1. Monotone Nonsubmodular Maximization
Supermodular Degree

2. k-Extendible System

3. Independent System
Consider a finite set V and a collection of subsets of V. (V, ) is called an independent system if
i.e., it is hereditary.
Each subset in is called an independent set.

4. Matroid

5. k-extendible

7. k-intersection

8. Lemma 1

9. Supermodular Degree
M. Feldman and R. Izsak, “Constrained monotone function maximiza-
tion and the supermodular degree,” in ACM-SIAM SODA, 2014.

10. Definition

11. Monotone Function Max

12. Greedy Approximation
Theorem 1

13. Proof

16. Monotone Function Max

17. Greedy Approximation
Theorem 1

18. Proof
Monotone!

21. Applications
Uriel Feige and Rani Izsak. Welfare maximization and the supermodular
degree. In ITCS, pages 247–256, 2013.
Rani Izsak: Working Together: Committee Selection and the Supermodular
Degree. AAMAS 2017:
Moran Feldman, Rani Izsak: Building a Good Team: Secretary Problems
and the Supermodular Degree. SODA 2017:

22. Submodularity Ratio and Curvature
Andrew An Bian, Joachim M. Buhmann, Andreas Krause,Sebastian Tschiatschek:
Guarantees for Greedy Maximization of Non-submodular Functions with Applications,
arXiv: v3 [cs.DM] 13 June 2017

23. Submodularity Ratio

24. Curvature

25. Greedy
Theorem

26. Thank You, end