تقرير
On the Correlation Gap of Matroids
| العنوان: | On the Correlation Gap of Matroids |
|---|---|
| المؤلفون: | Husić, Edin, Koh, Zhuan Khye, Loho, Georg, Végh, László A. |
| سنة النشر: | 2022 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Computer Science - Data Structures and Algorithms, Computer Science - Computer Science and Game Theory |
| الوصف: | A set function can be extended to the unit cube in various ways; the correlation gap measures the ratio between two natural extensions. This quantity has been identified as the performance guarantee in a range of approximation algorithms and mechanism design settings. It is known that the correlation gap of a monotone submodular function is at least $1-1/e$, and this is tight for simple matroid rank functions. We initiate a fine-grained study of the correlation gap of matroid rank functions. In particular, we present an improved lower bound on the correlation gap as parametrized by the rank and girth of the matroid. We also show that for any matroid, the correlation gap of its weighted matroid rank function is minimized under uniform weights. Such improved lower bounds have direct applications for submodular maximization under matroid constraints, mechanism design, and contention resolution schemes. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2209.09896 |
| رقم الأكسشن: | edsarx.2209.09896 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |