arXiv subjects

Christian Schulz

Publications and source records attributed to Christian Schulz.

At least 19 recordsLinked to original sources

arXiv2026

Agentic Algorithm Engineering: Improving Shared-Memory Exact Minimum Cuts

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 the cut edges. Over the last years, we engineered a range of fast algorithms for this problem. Our fastest exact algorithm uses an inexact algorithm to obtain a better bound for the problem, reductions that depend on this bound, improved data structures and parallel contraction routines. It is available in the open-source package VieCut and, on real-world instances, outperformed the previously fastest solvers by a factor of up to 2.5 sequentially and up to 12.9 when run in parallel. We improve this algorithm using agentic algorithm engineering (AAE), a methodology that we introduce here, in which autonomous large language model agents run the algorithm engineering cycle on an existing code base: they form hypotheses about where running time is lost, implement them, benchmark the result on a fixed instance set and keep or discard the change. Even though we had already tuned our algorithm by hand extensively, the agent finds significant optimizations, in particular on the DIMACS core instances: factors of 1.28 (sequential) and 1.63 (32 threads) on real-world k-cores, and 6.26 and 127 on the DIMACS core instances.

cs.AI↗

arXiv2026

SIGMA: A Versatile Streaming Graph Partitioner for Vertex- and Edge-Balanced Distributed GNN Training

Distributed Graph Neural Network (GNN) training depends critically on how the underlying graph is partitioned across compute resources. Existing graph partitioners focus either on vertex partitioning or edge partitioning and typically optimize only a single communication objective (edge cut or vertex cut) under a single balance constraint (vertex balance or edge balance). We present SIGMA (Streaming Integrated Graph Partitioning with Multi-objective Awareness), a versatile streaming graph partitioner that supports both vertex and edge partitioning within a unified multi-objective, multi-constraint framework. Depending on the target distributed GNN system, SIGMA can be configured for edgecut-oriented vertex partitioning or vertex-cut-oriented edge partitioning while simultaneously accounting for both vertex and edge balancing. A clustering-based preprocessing stage incorporates global graph structure to improve partition quality while preserving the efficiency and scalability advantages of streaming partitioning. We evaluate SIGMA on six benchmark graphs spanning diverse domains and scales using two distributed GNN training systems: Dist-GNN (edge-partitioned) and DistDGL (vertex-partitioned). Across both settings, SIGMA consistently achieves strong performance, showing its ability to navigate complex trade-offs between partition quality, training efficiency, and memory consumption, frequently outperforming streaming baselines while remaining competitive with high-quality in-memory partitioners such as METIS, KaHIP and HEP. These results demonstrate that a unified streaming partitioner can effectively address the communication, compute, and memory challenges of distributed GNN training across fundamentally different system architectures.

cs.DC↗

arXiv2026

Advances in Exact and Approximate Group Closeness Centrality Maximization

In the NP-hard Group Closeness Centrality Maximization problem, the input is a graph $G = (V,E)$ and a positive integer $k$, and the task is to find a set $S \subseteq V$ of size $k$ that minimizes group farness $f(S) = \sum_{v \in V} \min_{s \in S}\text{dist}(v,s)$. The state-of-the-art exact algorithm iteratively solves ILPs of increasing size until the final ILP can provably represent an optimal solution. We introduce a new data reduction technique that eliminates variables from the ILP by proving that certain vertices have their distance to any optimal solution structurally determined by a neighbor. Additionally, we bootstrap the exact solver with an approximate solution to produce near-sufficient ILPs from the first iteration, reducing the number of needed iterations. Our improvements yield a speedup by a factor of $4.5$ over the next best exact algorithm and can achieve speedups by up to a factor of $34.1$. Furthermore, we add reduction techniques to a $1/5$-approximation algorithm, and show that these adaptations do not compromise its approximation guarantee. The improved algorithm achieves mean speedups of up to $1.6$ and a maximum speedup of $9.6$ times. Finally, we settle an open question by proving that a widely used greedy algorithm admits arbitrarily poor approximation ratios.

