and memory problem, we optimized the twice partitioning with fine-grained GPU scheduling to reduce the 10 overhead between the CPU memory and disk. For low GPU utilization caused by the GPU load imbalance problem, we proposed balanced partitioning and dynamic scheduling methods to accelerate the training speed in different cases. With the above methods, we proposed fine-grained partitioning KGE, an efficient KGE training framework with multiple GPUs. We conducted experiments on some benchmarks of the knowledge graph, and the results show that our method achieves speedup compared to existing framework on the training of KGE.

Scalable timing-aware network design via lagrangian decomposition

This paper addresses instances of the temporal fixed-charge multi-commodity flow (tfMCF) problem that arise in a very large scale dynamic transportation application. We model the tfMCF as a discrete-time Resource Task Network (RTN) with cyclic schedule, and formulate it as a mixed-integer program. These problems are notoriously hard to solve due to their time-expanded nature, and their size renders their direct solution difficult. We exploit synergies between flows of certain commodities in the formulation to devise model condensation techniques that reduce the number of variables and constraints by a factor of 25%–50%. We propose a solution algorithm that includes balanced graph partitioning, Lagrangian decomposition and a linear programming filtering heuristic. Computational results show that the proposed algorithm allows the solution of previously intractable instances, and the primal solution obtained by the heuristic step is within 2% duality gap of the linear relaxation of the original problem.

Balanced Domain Partitioning for Software Defined Networks

Software Defined Networking (SDN) has been widely adopted to enable the network programmability by decoupling the controller logic from the data plane. Domain partitioning is essential for SDN-enabled communication networks to partition the oversized network topology into controllable and administrative domains. Existing domain partitioning algorithms failed to take the connectivity, balance constraint, compactness, and traffic cohesion into consideration simultaneously which are required by SDN communications. This paper formulates the domain partitioning problem and proposed a novel balanced network partitioning (BaDoP) algorithm, which can enhance the balance of the partitioned domains, and optimize the compactness and traffic cohesion with connectivity constraint always guaranteed. BaDoP employs Bubble algorithm to find initial domain partitioning, and improves the domain partitioning iteratively by moving border nodes among the partitioned domains guided by the negative cycles or shortest paths on an auxiliary graph which is an abstract view of the current domain partitioning. The simulation results indicates that our BaDoP algorithm outperforms the previous algorithms and can achieve significant improvement for the balance of the partitioned domains.

Two Channel Filter Banks on Arbitrary Graphs With Positive Semi Definite Variation Operators

We propose novel two-channel filter banks for signals on graphs. Our designs can be applied to arbitrary graphs, given a positive semi definite variation operator, while using arbitrary vertex partitions for downsampling. The proposed generalized filter banks (GFBs) also satisfy several desirable properties including perfect reconstruction and critical sampling, while having efficient implementations. Our results generalize previous approaches that were only valid for the normalized Laplacian of bipartite graphs. Our approach is based on novel graph Fourier transforms (GFTs) given by the generalized eigenvectors of the variation operator. These GFTs are orthogonal in an alternative inner product space which depends on the downsampling and variation operators. Our key theoretical contribution is showing that the spectral folding property of the normalized Laplacian of bipartite graphs, at the core of bipartite filter bank theory, can be generalized for the proposed GFT if the inner product matrix is chosen properly. In addition, we study vertex domain and spectral domain properties of GFBs and illustrate their probabilistic interpretation using Gaussian graphical models. While GFBs can be defined given any choice of a vertex partition for downsampling, we propose an algorithm to optimize these partitions with a criterion that favors balanced partitions with large graph cuts, which are shown to lead to efficient and stable GFB implementations. Our numerical experiments show that partition-optimized GFBs can be implemented efficiently on 3D point clouds with hundreds of thousands of points (nodes), while also improving the color signal representation quality over competing state-of-the-art approaches.

