Deterministic Parallel High-Quality Hypergraph Partitioning

TL;DR

The paper tackles deterministic parallel hypergraph partitioning, aiming to achieve the high solution quality of non-deterministic state-of-the-art methods while ensuring reproducibility. It introduces two deterministic solvers, DetJet and DetFlows, by generalizing Jet refinement to hypergraphs with a fast afterburner and a new deterministic rebalancing, and by building a deterministic flow-based refinement atop a fast non-deterministic max-flow procedure. The results show DetJet matching or surpassing Mt-KaHyPar-Default quality at a modest slowdown, while DetFlows provides a small quality uplift at a noticeably higher runtime, with strong scaling up to 64 cores. The paper also delivers improvements to deterministic coarsening and presents a thorough experimental evaluation across diverse benchmarks, establishing deterministic parallel partitioning as a competitive alternative with reproducible performance—crucial for applications like VLSI design.

Abstract

We present a deterministic parallel multilevel algorithm for balanced hypergraph partitioning that matches the state of the art for non-deterministic algorithms. Deterministic parallel algorithms produce the same result in each invocation, which is crucial for reproducibility. Moreover, determinism is highly desirable in application areas such as VLSI design. While there has been tremendous progress in parallel hypergraph partitioning algorithms recently, deterministic counterparts for high-quality local search techniques are missing. Consequently, solution quality is severely lacking in comparison to the non-deterministic algorithms. In this work we close this gap. First, we present a generalization of the recently proposed Jet refinement algorithm. While Jet is naturally amenable to determinism, significant changes are necessary to achieve competitive performance on hypergraphs. We also propose an improved deterministic rebalancing algorithm for Jet. Moreover, we consider the powerful but slower flow-based refinement and introduce a scheme that enables deterministic results while building upon a non-deterministic maximum flow algorithm. As demonstrated in our thorough experimental evaluation, this results in the first deterministic parallel partitioner that is competitive to the highest quality solvers. With Jet refinement, we match or exceed the quality of Mt-KaHyPar's non-deterministic default configuration while being only 15\% slower on average. We observe self-relative speedups of up to 55 on 64 cores with a 22.5$\times$ average speedup. Our deterministic flow-based refinement exceeds the quality of the non-deterministic variant by roughly 1\% on average but requires 31\% more running time.

Figures (13)

• Figure 1: The quality gap between non-deterministic solvers (Mt-KaHyPar-{Default, Flows}) and deterministic solvers (BiPart, Mt-KaHyPar-SDet). Higher and to the left is better. Refer to Section \ref{['sec:exp-setup']} for details on the plot.
• Figure 2: Venn diagram style visualization of the vertex sets during flow-based refinement. Flow augmentation and computing $S_r, T_r$ on the left. Adding $S_r$ to $S$ and piercing the source-side cut on the right. $S$ in blue, $S_r \setminus S$ in yellow, $T$ in green, $T_r\setminus T$ in red, $V \setminus (S_r \cup T_r)$ in white. Taken from Ref. REBAHFC with minor adaptations.
• Figure 3: Synchronous Coarsening
• Figure 4: Impact of improved coarsening on solution quality, on all instances.
• Figure 5: Comparison of solution quality for different temperature settings for Jet refinement on hypergraphs (left), irregular graphs (center) and regular graphs (right). $\tau_c$ denotes the temperature value used for coarse levels, while $\tau_f$ denotes the value used for the finest level of the input. The dynamic configuration uses three rounds with values between $0.75$ and $0$.