cs.DS↗

arXiv2026

Efficient Parallel Algorithms for Hypergraph Matching

We present efficient parallel algorithms for computing maximal matchings in hypergraphs. Our algorithm finds locally maximal edges in the hypergraph and adds them in parallel to the matching. In the CRCW PRAM models our algorithms achieve $O(\log{\log{\Delta}}\log{m})$ time with $O(\kappa\log {m})$ work w.h.p. where $m$ is the number of hyperedges, and $\kappa$ is the sum and $\Delta$ is the maximum of all vertex degrees. The CREW PRAM model algorithm has a running time of $O((\log{\Delta}+\log{d})\log{m})$ and requires $O(\kappa \log {m})$ work w.h.p. It can be implemented work-optimal with $O(\kappa)$ work in $O((\log{m}+\log{n})\log{m})$ time. We prove a~$1/d$-approximation guarantee for our algorithms. We evaluate our algorithms experimentally by implementing and running the proposed algorithms on the GPU using CUDA and Kokkos. Our experimental evaluation demonstrates the practical efficiency of our approach on real-world hypergraph instances, yielding a speed up of up to 76 times compared to a single-core CPU algorithm.

cs.DS↗

arXiv2026

BuffCut: Prioritized Buffered Streaming Graph Partitioning

Streaming graph partitioners enable resource-efficient and massively scalable partitioning, but one-pass assignment heuristics are highly sensitive to stream order and often yield substantially higher edge cuts than in-memory methods. We present BuffCut, a buffered streaming partitioner that narrows this quality gap, particularly when stream ordering is adversarial, by combining prioritized buffering with batch-wise multilevel assignment. BuffCut maintains a bounded priority buffer to delay poorly informed decisions and regulate the order in which nodes are considered for assignment. It incrementally constructs high-locality batches of configurable size by iteratively inserting the highest-priority nodes from the buffer into the batch, effectively recovering locality structure from the stream. Each batch is then assigned via a multilevel partitioning algorithm. Experiments on diverse real-world and synthetic graphs show that BuffCut consistently outperforms state-of-the-art buffered streaming methods. Compared to the strongest prioritized buffering baseline, BuffCut achieves 20.8% fewer edge cuts while running 2.9 times faster and using 11.3 times less memory. Against the next-best buffered method, it reduces edge cut by 15.8% with only modest overheads of 1.8 times runtime and 1.09 times memory.

cs.DB↗

arXiv2026

Data Reductions for the Strong Maximum Independent Set Problem in Hypergraphs

This work addresses the well-known Maximum Independent Set problem in the context of hypergraphs. While this problem has been extensively studied on graphs, we focus on its strong extension to hypergraphs, where edges may connect any number of vertices. A set of vertices in a hypergraph is strongly independent if there is at most one vertex per edge in the set. One application for this problem is to find perfect minimal hash functions. We propose nine new data reduction rules specifically designed for this problem. Our reduction routine can serve as a preprocessing step for any solver. We analyze the impact on the size of the reduced instances and the performance of several subsequent solvers when combined with this preprocessing. Our results demonstrate a significant reduction in instance size and improvements in running time for subsequent solvers. The preprocessing routine reduces instances, on average, to 22% of their original size in 6.76 seconds. When combining our reduction preprocessing with the best-performing exact solver, we observe an average speedup of 3.84x over not using the reduction rules. In some cases, we can achieve speedups of up to 53x. Additionally, one more instance becomes solvable by a method when combined with our preprocessing.

cs.DS↗

arXiv2025

Trigonal Distortion Driven Ground States in VX3 (X = Br and I)

Transition-metal halides V$X_3$ ($X$ = Br and I) have emerged as promising candidates for two dimensional spintronic and quantum applications due to their layer-dependent magnetism and tunable electronic states. However, experimental insights into their ground state electronic structures remain limited. Here, we present a comprehensive investigation of V$X_3$ using high resolution resonant inelastic x-ray scattering (RIXS) combined with ligand field multiplet calculations. The RIXS spectra reveal distinct $dd$ and charge-transfer excitations, allowing precise determination of electronic structure parameters, including the crystal field splitting, trigonal distortion, and Racah parameters. The determined parameters showed clear variation, indicating an increase in covalency from Br to I. The trigonal distortion parameters $\Delta_{D_{3d}}$ were determined to be -0.096 eV in VBr$_3$ and 0.07 eV in VI$_3$, indicating a sign opposition between the two compounds, reflecting good agreement with experimental RIXS data. Cluster model calculations yield a high-spin V$^{3+}$ $(S = 1)$ configuration, with an $e'^2_g$ ground state in VBr$_3$ and an $e'^1_ga^1_{1g}$ ground state in VI$_3$, consistent with trigonal elongation and compression, respectively. Our findings provide the most complete experimental determination of the low energy electronic structure in V$X_3$, offering valuable insights for designing 2D magnetic and spintronic materials based on vanadium halides.