Fuzzy-Based Balanced Partitioning Under Capacity and Size-Tolerance Constraints in Distributed Quantum Circuits

Fuzzy-Based Balanced Partitioning Under Capacity and Size-Tolerance Constraints in Distributed Quantum Circuits

A Novel Classification Method Based on Stacking Ensemble for Imbalanced Problems

Imbalanced problems are a significant challenge in data-driven diagnosis technology, as the data collected from the scenario of engineering is usually imbalanced. Imbalanced data poses a negative effect on classification algorithms and reduces the recognition performance of the minority samples. To address this challenge, ensemble classifiers have gained significant attention due to their superior performance compared to the individual classifiers. In this paper, we provide improvements at both the data and algorithm levels by using the stacking ensemble. At the data level, a Data-Space balanced Partition (DSP) method based on under-sampling is proposed, which recursively partitions the imbalanced data-space into relatively balanced data-subspaces. At the algorithm level, we propose a cost-sensitive stacking approach, which adjusts the weights of different categories to enhance the algorithm’s attention to the minority class. Based on these two improvements, a novel classification method for imbalanced problems, Data-Space balanced Partition based on Cost-sensitive Stacking learning (DPCStacking), is proposed. The proposed method is evaluated on 38 imbalanced datasets from KEEL. The experimental results demonstrate the effectiveness of the proposed improvements. Compared to the other six algorithms specifically designed to address imbalanced problems, the DPCStacking algorithm achieves the highest Average Accuracy (AAcc) and True Positive Rate (TPR) of 0.876 and 0.876, respectively.

Computing Balanced Convex Partitions of Lines

Computing Balanced Convex Partitions of Lines

Structural regulation and dynamic behaviour of organelles during plant meiosis.

Eukaryotes use various mechanisms to maintain cell division stability during sporogenesis, and in particular during meiosis to achieve production of haploid spores. In addition to establishing even chromosome segregation in meiosis I and II, it is crucial for meiotic cells to guarantee balanced partitioning of organelles to the daughter cells, to properly inherit cellular functions. In plants, cytological studies in model systems have yielded insights into the meiotic behaviour of different organelles, i.e., clearly revealing a distinct organization at different stages throughout meiosis indicating for an active regulatory mechanism determining their subcellular dynamics. However, how, and why plant meiocytes organize synchronicity of these elements and whether this is conserved across all plant genera is still not fully elucidated. It is generally accepted that the highly programmed intracellular behaviour of organelles during meiosis serves to guarantee balanced cytoplasmic inheritance. However, recent studies also indicate that it contributes to the regulation of key meiotic processes, like the organization of cell polarity and spindle orientation, thus exhibiting different functionalities than those characterized in mitotic cell division. In this review paper, we will outline the current knowledge on organelle dynamics in plant meiosis and discuss the putative strategies that the plant cell uses to mediate this programmed spatio-temporal organization in order to safeguard balanced separation of organelles. Particular attention is thereby given to putative molecular mechanisms that underlie this dynamic organelle organization taken into account existing variations in the meiotic cell division program across different plant types. Furthermore, we will elaborate on the structural role of organelles in plant meiosis and discuss on organelle-based cellular mechanisms that contribute to the organization and molecular coordination of key meiotic processes, including spindle positioning, chromosome segregation and cell division. Overall, this review summarizes all relevant insights on the dynamic behaviour and inheritance of organelles during plant meiosis, and discusses on their functional role in the structural and molecular regulation of meiotic cell division.

Cardinality constrained connected balanced partitions of trees under different criteria

In this paper we study the problem of partitioning a tree with n weighted vertices into p connected components. For each component, we measure its gap, that is, the difference between the maximum and the minimum weight of its vertices, with the aim of minimizing the sum of such differences. We present an O(n3p2) time and O(n3p) space algorithm for this problem. Then, we generalize it, requiring a minimum of ϵ≥1 nodes in each connected component, and provide an O(n3p2ϵ2) time and O(n3pϵ) space algorithm to solve this new problem version. We provide a refinement of our analysis involving the topology of the tree and an improvement of the algorithms for the special case in which the weights of the vertices have a heap structure. All presented algorithms can be straightforwardly extended to other similar objective functions. Actually, for the problem of minimizing the maximum gap with a minimum number of nodes in each component, we propose an algorithm which is independent of ϵ and requires O(n2lognp2) time and O(n2p) space.

