We propose two one-pass streaming algorithms for the NP-hard hypergraph matching problem. The first algorithm stores a small subset of potential matching edges in a stack using dual variables to select edges. It has an approximation guarantee of 1/(d(1+ε)) and requires 𝒪((n/ε)log²n) bits of memory, where n is the number of vertices in the hypergraph, d is the maximum number of vertices in a hyperedge, and ε > 0 is a parameter to be chosen. The second algorithm computes, stores, and updates a single matching as the edges stream, with an approximation ratio dependent on a parameter α. Its best approximation guarantee is 1/((2d-1) + 2 √{d(d-1)}), and it requires only 𝒪(n) memory. We have implemented both algorithms and compared them with respect to solution quality, memory consumption, and running times on two diverse sets of hypergraphs with a non-streaming greedy and a naive streaming algorithm. Our results show that the streaming algorithms achieve much better solution quality than naive algorithms when facing adverse orderings. Furthermore, these algorithms reduce the memory required by a factor of 13 in the geometric mean on our test problems, and also outperform the offline Greedy algorithm in running time.

We introduce the poly-streaming model, a generalization of streaming models of computation in which k processors process k data streams containing a total of N items. The algorithm is allowed 𝒪(f(k)⋅M₁) space, where M₁ is either o (N) or the space bound for a sequential streaming algorithm. Processors may communicate as needed. Algorithms are assessed by the number of passes, per-item processing time, total runtime, space usage, communication cost, and solution quality. We design a single-pass algorithm in this model for approximating the maximum weight matching (MWM) problem. Given k edge streams and a parameter ε > 0, the algorithm computes a (2+ε)-approximate MWM. We analyze its performance in a shared-memory parallel setting: for any constant ε > 0, it runs in time 𝒪̃(L_{max}+n), where n is the number of vertices and L_{max} is the maximum stream length. It supports 𝒪(1) per-edge processing time using 𝒪̃(k⋅n) space. We further generalize the design to hierarchical architectures, in which k processors are partitioned into r groups, each with its own shared local memory. The total intergroup communication is 𝒪̃(r⋅n) bits, while all other performance guarantees are preserved. We evaluate the algorithm on a shared-memory system using graphs with trillions of edges. It achieves substantial speedups as k increases and produces matchings with weights significantly exceeding the theoretical guarantee. On our largest test graph, it reduces runtime by nearly two orders of magnitude and memory usage by five orders of magnitude compared to an offline algorithm.

We study exascale parallel algorithms for the selection of intervention or monitoring strategies in massive realistic socio-technical networks through scalable Influence Maximization (InfMax) algorithms.We employ novel techniques to enable efficient scaling on up to 8k nodes of OLCF Frontier, with 65k AMD GPUs and 458k AMD CPU cores.Current state-of-the-art InfMax tools are limited to networks with only a few million actors (vertices) and a few hundred million interactions (edges).By overcoming these limitations, ICS '25, June 08-11, 2025, Salt Lake City, UT, USA Minutoli et al.we show that our approach is capable of processing a realistic social contact network of the United States with 285 million nodes and about 8 billion edges.This two ordersof-magnitude improvement over the previous state-of-theart is obtained by leveraging algorithmic advancements for the InfMax problem and designing several problem-specific approaches to overlap communication with computation, improve GPU efficiency, and lower the application's memory requirements.We evaluate strong scaling for computing 10k most influential seeds using up to 8k nodes of an exascale system, and weak scaling from 128 to 8k system nodes for seed sets ranging from 625 to 40k seeds.We achieve the fastest-known runtime of 25 minutes while performing 48 million diffusion simulations totaling 2.31 petabytes to identify 40k influential seeds using 8k nodes, and take 5.75 minutes to identify 10k seeds while using 4k nodes.

