Marco Ronzani

Marco Ronzani, Cristina Silvano

Hypergraph partitioning is a recurring NP-hard problem in engineering; its efficient solution at scale hinges on parallelism. This work proposes a GPU-centric algorithm for multi-level hypergraph partitioning aimed at a specific set of problem constraints: limited size and distinct inbound hyperedges per partition. Manipulating hypergraphs requires deeply nested traversals and concurrent decision-making; our constraints impose further set operations amidst that. In turn, we design algorithms around the GPU's hierarchical parallelism and our problem's specifics. When forming partitions, we materialize the hypergraph's incidence structure and unique neighborhoods in memory to exploit set sparsity and batch node-pairing scores in shared memory. Upon refining partitions, we chain node moves into improving paths and cycles, checking their validity via cumulative set size variations reduced in parallel over moves. Thus, our dominant kernels exhibit a span linear in local hypergraph parameters. Results show an average 380x speedup and a 1.2-2.0x reduction in connectivity compared to a sequential multi-level partitioner. With minor changes, we also support k-way balanced partitioning, running 5x faster than CPU methods with a ~5% quality loss for k=2, outperforming an existing GPU partitioner at comparable runtime, with no measurable overhead from the added constraints handling logic.

Marco Ronzani, Cristina Silvano

Executing Spiking Neural Networks (SNNs) on neuromorphic hardware poses the problem of mapping neurons to cores. SNNs operate by propagating spikes between neurons that form a graph through synapses. Neuromorphic hardware mimics them through a network-on-chip, transmitting spikes, and a mesh of cores, each managing several neurons. Its operational cost is tied to spike movement and active cores. A mapping comprises two tasks: partitioning the SNN's graph to fit inside cores and placement of each partition on the hardware mesh. Both are NP-hard problems, and as SNNs and hardware scale towards billions of neurons, they become increasingly difficult to tackle effectively. In this work, we propose to raise the abstraction of SNNs from graphs to hypergraphs, redesigning mapping techniques accordingly. The resulting model faithfully captures the replication of spikes inside cores by exposing the notion of hyperedge co-membership between neurons. We further show that the overlap and locality of hyperedges strongly correlate with high-quality mappings, making these properties instrumental in devising mapping algorithms. By exploiting them directly, grouping neurons through shared hyperedges, communication traffic and hardware resource usage can be reduced be yond what just contracting individual connections attains. To substantiate this insight, we consider several partitioning and placement algorithms, some newly devised, others adapted from literature, and compare them over progressively larger and bio-plausible SNNs. Our results show that hypergraph based techniques can achieve better mappings than the state-of-the-art at several execution time regimes. Based on these observations, we identify a promising selection of algorithms to achieve effective mappings at any scale.

Marco Ronzani, Cristina Silvano

Hypergraph partitioning is a pervasive NP-hard problem, and accelerating its computation on GPU can both slice time-to-solution and raise quality of results. In this work, we implement a multi-level hypergraph partitioning algorithm on GPU targeting a specific set of problem constraints: bounded per-partition size and distinct inbound hyperedges. Manipulating hypergraphs requires long orders of nested iterations, and enforcing these constraints introduces further set operations amidst them. Hence, we design algorithms around our problem's specifics, materializing the hypergraph's incidence structure in memory and exploiting set sparsity. Our results show competitive speedups as high as 940x and 2-26% better results in connectivity over a sequential multi-level partitioner.