Improving bacterial genome assembly using a test of strand orientation.

The complexity of genome assembly is due in large part to the presence of repeats. In particular, large reverse-complemented repeats can lead to incorrect inversions of large segments of the genome. To detect and correct such inversions in finished bacterial genomes, we propose a statistical test based on tetranucleotide frequency (TNF), which determines whether two segments from the same genome are of the same or opposite orientation. In most cases, the test neatly partitions the genome into two segments of roughly equal length with seemingly opposite orientations. This corresponds to the segments between the DNA replication origin and terminus, which were previously known to have distinct nucleotide compositions. We show that, in several cases where this balanced partition is not observed, the test identifies a potential inverted misassembly, which is validated by the presence of a reverse-complemented repeat at the boundaries of the inversion. After inverting the sequence between the repeat, the balance of the misassembled genome is restored. Our method identifies 31 potential misassemblies in the NCBI database, several of which are further supported by a reassembly of the read data. A github repository is available at https://github.com/gcgreenberg/Oriented-TNF.git. Supplementary data are available at Bioinformatics online.

A hierarchical approach for building distributed quantum systems

In this paper, a multi-layer hierarchical architecture is proposed for distributing quantum computation. In a distributed quantum computing (DQC), different units or subsystems communicate by teleportation in order to transfer quantum information. Quantum teleportation requires classical and quantum resources and hence, it is essential to minimize the number of communications among these subsystems. To this end, a two-level hierarchical optimization method is proposed to distribute the qubits among different parts. In Level I, an integer linear programming model is presented to distribute a monolithic quantum system into K balanced partitions which results in the minimum number of non-local gates. When a qubit is teleported to a destination part, it can be used optimally by other gates without being teleported back to the destination part. In Level II, a data structure is proposed for quantum circuit and a recursive function is applied to minimize the number of teleportations. Experimental results show that the proposed approach outperforms the previous ones.

BaPipe: Balanced Pipeline Parallelism for DNN Training

The size of deep neural networks (DNNs) grows rapidly as the complexity of the machine learning algorithm increases. Distributed deep learning based on model parallelism has been widely used to satisfy the requirements of DNN training related to computation and memory. In this paper, we propose a training framework for pipeline parallelism called BaPipe (Balanced Pipeline) that can automatically explore methods to schedule pipeline parallelism and balanced partition strategies for DNN training on heterogeneous accelerator clusters. In BaPipe, each accelerator calculates the forward and backward propagation for the assigned partition of networks to implement an intra-batch pipeline parallelism strategy. By considering the parameters of DNN models as well as the computation, memory, and communication resources of each accelerator, BaPipe automatically selects the most suitable method of pipeline scheduling from among multiple proposed scheduling modes. It also uses a novel strategy to automatically investigate load balancing in the context of inter-layer partition, intra-layer partition, and coarse-grained partition. We trained such DNNs as VGG-16, ResNet-50, and Google’s Neural Machine Translation (GNMT) on GPU clusters, and simulated the training-related performance of FPGA clusters. Compared with the state-of-the-art frameworks for data parallelism (DP) and pipeline parallelism, BaPipe provides a speedup of [Formula: see text] and [Formula: see text] of memory reduction on various homogeneous and heterogeneous platforms.

GON: End-to-end optimization framework for constraint graph optimization problems

Real-world computational applications often require solving combinatorial optimization problems on graphs, i.e., graph optimization problems (GOPs). An emerging trend is using graph neural networks (GNNs) to tackle GOPs. However, for GOPs with constraints, a great challenge faced by GNNs-based methods is to produce optimal solutions that satisfy the constraints. Existing methods relying on supervised learning require a large amount of labeled data, while unsupervised learning methods often require designing elaborate network architectures. To address these limitations, we propose an end-to-end optimization framework for constraint GOPs, coined Graph Optimization Network (GON). GON is a simple and effective method aiming to address general GOPs without designing specific network architectures for different problems. The proposed framework is evaluated on two typical constraint GOPs, one with only soft constraints (the balanced graph partitioning problem) and the other with hard constraints (the maximum independent set problem). We model the two problems as node assignment problems and design the corresponding constraint-aware loss function for each so that the model can be directly optimized to generate optimal solutions that satisfy the constraints. Experiments on various benchmarks show that the proposed GON equipped with a vanilla GNN can achieve excellent performance on both GOPs, superior to state-of-the-art methods. The results suggest that GON is a promising solver to address NP-hard GOPs.