Influence maximization—the problem of identifying a subset of k influential seeds (vertices) in a network—is a classical problem in network science with numerous applications. The problem is NP-hard, but there exist efficient polynomial time approximations. However, scaling these algorithms still remain a daunting task due to the complexities associated with steps involving stochastic sampling and large-scale aggregations. In this paper, we present a new parallel distributed approximation algorithm for influence maximization with provable approximation guarantees. Our approach, which we call GreediRIS , leverages the RandGreedi framework—a state-of-the-art approach for distributed submodular optimization—for solving a step that computes a maximum k cover. GreediRIS combines distributed and streaming models of computations, along with pruning techniques, to effectively address the communication bottlenecks of the algorithm. Experimental results on up to 512 nodes (32K cores) of the NERSC Perlmutter supercomputer show that GreediRIS can achieve good strong scaling performance, preserve quality, and significantly outperform the other state-of-the-art distributed implementations. For instance, on 512 nodes, the most performant variant of GreediRIS achieves geometric mean speedups of 28.99× and 36.35× for two different diffusion models, over a state-of-the-art parallel implementation. We also present a communication-optimized version of GreediRIS that further improves the speedups by two orders of magnitude. • A new distributed streaming algorithm for RIS -based InfMax on distributed parallel platforms. • A truncation technique, to provide a knob to control communication overhead with a tradeoff in quality. • Presented algorithms have provable worst-case approximation guarantees. • Significant performance gains demonstrated on 512 compute nodes (32K cores) of a supercomputer.

We design and implement two single-pass semi-streaming algorithms for the maximum weight $k$-disjoint matching ($k$-DM) problem. Given an integer $k$, the $k$-DM problem is to find $k$ pairwise edge-disjoint matchings such that the sum of the weights of the matchings is maximized. For $k \geq 2$, this problem is NP-hard. Our first algorithm is based on the primal-dual framework of a linear programming relaxation of the problem and is $\frac{1}{3+\varepsilon}$-approximate. We also develop an approximation preserving reduction from $k$-DM to the maximum weight $b$-matching problem. Leveraging this reduction and an existing semi-streaming $b$-matching algorithm, we design a $(\frac{1}{2+\varepsilon})(1 - \frac{1}{k+1})$-approximate semi-streaming algorithm for $k$-DM. For any constant $\varepsilon > 0$, both of these algorithms require $O(nk \log_{1+\varepsilon}^2 n)$ bits of space. To the best of our knowledge, this is the first study of semi-streaming algorithms for the $k$-DM problem. We compare our two algorithms to state-of-the-art offline algorithms on 95 real-world and synthetic test problems, including thirteen graphs generated from data center network traces. On these instances, our streaming algorithms used significantly less memory (ranging from 6$\times$ to 512$\times$ less) and were faster in runtime than the offline algorithms. Our solutions were often within 5% of the best weights from the offline algorithms. We highlight that the existing offline algorithms run out of 1 TB memory for most of the large instances ($>1$ billion edges), whereas our streaming algorithms can solve these problems using only 100 GB memory for $k=8$.

A coloring of a graph is an assignment of colors to vertices such that no two neighboring vertices have the same color. The need for memory-efficient coloring algorithms is motivated by their application in computing clique partitions of graphs arising in quantum computations where the objective is to map a large set of Pauli strings into a compact set of unitaries. We present Picasso, a randomized memory-efficient iterative parallel graph coloring algorithm with theoretical sublinear space guarantees under practical assumptions. The parameters of our algorithm provide a trade-off between coloring quality and resource consumption. To assist the user, we also propose a machine learning model to predict the coloring algorithm’s parameters considering these trade-offs. We provide a sequential and parallel implementation of the proposed algorithm.We perform an experimental evaluation on a 64-core AMD CPU equipped with 512 GB of memory and an Nvidia A100 GPU with 40GB of memory. For a small dataset where existing coloring algorithms can be executed within the 512 GB memory budget, we show up to 68× memory savings. On massive datasets, we demonstrate that GPU-accelerated Picasso can process inputs with 49.5× more Pauli strings (vertex set in our graph) and 2,478× more edges than state-of-the-art parallel approaches.

