الملخص
We study the offline gap between deterministic calibration distance C and its fractional relaxation L for binary unit-weight sequences under total absolute-change cost. We sharpen the offline comparison C <= L + O(sqrt(T)) (Qiao and Zheng, 2024, Theorem 2) to the sharp worst-case order Theta(T^(1/3)). If Delta_T is the supremum of C - L over length-T inputs, then T^(1/3)/1000 <= Delta_T <= 41T^(1/3) for T >= 216. The upper bound holds for every input, while each T >= 216 has a rational lower-bound input. For every input with m distinct forecasts, C <= L + m, and the unrestricted-sample worst-case sparse order is Theta(m). For rational forecasts and accuracy, with binary-encoded multiplicities of separately assignable unit identities, a grid-free polynomial-bit-time procedure returns B <= L <= U, U - B < eta, and an exactly calibrated compact repair of cost at most U + m <= L + m + eta.
الكلمات المفتاحية
الموضوع
بيانات النشر
- المجلة
- غير متاح
- وصول مفتوح
- وصول مفتوح أخضر
اقتبس هذه المقالة
APA 7
Wang, Z., & Yang, X. (2026). Sharp Integrality Gaps in Calibration Distance. https://omanscience.com/ar/articles/sharp-integrality-gaps-in-calibration-distance
MLA 9
Wang, Zinan, and Xinhao Yang. "Sharp Integrality Gaps in Calibration Distance." https://omanscience.com/ar/articles/sharp-integrality-gaps-in-calibration-distance.
شيكاغو (المؤلف–التاريخ)
Wang, Zinan, and Xinhao Yang. 2026. "Sharp Integrality Gaps in Calibration Distance." https://omanscience.com/ar/articles/sharp-integrality-gaps-in-calibration-distance.
هارفارد
Wang, Z. and Yang, X. (2026) 'Sharp Integrality Gaps in Calibration Distance', Available at: https://omanscience.com/ar/articles/sharp-integrality-gaps-in-calibration-distance.
فانكوفر
Wang Z, Yang X. Sharp Integrality Gaps in Calibration Distance. https://omanscience.com/ar/articles/sharp-integrality-gaps-in-calibration-distance
IEEE
Z. Wang, and X. Yang, "Sharp Integrality Gaps in Calibration Distance," https://omanscience.com/ar/articles/sharp-integrality-gaps-in-calibration-distance.