用于贪心图着色的退化引导列表压缩
Degeneracy-Guided List Compression for Greedy Graph Coloring
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中文总结 AI 辅助
研究在颜色采样前利用图结构进行贪心图着色的退化引导列表压缩。提出曝光校准排序框架及其实例P-SAPST，刻画历史鲁棒贪心恢复下所需局部预算，给出理论描述并评估，该方法能降低列表大小、提高贪心成功率，还介绍了P-SAPST Lite及性能表现。
中文摘要 AI 辅助
我们研究在颜色采样之前图结构可用时，用于贪心图着色的退化引导列表压缩。我们的曝光校准排序框架根据每个顶点在颜色独立顺序中的反向邻域为其分配一个独立的均匀列表。其经过认证的实例，即剖析结构感知非对称调色板稀疏化（Profiled Structure Aware Asymmetric Palette Sparsification，简称P-SAPST），反转最小度移除序列，并从移除剖析中获得每个反向曝光。对于每个固定剖析，我们刻画了历史鲁棒贪心恢复下独立均匀列表所需的精确局部预算。该剖析在高度森林和一个核心边缘族上产生线性列表体积，在该核心边缘族上，倒数秩分配需要Θ(n log^2 n)个采样颜色。精确的冲突期望、集中度和密集曝光障碍完成了理论描述。评估包含在SAPBench和两个SNAP网络上的40320次运行。在定理规模上，相对于校准后的APST，P-SAPST将平均列表大小减少了47.6%，同时实现了99.8%的观察到的贪心成功率。P-SAPST Lite用度顺序代替剥皮，并在同一框架内提供了一个低延迟顺序选择。在具有250000个顶点和多达1251868条边的压力图上，Lite获得的有效载荷率为0.865，而校准后的APST为7.886。在电子邮件Enron上，相应的比率分别为0.193和5.814。压缩在中心主导和幂律图上最强，在密集曝光障碍附近消失。该方法通过处理可以重用结构计划的离线模式，对边缘 oblivious 流APST进行了补充。
英文摘要
We study degeneracy guided list compression for greedy graph coloring when graph structure is available before colors are sampled. Our exposure calibrated ordering framework assigns each vertex an independent uniform list according to its backward neighborhood in a color independent order. Its certified instantiation, Profiled Structure Aware Asymmetric Palette Sparsification, or P-SAPST, reverses a minimum degree removal sequence and obtains every backward exposure from the removal profile. For each fixed profile, we characterize the exact local budget required by independent uniform lists under history robust greedy recovery. The profile yields linear list volume on high degree forests and on a core fringe family where reciprocal rank allocation requires Theta(n log^2 n) sampled colors. Exact conflict expectation, concentration, and a dense exposure barrier complete the theoretical description. The evaluation contains 40,320 runs over SAPBench and two SNAP networks. At the theorem scale, P-SAPST reduces mean list size by 47.6 percent relative to calibrated APST while attaining 99.8 percent observed greedy success. P-SAPST Lite replaces peeling with a degree order and provides a lower latency order choice within the same framework. On stress graphs with 250,000 vertices and up to 1,251,868 edges, Lite obtains a payload ratio of 0.865, while calibrated APST obtains 7.886. On email Enron, the corresponding ratios are 0.193 and 5.814. Compression is strongest on hub dominated and power law graphs and disappears near the dense exposure barrier. The method complements edge oblivious streaming APST by addressing an offline regime in which structural plans can be reused.