We propose AGS-GNN, a novel attribute-guided sampling algorithm for Graph Neural Networks (GNNs). AGS-GNN exploits the node features and the connectivity structure of a graph while simultaneously adapting for both homophily and heterophily in graphs. In homophilic graphs, vertices of the same class are more likely to be adjacent, but vertices of different classes tend to be adjacent in heterophilic graphs. GNNs have been successfully applied to homophilic graphs, but their utility to heterophilic graphs remains challenging. The state-of-the-art GNNs for heterophilic graphs use the full neighborhood of a node instead of sampling it, and hence do not scale to large graphs and are not inductive. We develop dual-channel sampling techniques based on feature-similarity and feature-diversity to select subsets of neighbors for a node that capture adaptive information from homophilic and heterophilic neighborhoods. Currently, AGS-GNN is the only algorithm that explicitly controls homophily in the sampled subgraph through similar and diverse neighborhood samples. For diverse neighborhood sampling, we employ submodularity, a novel contribution in this context. We pre-compute the sampling distribution in parallel, achieving the desired scalability. Using an extensive dataset consisting of 35 small (< 100K nodes) and large (- 100K nodes) homophilic and heterophilic graphs, we demonstrate the superiority of AGS-GNN compared to the state-of-the-art approaches. AGS-GNN achieves test accuracy comparable to the best-performing heterophilic GNNs, even outperforming methods that use the entire graph for node classification. AGS-GNN converges faster than methods that sample neighborhoods randomly, and can be incorporated into existing GNN models that employ node or graph sampling.

Weighted matching identifies a maximal subset of edges in a graph such that these edges do not share any vertices in common with each other. As a prototypical graph problem, matching has numerous applications in science and engineering, such as linear algebra, multi-level graph algorithms, computer vision and machine learning. There is a critical need for efficient matching algorithms. However, there are challenges in developing efficient, parallel graph matching methods on contemporary GPGPU systems, due to common complexities in general graph processing, such as irregular memory access patterns and load imbalances. Furthermore, increasingly massive graph sizes and resultant intermediate data commonly exceeds available GPU memory. Although dense-GPU systems are mainstream and offer accelerated on-node interconnection to enhance data access bandwidth, data dependencies and device synchronization costs in multi-GPU enabled massive-graph processing create challenges to sustainable scalability.Considering these challenges, we present efficient approximation algorithms for locally dominant matching, and we demonstrate scalability via batching and distributing graph data across multiple NVIDIA A100/V100 GPUs of NVIDIA DGX dense-GPU platforms. Our locally dominant (pointer-based) matching method exhibits 2–45× performance improvements compared to state-of-the-art single-GPU and multithreaded CPU matching implementations on a variety of real-world and synthetic graphs. We show competitive quality comparisons and detailed analysis of GPU-data distribution considerations for practical and efficient weighted graph matching on GPUs.

Graph algorithms with polynomial space and time requirements often become infeasible for massive graphs with billions of edges or more. State-of-the-art approaches therefore employ approximate serial, parallel, and distributed algorithms to tackle these challenges. However, such approaches require storing the entire graph in memory and thus need access to costly computing resources such as clusters and supercomputers. In this paper, we present practical streaming approaches for solving massive graph problems using limited memory for two prototypical graph problems: maximum weighted matching and minimum weighted edge cover. For matching, we conduct a thorough computational study on two of the semi-streaming algorithms including a recent breakthrough result that achieves a 1/(2+ε)-approximation of the weight while using O(n log W /ε) memory (here n is the number of vertices and W is the maximum edge weight), designed by Paz and Schwartzman [SODA, 2017]. Empirically, we show that the semi-streaming algorithms produce matchings whose weight is close to the best 1/2-approximate offline algorithm while requiring less time and an order-of-magnitude less memory. For minimum weighted edge cover, we develop three novel semi-streaming algorithms. Two of these algorithms require a single pass through the input graph, require O(n log n) memory, and provide a 2-approximation guarantee on the objective. We also leverage a relationship between approximate maximum weighted matching and approximate minimum weighted edge cover to develop a two-pass 3/2+ε-approximate algorithm with the memory requirement of Paz and Schwartzman’s semi-streaming matching algorithm. These streaming approaches are compared against the state-of-the-art 3/2-approximate offline algorithm. The semi-streaming matching and the novel edge cover algorithms proposed in this paper can process graphs with several billions of edges in under 30 minutes using 6 GB of memory, which is at least an order of magnitude improvement from the offline (non-streaming) algorithms. For the largest graph, the best alternative offline parallel approximation algorithm (GPA+ROMA) could not finish in three hours even while employing hundreds of processors and 1 TB of memory. We also demonstrate an application of semi-streaming algorithm by computing a matching using linearly bounded memory on intersection graphs derived from three machine learning datasets, while the existing offline algorithms could not complete on one of these datasets since its memory requirement exceeded 1TB.