cond-mat.mtrl-sci↗

arXiv2025

GPU-Accelerated Algorithms for Process Mapping

Process mapping asks to assign vertices of a task graph to processing elements of a supercomputer such that the computational workload is balanced while the communication cost is minimized. Motivated by the recent success of GPU-based graph partitioners, we propose two GPU-accelerated algorithms for this optimization problem. The first algorithm employs hierarchical multisection, which partitions the task graph alongside the hierarchy of the supercomputer. The method utilizes GPU-based graph partitioners to accelerate the mapping process. The second algorithm integrates process mapping directly into the modern multilevel graph partitioning pipeline. Vital phases like coarsening and refinement are accelerated by exploiting the parallelism of GPUs. The first algorithm has, on average, about 12 percent higher communication costs than the state-of-the-art solver and thus remains competitive with it. However, in terms of speed, it vastly outperforms the competitor with a geometric mean speedup of 22 times and a maximum speedup of 934 times. The second approach is even faster, with a geometric mean speedup of 1454 times and a peak speedup of 12376 times. Compared to other algorithms that prioritize speed over solution quality, this approach has the same quality but much greater speedups. To our knowledge, these are the first GPU-based algorithms for process mapping.

cs.DC↗

arXiv2025

Near-Optimal Minimum Cuts in Hypergraphs at Scale

The hypergraph minimum cut problem aims to partition its vertices into two blocks while minimizing the total weight of the cut hyperedges. This fundamental problem arises in network reliability, VLSI design, and community detection. We present HeiCut, a scalable algorithm for computing near-optimal minimum cuts in both unweighted and weighted hypergraphs. HeiCut aggressively reduces the hypergraph size through a sequence of provably exact reductions that preserve the minimum cut, along with an optional heuristic contraction based on label propagation. It then solves a relaxed Binary Integer Linear Program (BIP) on the reduced hypergraph to compute a near-optimal minimum cut. Our extensive evaluation on over 500 real-world hypergraphs shows that HeiCut computes the exact minimum cut in over 85% of instances using our exact reductions alone, and offers the best solution quality across all instances. It solves over twice as many instances as the state-of-the-art within set computational limits, and is up to five orders of magnitude faster.

cs.DS↗

arXiv2025

From Theory to Practice: Engineering Approximation Algorithms for Dynamic Orientation

Dynamic graph algorithms have seen significant theoretical advancements, but practical evaluations often lag behind. This work bridges the gap between theory and practice by engineering and empirically evaluating recently developed approximation algorithms for dynamically maintaining graph orientations. We comprehensively describe the underlying data structures, including efficient bucketing techniques and round-robin updates. Our implementation has a natural parameter $\lambda$, which allows for a trade-off between algorithmic efficiency and the quality of the solution. In the extensive experimental evaluation, we demonstrate that our implementation offers a considerable speedup. Using different quality metrics, we show that our implementations are very competitive and can outperform previous methods. Overall, our approach solves more instances than other methods while being up to 112 times faster on instances that are solvable by all methods compared.

cs.DS↗

arXiv2025

Electronic Energy Scales of Cr$X_3$ ($X$ = Cl, Br, and I) using High-resolution X-ray Scattering