Optimal scan planning for surveying large sites with static and mobile mapping systems

Since the last two decades, the use of laser scanners for generating accurate and dense 3D models has been rapidly growing in multiple disciplines. The reliance on human-expertise to perform an efficient scanning in terms of completeness and quality encouraged the researchers to develop strategies for carrying out an optimized and automated scan planning. Nevertheless, due to the predominant use of static terrestrial laser scanners (TLS), the most of developed methods have been focused on scan optimization by fixing standpoints on basis of static scanning. The increasing use of portable mobile laser scanning systems (MLS) enables faster non-stop acquisition which demands the planning of optimal scan trajectories. Therefore, a novel method addressing the absence of dynamic scan planning is proposed considering specific MLS constraints such as maximum acquisition time or closed-loops requirement. First, an initial analysis is carried out to determinate key-positions to reach during data acquisition. From these positions a navigable graph is generated to compute routes satisfying specific MLS constraints by a three-step process. This starts by estimating the number of routes necessary to subsequently carry out a coarse graph partition based on Kmedoids clustering. Next, a balancing algorithm was implemented to compute a balanced graph partition by node exchanging. Finally, partitions are extended by adding key nodes from their adjacent ones in order to provide a desirable overlapping between scans. The method was tested by simulating three laser scanner configurations in four indoor and outdoor real case studies. The acquisition quality of the computed scan planning was evaluated in terms of 3D completeness and point cloud density with the simulator Helios++.

Balanced-partitioning treemapping method for digital hierarchical dataset

BackgroundThe problem of visualizing a hierarchical dataset is an important and useful technique in many real-life situations. Folder systems, stock markets, and other hierarchical-related datasets can use this technique to better understand the structure and dynamic variation of the dataset. Traditional space-filling(square)-based methods have the advantages of compact space usage and node size as opposed to diagram-based methods. Spacefilling-based methods have two main research directions: static and dynamic performance. MethodsThis study presented a treemapping method based on balanced partitioning that enables excellent aspect ratios in one variant, good temporal coherence for dynamic data in another, and in the third, a satisfactory compromise between these two aspects. To layout a treemap, all the children of a node were divided into two groups, which were then further divided until groups of single elements were reached. After this, these groups were combined to form a rectangle representing the parent node. This process was performed for each layer of the hierarchical dataset. For the first variant from the partitioning, the child elements were sorted and two groups, sized as equally as possible, were built from both big and small elements (size-balanced partition). This achieved satisfactory aspect ratios for the rectangles but less so temporal coherence (dynamic). For the second variant, the sequence of children was taken and from this, groups, sized as equally as possible, were created without the need for sorting (sequence-based, good compromise between aspect ratio and temporal coherency). For the third variant, the children were split into two groups of equal cardinalities, regardless of their size (number-balanced, worse aspect ratios but good temporal coherence). ResultsThis study evaluated the aspect ratios and dynamic stability of the employed methods and proposed a new metric that measures the visual difference between rectangles during their movement to represent temporally changing inputs. ConclusionThis study demonstrated that the proposed method of treemapping via balanced partitioning outperformed the state-of-the-art methods for several real-world datasets.

