edge-wise graph partitioning

This paper studies the graph edge partitioning problem: partitioning the edges of a graph into $k$ nearly equal-sized subsets to minimize the vertex replication factor—the number of vertices assigned to multiple partitions. To overcome the limited expressiveness of conventional symmetric intersecting families, we introduce the “balanced intersecting system,” a novel combinatorial structure that relaxes symmetry constraints and improves adaptability to arbitrary $k$. Leveraging tools from combinatorial design, intersecting family theory, and asymptotic analysis, we construct an edge partition achieving a replication factor of $sqrt{n}(1+o(1))$, matching the theoretical lower bound for this problem. Our method ensures near-perfect load balancing across partitions and is universally applicable to any $k$, thereby significantly advancing both the theoretical foundations and practical applicability of graph partitioning in distributed graph processing.

This study investigates the role of task replication in graph partitioning and DAG scheduling, aiming to substantially reduce or even eliminate inter-processor communication with minimal computational overhead. It presents the first systematic analysis of how replication affects the computational complexity of these two problems and introduces an optimal replication model based on integer linear programming (ILP) alongside an efficient heuristic algorithm tailored for large-scale DAGs. Experimental results demonstrate that, in hypergraph partitioning, communication cost is reduced by 17%–65% on average, with complete elimination in certain scenarios; in DAG scheduling, reductions range from 11.61% to 23.13% on average, reaching as high as 58.17%. These findings confirm the effectiveness and practical value of replication strategies.

To address the high overhead of dynamic data repartitioning in multi-core HPC systems under time-varying workloads, this paper proposes a lightweight, hierarchical partitioning method jointly driven by geometric and statistical principles. The method integrates space-filling curve ordering, greedy knapsack-based load balancing, and hierarchical data decomposition to support efficient dynamic partitioning of 2D/3D structured grids, point sets, and general graphs. It introduces, for the first time, an adaptive repartitioning mechanism guided by real-time feedback on data distribution, substantially reducing computational and communication overhead in frequently updated scenarios. Implemented via a hybrid parallel programming model (MPI + OpenMP) on modern many-core architectures, experimental results demonstrate a 3.2–5.7× speedup in partitioning time and a load imbalance ratio below 3.1%. This approach provides timely, low-overhead data partitioning support for parallel algorithms in large-scale scientific computing.

Balanced graph partitioning for irregular graphs (e.g., social networks) remains challenging due to the strict constraint of maintaining block-size balance during local search. Method: This work relaxes this constraint by introducing an unconstrained node-movement strategy that permits significant temporary imbalance. It systematically validates that controlled, transient imbalance improves solution quality; designs a heuristic candidate-node selection scheme and a dynamic imbalance control mechanism; and develops a multi-stage, highly parallelized rebalancing algorithm. Contribution/Results: Evaluated on standard benchmarks, the method achieves solutions within 75% of the optimal objective value, reduces edge-cut ratio by 9.6% over the second-best approach, and incurs only a 7.7% geometric mean runtime overhead—demonstrating both high solution quality and strong scalability.

To address the scalability limitations of spectral clustering in large-scale graph clustering, this paper proposes a parallel multi-scale framework. First, a parallelizable structure-preserving graph coarsening algorithm is designed to generate multiple high-fidelity coarse graphs. Second, spectral clustering is executed in parallel on these coarse graphs. Third, optimal transport is introduced—novelly—to align and fuse the resulting multiple partitions, thereby enhancing consistency and clustering quality. By integrating graph coarsening, parallel computation, and optimal transport theory, the method achieves significant speedup while preserving structural fidelity: it delivers several-fold runtime reduction on both synthetic and real-world datasets, while outperforming existing baselines in NMI and F1 scores. Key contributions are: (1) the first structure-preserving coarsening scheme supporting parallel coarsening; and (2) the first application of optimal transport for multi-partition fusion to improve clustering robustness and accuracy.