Chromium tri-halides Cr$X_3$ ($X$ = Cl, Br, and I) have recently become a focal point of research due to their intriguing low-temperature,layer-dependent magnetism that can be manipulated by an electric field. This makes them essential candidates for spintronics applications. These magnetic orders are often related to the electronic structure parameters, such as spin-orbit coupling (SOC), Hund's coupling ($J_H$), $p-d$ covalency, and inter-orbital Coulomb interactions. Accurately determining such parameters is paramount for understanding Cr$X_3$ physics. We have used ultra high-resolution resonant inelastic x-ray scattering (RIXS) spectroscopy to study Cr$X_3$ across phase transition temperatures. Ligand field multiplet calculations were used to determine the electronic structure parameters by incorporating the crystal field interactions in a distorted octahedral with $C_3$ symmetry. These methods provide the most detailed description of Cr$X_3$ magneto-optical and electronic energetic (terms) to date. For the first time, the crystal field distortion parameters $D\sigma$ and $D\tau$ were calculated, and the energies of $d$ orbitals have been reported. Our RIXS spectroscopic measurements reveal a clear energy separation between spin-allowed quartet states and spin-forbidden doublet states in Cr$X_3$. The role of SOC in Cr $2p$ orbitals for the spin-flip excitations has been demonstrated. The determined 10$Dq$ values are in good agreement with the spectrochemical series, and Racah B follows the Nephelauxetic effect. Such precise measurements offer insights into the energy design of spintronic devices that utilize quantum state tuning within 2D magnetic materials.

cond-mat.mtrl-sci↗

arXiv2025

Shared-Memory Hierarchical Process Mapping

Modern large-scale scientific applications consist of thousands to millions of individual tasks. These tasks involve not only computation but also communication with one another. Typically, the communication pattern between tasks is sparse and can be determined in advance. Such applications are executed on supercomputers, which are often organized in a hierarchical hardware topology, consisting of islands, racks, nodes, and processors, where processing elements reside. To ensure efficient workload distribution, tasks must be allocated to processing elements in a way that ensures balanced utilization. However, this approach optimizes only the workload, not the communication cost of the application. It is straightforward to see that placing groups of tasks that frequently exchange large amounts of data on processing elements located near each other is beneficial. The problem of mapping tasks to processing elements considering optimization goals is called process mapping. In this work, we focus on minimizing communication cost while evenly distributing work. We present the first shared-memory algorithm that utilizes hierarchical multisection to partition the communication model across processing elements. Our parallel approach achieves the best solution on 95 percent of instances while also being marginally faster than the next best algorithm. Even in a serial setting, it delivers the best solution quality while also outperforming previous serial algorithms in speed.

cs.DC↗

arXiv2025

Semi-Streaming Algorithms for Hypergraph Matching

We propose two one-pass streaming algorithms for the $\mathcal{NP}$-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 $\frac{1}{d(1+\varepsilon)}$ and requires $\mathcal{O}((\frac{n}{\varepsilon}) \log^2{n})$ bits of memory, where $n$ is the number of vertices in the hypergraph, $d$ is the maximum number of vertices in a hyperedge, and $\epsilon > 0$ 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 $\alpha$. Its best approximation guarantee is $\frac{1}{(2d-1) + 2 \sqrt{d(d-1)}}$, and it requires only $\mathcal{O}(n)$ 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.

cs.DS↗

arXiv2025

Finding Maximum Weight 2-Packing Sets on Arbitrary Graphs

A 2-packing set for an undirected, weighted graph G=(V,E,w) is a subset S of the vertices V such that any two vertices are not adjacent and have no common neighbors. The Maximum Weight 2-Packing Set problem that asks for a 2-packing set of maximum weight is NP-hard. Next to 13 novel data reduction rules for this problem, we develop two new approaches to solve this problem on arbitrary graphs. First, we introduce a preprocessing routine that exploits the close relation of 2-packing sets to independent sets. This makes well-studied independent set solvers usable for the Maximum Weight 2-Packing Set problem. Second, we propose an iterative reduce-and-peel approach that utilizes the new data reductions. Our experiments show that our preprocessing routine gives speedups of multiple orders of magnitude, while also improving solution quality, and memory consumption compared to a naive transformation to independent set instances. Furthermore, it solves 44 % of the instances tested to optimality. Our heuristic can keep up with the best-performing maximum weight independent set solvers combined with our preprocessing routine. Additionally, our heuristic can find the best solution quality on the biggest instances in our data set, outperforming all other approaches.

cs.DS↗

arXiv2025

Self-Normalized Inference in (Quantile, Expected Shortfall) Regressions for Time Series