Research on Routing Equalization Algorithm of Inter-Satellite Partition for Low-Orbit Micro-Satellites

Low-orbit micro-satellite technology has developed rapidly in recent years due to its advantages of low time delay, low cost and short research period. However, among the existing inter-satellite routing algorithms, the classical flooding and greedy algorithms and their derivatives also have some limitations. The path delay calculated by the flooding algorithm is small but the calculation is large, while the greedy algorithm is the opposite. In this paper, a balanced inter-satellite routing algorithm based on partition routing is proposed. This paper presents the simulation experiments for the following indexes of the classic inter-satellite routing algorithms and the balanced partition routing algorithm: computation complexity, single-node computation pressure, routing path delay, path delay variance (data in Topo table satisfy μ =5, σ2=10). The results reveal that the balanced partition routing algorithm achieves better performance. In this paper, two optimization directions of the balanced partition routing algorithm are simulated under conditions that the data in the Topo table satisfy μ =5, σ2= 6, σ2=10 and σ2=15, respectively, when comparing their performance indicators. The experiments show that these two optimization methods can be adapted to various application scenarios and can further reduce the hardware cost of satellite nodes.

Pushing Collaborative Data Deduplication to the Network Edge: An Optimization Framework and System Design

Edge computing has become a new computing paradigm with explosive growth in recent years. We consider the problem of pushing data deduplication to the network edge and propose a new framework for distributed edge-facilitated deduplication (EF-dedup). Deduplication at the network edge allows us to exploit the high degree of geographic- and temporal-correlation in edge data to achieve space efficiency. By leveraging distributed computing power available on the edge in a collaborative fashion, the edge nodes can effectively suppress duplicated edge data, consuming considerably less space and WAN bandwidth. To this end, we partition the edge nodes into disjoint collaborative clusters, maintain a deduplication index structure across them using a distributed key-value store and perform deduplication within those clusters. However, this partitioning problem is very challenging and requires the optimization of a novel tradeoff: edge nodes with highly correlated data may not always be within the same edge cloud, with non-trivial network cost among them. We formulate a joint storage and network optimization problem with different design objectives, such as arbitrary partitioning and balanced partitioning of edge nodes. The problem is shown to be NP-Hard in general. Then, an optimization framework with efficient algorithms is developed and is proven to achieve a closed-form competitive ratio. Our experiments, performed on edge nodes in a corporate lab <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> and a central cloud at AWS, demonstrate that EF-dedup achieves 67.4 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula> 133.7% better deduplication throughput than sole cloud-based techniques and achieves 20.0-62.6 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> lesser aggregate cost in terms of the network-storage trade-off as compared to approaches that solely favor one over the other.

Shift of pairwise similarities for data clustering

Several clustering methods (e.g., Normalized Cut and Ratio Cut) divide the Min Cut cost function by a cluster dependent factor (e.g., the size or the degree of the clusters), in order to yield a more balanced partitioning. We, instead, investigate adding such regularizations to the original cost function. We first consider the case where the regularization term is the sum of the squared size of the clusters, and then generalize it to adaptive regularization of the pairwise similarities. This leads to shifting (adaptively) the pairwise similarities which might make some of them negative. We then study the connection of this method to Correlation Clustering and then propose an efficient local search optimization algorithm with fast theoretical convergence rate to solve the new clustering problem. In the following, we investigate the shift of pairwise similarities on some common clustering methods, and finally, we demonstrate the superior performance of the method by extensive experiments on different datasets.

Parameterized complexity of satisfactory partition problem

Given an undirected graph G, we study the Satisfactory Partition problem, where the goal is to decide whether it is possible to partition the vertex set of G into two parts such that each vertex has at least as many neighbours in its own part as in the other part. The Balanced Satisfactory Partition problem is a variant of the above problem where the two partite sets are required to have the same cardinality. Both problems are known to be NP-complete. This problem was introduced by Gerber and Kobler (2000) [9] and further studied by other authors, but its parameterized complexity remains open until now. We enhance our understanding of the problem from the viewpoint of parameterized complexity. The main results of the paper are the following: (1) Satisfactory Partition is polynomial-time solvable for block graphs, (2) Satisfactory Partition and Balanced Satisfactory Partition are fixed parameter tractable (FPT) when parameterized by neighbourhood diversity. (3) Satisfactory Partition and its balanced version can be solved in polynomial time for graphs of bounded clique-width, and (4) Balanced Satisfactory Partition is W[1]-hard when parameterized by treewidth.