arXiv subjects

Henning Woydt

Publications and source records attributed to Henning Woydt.

3 recordsLinked to original sources

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↗

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

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↗