The paper revisits the Boykov‑Kolmogorov (BK) algorithm for computing minimum s‑t cuts in graphs, improving its theoretical time complexity to O(mn|C|). It introduces a faster variant, the fast BK (fBK) algorithm, with complexity O(m|C|), and proposes a compact graph representation enabling the algorithms to handle graphs with up to 10^9 vertices and 10^10 edges on a 128 GB machine. Experiments show that the compact BK implementation (cBK) outperforms other BK variants, underscoring the value of memory‑efficient designs.
arXiv:2609.07204v1 Announce Type: new Abstract: The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weighted sum of t...
arXiv:2609.01441v1 Announce Type: new Abstract: Graph neural networks (GNN) based on message passing are provably no more powerful than the one-dimensional Weisfeiler--Leman colour-refinement test (1...
The paper introduces linear‑time randomized algorithms for unbiased approximation of general random walk kernels (RWKs) on sparse graphs, covering both labelled and unlabelled cases. By sampling dependent random walks and constructing novel graph embeddings in ρ^d, the method avoids building the direct product graph, enabling scaling to massive datasets that cannot fit on a single machine. The authors provide exponential concentration bounds for the estimator’s sharpness and demonstrate up to 27× speed‑ups and 128× larger graph handling compared to previous cubic‑time approaches.
arXiv:2510.23039v2 Announce Type: replace Abstract: Approximate Nearest Neighbor (ANN) search and Approximate Kernel Density Estimation (A-KDE) are fundamental problems at the core of modern machine...
The paper presents a method for reliably scheduling operator execution in real‑time inference on small devices, achieving exact peak‑memory predictions and certified optimality. By profiling the generated program and modeling its memory usage, the authors can permute statements to match the modeled peak, guaranteeing bitwise‑identical results on CPUs and characterizing GPU limitations. They also provide efficient lower‑bound traps and analyze selective recomputation, showing it is NP‑hard in general but can reduce peak memory on certain architectures.
arXiv:2608. 14999v1 Announce Type: cross Abstract: Constructing special graphs is an important task within graph theory and computer science.
Decoupled Prune-and-Reconstruct (DPR) introduces a double‑layer sparsification strategy for graph neural networks that first prunes nodes to reduce memory usage and then reconstructs the full graph during inference. By training on a compact core of 30% of the nodes, DPR achieves 96.9% of the accuracy of a dense model while using only 1,450 MiB of peak memory on a single 6 GB GPU, outperforming edge‑sparsification baselines and reducing training memory by 50.1%. The method scales to millions of nodes, enabling all‑node inference on VRAM‑limited hardware without incurring a permanent accuracy loss.
The paper introduces EDiS, an Edge‑Disjoint Subgraph sparsification framework that separates a one‑time structural extraction of a graph into cacheable edge‑disjoint subgraphs from the per‑epoch graph composition. By recombining these cached subgraphs under edge‑budget constraints, EDiS avoids repeated sampling or recomputation while allowing varying training graphs across epochs. Experiments on 19 node‑classification benchmarks show that EDiS outperforms 17 baselines in accuracy/ROC‑AUC, achieving the lowest average rank and gap‑to‑best, especially at tight edge budgets.
The paper introduces GPU-based parallelization techniques for constructing the Gabriel graph, a proximity graph used in computational geometry and machine learning. By mapping thread indices to vertex pairs, employing a bitmask-based edge-list construction, and using thread coarsening, the authors achieve up to 8484× speedups over a CPU baseline without sacrificing accuracy. The accelerated graph enables efficient large‑margin classification and a new density‑aware clustering method that competes with DBSCAN while eliminating the need for a density radius parameter.
Graph functional dependencies (GFD) are a recently-developed concept aimed at capturing both topological structures in graphs and functional dependencies between attributes. The process of verifying whether a given GFD holds over a particular graph is referred to as GFD validation.
arXiv:2510.03899v3 Announce Type: replace-cross Abstract: Balancing resource efficiency and fairness is critical in networked systems that support modern learning applications. We introduce the \emph...
arXiv:2605. 21510v2 Announce Type: replace-cross Abstract: Reference-based graph compression encodes each vertex's neighbor list as differences from a nearby encoded list.