This paper proposes valid inference tools, based on self-normalization, in time series expected shortfall regressions and, as a corollary, also in quantile regressions. Extant methods for such time series regressions, based on a bootstrap or direct estimation of the long-run variance, are computationally more involved, require the choice of tuning parameters and have serious size distortions when the regression errors are strongly serially dependent. In contrast, our inference tools only require estimates of the (quantile, expected shortfall) regression parameters that are computed on an expanding window, and are correctly sized as we show in simulations. Two empirical applications to stock return predictability and to Growth-at-Risk demonstrate the practical usefulness of the developed inference tools.

econ.EM↗

arXiv2025

CluStRE: Streaming Graph Clustering with Multi-Stage Refinement

We present CluStRE, a novel streaming graph clustering algorithm that balances computational efficiency with high-quality clustering using multi-stage refinement. Unlike traditional in-memory clustering approaches, CluStRE processes graphs in a streaming setting, significantly reducing memory overhead while leveraging re-streaming and evolutionary heuristics to improve solution quality. Our method dynamically constructs a quotient graph, enabling modularity-based optimization while efficiently handling large-scale graphs. We introduce multiple configurations of CluStRE to provide trade-offs between speed, memory consumption, and clustering quality. Experimental evaluations demonstrate that CluStRE improves solution quality by 89.8%, operates 2.6 times faster, and uses less than two-thirds of the memory required by the state-of-the-art streaming clustering algorithm on average. Moreover, our strongest mode enhances solution quality by up to 150% on average. With this, CluStRE achieves comparable solution quality to in-memory algorithms, i.e. over 96% of the quality of clustering approaches, including Louvain, effectively bridging the gap between streaming and traditional clustering methods.

cs.LG↗

arXiv2024

Accelerating Reductions Using Graph Neural Networks and a New Concurrent Local Search for the Maximum Weight Independent Set Problem

The Maximum Weight Independent Set problem is a fundamental NP-hard problem in combinatorial optimization with several real-world applications. Given an undirected vertex-weighted graph, the problem is to find a subset of the vertices with the highest possible weight under the constraint that no two vertices in the set can share an edge. An important part of solving this problem in both theory and practice is data reduction rules, which several state-of-the-art algorithms rely on. However, the most complicated rules are often not used in applications since the time needed to check them exhaustively becomes infeasible. In this work, we introduce three main results. First, we introduce several new data reduction rules and evaluate their effectiveness on real-world data. Second, we use a machine learning screening algorithm to speed up the reduction phase, thereby enabling more complicated rules to be applied. Our screening algorithm consults a Graph Neural Network oracle to decide if the probability of successfully reducing the graph is sufficiently large. For this task, we provide a dataset of labeled vertices for use in supervised learning. We also present the first results for this dataset using established Graph Neural Network architectures. Third, we present a new concurrent metaheuristic called Concurrent Difference-Core Heuristic. On the reduced instances, we use our new metaheuristic combined with iterated local search, called CHILS (Concurrent Hybrid Iterated Local Search). For this iterated local search, we provide a new implementation specifically designed to handle large graphs of varying densities. CHILS outperforms the current state-of-the-art on all commonly used benchmark instances, especially the largest ones.

math.OC↗

arXiv2024

A Comprehensive Survey of Data Reduction Rules for the Maximum Weighted Independent Set Problem

The Maximum Weight Independent Set (MWIS) problem, as well as its related problems such as Minimum Weight Vertex Cover, are fundamental NP-hard problems with numerous practical applications. Due to their computational complexity, a variety of data reduction rules have been proposed in recent years to simplify instances of these problems, enabling exact solvers and heuristics to handle them more effectively. Data reduction rules are polynomial time procedures that can reduce an instance while ensuring that an optimal solution on the reduced instance can be easily extended to an optimal solution for the original instance. Data reduction rules have proven to be especially useful in branch-and-reduce methods, where successful reductions often lead to problem instances that can be solved exactly. This survey provides a comprehensive overview of data reduction rules for the MWIS problem. We also provide a reference implementation for these reductions. This survey will be updated as new reduction techniques are developed, serving as a centralized resource for researchers and practitioners.

cs.DS↗