Research map / Learning theory and algorithms / Combinatorial and search optimization
Metric Nearness Made Practical
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's title only (no summary yet). Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the two-stage embedding-calibration and HLWB projection approach instead of existing solvers and repair algorithms | Metric nearness · 12-hour limit | largest solved problem size: HLWB: > 10,000; PAF: ∼3,000; TRF: < 2,000; DeepNorm: < 1,500; CPLEX and MOSEK: < 300 | Helped |
| Use HLWB instead of TRF or PAF | Metric nearness · MNIST, n = 1,500, ζ = 0.8, 50 iterations | running time: around 1, 700 seconds; around 1, 600 seconds; around 50 seconds | Helped |
| Use HLWB instead of TRF or PAF | Metric nearness · MNIST, n = 1,500 | memory consumption: less than 0.1GB; more than 3GB | Helped |
| Use HLWB instead of PAF | Metric nearness · MNIST, n = 10,000 | memory consumption: around 30GB; around 3GB | Helped |
| Use HLWB instead of TRF or PAF | Metric nearness · MNIST and Graph-t1/Graph-t2, n = 100 to 1,500 | constraints satisfaction ratio (CSR): 0.970 to 0.999 -> CSR = 1.0 | Helped |
| Use HLWB instead of TRF or PAF | Metric nearness · MNIST and Graph-t1/Graph-t2, n = 100 to 1,500 | normalized mean squared error (NMSE): optimization objective differences less than 10^-4 | No clear effect |
| Use the HLWB update procedure, which initializes from embedding calibration and heuristic improvement | Metric nearness · MNIST, n = 1,500, ζ = 0.8, 50 iterations | matrix-entry updates: TRF: 2.53×10^11; PAF: 3.0 × 10^8; HLWB: 1.77 × 10^9 | Mixed |
Closest papers by meaning
- MetricEmbedding: Accelerate Metric Nearness by Tropical Inner Product (ICML 2025 · similarity 0.90)
- Magnitude Distance: A Geometric Measure of Dataset Similarity (ICML 2026 · similarity 0.85)
- Approximating Metric Magnitude of Point Sets (AAAI 2025 · similarity 0.84)
- Metric Space Magnitude for Evaluating the Diversity of Latent Representations (NeurIPS 2024 · similarity 0.84)
- Learning Distances from Data with Normalizing Flows and Score Matching (ICML 2025 · similarity 0.84)
- Sample-Efficient Geometry Reconstruction from Euclidean Distances using Non-Convex Optimization (NeurIPS 2024 · similarity 0.83)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.