This work investigates the fundamental limits of minimizing vertex footprint—the maximum number of vertices appearing in any partition—in random hypergraph edge partitioning. Under a general model where each hyperedge is sampled independently, the paper proposes a novel deterministic partitioning algorithm that combines information-theoretic converse bounds with combinatorial optimization techniques to achieve near-optimal performance under mild partition constraints. It establishes, for the first time, a unified information-theoretic lower bound applicable to canonical hypergraph structures including degree-corrected, mixed-membership, and stochastic block models. Specifically, when the number of hyperedges satisfies $|X| \gtrsim nN \log N$, the footprint of any algorithm is, with high probability, at least $n/(2\sqrt{2} N^{1/d})$. The proposed method approaches this limit within a constant factor in both dense and sparse regimes while ensuring near-balanced hyperedge allocation across partitions.

Existing hypergraph partitioning methods struggle to balance solution quality and computational efficiency in large-k scenarios, particularly due to the prohibitive overhead of traditional memetic algorithms that repeatedly invoke independent multilevel partitioners. This work proposes a novel approach that deeply integrates recombination and mutation operators from memetic computing into the uncoarsening phase of a single multilevel partitioning framework, establishing a cross-granularity cooperative local search mechanism that eliminates redundant partitioner invocations. Evaluated on standard benchmarks, the proposed method significantly outperforms state-of-the-art techniques by more effectively escaping local optima while simultaneously achieving higher-quality partitions for large k without sacrificing efficiency.

This work addresses the disconnect between modular application design and execution in edge and cloud computing, particularly the challenges of uniformly modeling computational units, data sharing, and event dependencies. To bridge this gap, the paper proposes a domain-specific visual graph editor that enables users to define data and control flows through three core abstractions: kernel functions, shared memory nodes, and event triggers. The tool automatically generates deployable, machine-readable representations from these visual models. By integrating explicit execution semantics, modular design, and one-click deployment within a unified interface—combining visual modeling, domain-specific language (DSL) abstractions, event-driven architecture, and distributed shared memory—it significantly enhances the comprehensibility of execution order and dependencies. Evaluations in scenarios such as federated learning demonstrate its superior semantic expressiveness and direct deployability compared to general-purpose diagramming tools and conventional workflow editors.

This study addresses the absence of a unified theoretical framework for network partitioning clustering that accounts for both hard/soft assignment mechanisms and non-vertex-centered cluster prototypes. The authors systematically analyze four classical models: the hard-assignment p-median problem (PMP) and spectral clustering (SSC), alongside the soft-assignment probabilistic density clustering (PDC) and fuzzy c-means (FCM). They reveal, for the first time, that optimal solutions of PMP and PDC are inherently confined to graph vertices, whereas SSC and FCM can yield cluster centers located along edges. Through rigorous mathematical analysis of their structural properties and optimization behaviors under network topology, the work elucidates the critical roles of bottleneck points and vertex-constrained solutions, thereby establishing a theoretical foundation for efficient clustering algorithms in facility location, network design, and similarity search via graph embeddings.

This work addresses the NP-hard problem of large-scale hypergraph partitioning under constraints of bounded block sizes and the uniqueness of incident hyperedges per block. The authors propose an efficient GPU-accelerated multilevel partitioning algorithm that explicitly constructs incidence structures and neighborhood information to enable batch computation of vertex-pair gains in shared memory. By integrating path- and cycle-based move chains with parallel reduction for validating moves, the method innovatively leverages the hierarchical parallelism of GPUs while respecting problem-specific constraints. A linear-span kernel is designed to support k-way balanced partitioning with negligible overhead. Experimental results demonstrate an average speedup of 380× over state-of-the-art serial multilevel partitioners, along with 1.2–2.0× lower connectivity. For k=2, the approach achieves a 5× speedup over CPU-based methods with only ~5% quality degradation, significantly outperforming existing GPU partitioners.