Simplicial partitions are a fundamental structure in computational geometry, as they form the basis of optimal data structures for range searching and several related problems. Current algorithms are built on very specific spatial partitioning tools tailored for certain geometric cases. This severely limits their applicability to general set systems. In this work, we propose a simple greedy heuristic for constructing simplicial partitions of any set system. We present a thorough empirical evaluation of its behavior on a variety of geometric and non-geometric set systems, showing that it performs well on most instances.

NET4EXA aims to develop a next-generation high-performance interconnect for HPC and AI systems, addressing the increasing demands of large-scale infrastructures, such as those required for training Large Language Models. Building upon the proven BXI (Bull eXascale Interconnect) European technology used in TOP15 supercomputers, NET4EXA will deliver the new BXI release, BXIv3, a complete hardware and software interconnect solution, including switch and network interface components. The project will integrate a fully functional pilot system at TRL 8, ready for deployment into upcoming exascale and post-exascale systems from 2025 onward. Leveraging prior research from European initiatives like RED-SEA, the previous achievements of consortium partners and over 20 years of expertise from BULL, NET4EXA also lays the groundwork for the future generation of BXI, BXIv4, providing analysis and preliminary design. The project will use a hybrid development and co-design approach, combining commercial switch technology with custom IP and FPGA-based NICs. Performances of NET4EXA BXIv3 interconnect will be evaluated using a broad portfolio of benchmarks, scientific scalable applications, and AI workloads.

We study spanners in planar domains, including polygonal domains, polyhedral terrain, and planar metrics. Previous work showed that for any constant ε ∈ (0,1), one could construct a (2 + ε )-spanner with O (n log(n )) edges (SICOMP 2019), and there is a lower bound of Ω(n2) edges for any (2 — ε )-spanner (SoCG 2015). The main open question is whether a linear number of edges suffices and the stretch can be reduced to 2. We resolve this problem by showing that for stretch 2, one needs Ω(n log n ) edges, and for stretch 2 + ε for any fixed ε ∈ (0,1), O (n ) edges are sufficient. Our lower bound is the first super-linear lower bound for stretch 2.