We describe preliminary results from a multi-objective graph matching algorithm, in the coarsening step of an aggregation-based Algebraic MultiGrid (AMG) preconditioner, for solving large and sparse linear systems of equations on high-end parallel computers. We have two objectives. First, we wish to improve the convergence behavior of the AMG method when applied to highly anisotropic problems. Second, we wish to extend the parallel package PSCToolkit to exploit multi-threaded parallelism at the node level on multi-core processors. Our matching proposal balances the need to simultaneously compute high weights and large cardinalities by a new formulation of the weighted matching problem combining both these objectives using a parameter$\lambda$. We compute the matching by a parallel$2/3-\varepsilon$-approximation algorithm for maximum weight matchings. Results with the new matching algorithm show that for a suitable choice of the parameter$\lambda$we compute effective preconditioners in the presence of anisotropy, i.e., smaller solve times, setup times, iterations counts, and operator complexity.

We describe a paradigm for designing parallel algorithms via approximation, and illustrate it on the b-Edge Cover problem. A b-Edge Cover of minimum weight in a graph is a subset C of its edges such that at least a specified number b(v) of edges in C is incident on each vertex v, and the sum of the edge weights in C is minimum. The Greedy algorithm and a variant, the LSE algorithm, provide 3/2-approximation guarantees in the worst-case for this problem, but these algorithms have limited parallelism. Hence we design two new 2-approximation algorithms with greater concurrency. The MCE algorithm reduces the computation of a b-Edge Cover to that of finding a b'-Matching, by exploiting the relationship between these subgraphs in an approximation context. The LSENW is derived from the LSE algorithm using static edge weights rather than dynamically computing effective edge weights. This relaxation gives S-LSE a worse approximation guarantee but makes it more amenable to parallelization. We prove that both the MCE and S-LSE algorithms compute the same b-EDGE COVER with at most twice the weight of the minimum weight edge cover. In practice, the 2-approximation and 3/2-approximation algorithms compute edge covers of weight within 10% the optimal. We implement three of the approximation algorithms, MCE, LSE, and S-LSE, on shared memory multi-core machines, including an Intel Xeon and an IBM Power8 machine with 8 TB memory. The MCE algorithm is the fastest of these by an order of magnitude or more. It computes an edge cover in a graph with billions of edges in 20 seconds using two hundred threads on the IBM Power8. We also show that the parallel depth and work can be bounded for the Suitor and b-Suitor algorithms when edge weights are random.

Autism is a complex developmental disability that typically appears during the first three years of life. This is the result of a neurological disorder that affects the functioning of human brain. Children diagnosed with autism often are self-absorbed and seem to exist in a private world where they are unable to successfully communicate and interact with others. Sometimes they have difficulties in developing speaking skills and understanding what others say to them. Lack of fluency in the speech is one of the most frequently found problems with autistic children. The traditional methods for increasing fluency were found to be monotonous and hence, not much successful during our three months of observations over the participants of Autism Welfare Foundation (AWF) at Dhaka. Therefore, we developed an interactive computer game for the autistic children for improving the fluency in their speech. Our game produced encouraging results over a participant during three months of observation. In this paper, we describe our project and the outcomes.

Autism is a disorder of neural development which affects about one in every 150 kids on average. One of the major complexities regarding autistic children in social communication is the speech disorder. The problems related to speech disorder fall into different categories and unintelligibility in speech is one of them. Although there is no definite medicine or treatment for autism, doctors, therapists, and special teachers can help kids with autism overcome many difficulties by different physical and psychological therapies. In this paper we have demonstrated our newly developed interactive computer game which will be helpful in increasing intelligibility in the speeches of autistic children and can be used as a therapy besides the traditional approaches. During our five months of intervention with the autistic children of Autism Welfare Foundation (AWF) at Dhaka, we checked the effectiveness of this therapy and got some encouraging results.