Minimizing a submodular function arising from a concave function
نویسندگان
چکیده
منابع مشابه
Minimizing a Submodular Function from Samples
In this paper we consider the problem of minimizing a submodular function from training data. Submodular functions can be efficiently minimized and are consequently heavily applied in machine learning. There are many cases, however, in which we do not know the function we aim to optimize, but rather have access to training data that is used to learn it. In this paper we consider the question of...
متن کاملMinimizing a Monotone Concave Function with Laminar Covering Constraints
Let V be a finite set with |V | = n. A family F ⊆ 2 is called laminar if for all two sets X, Y ∈ F , X ∩ Y 6= ∅ implies X ⊆ Y or X ⊇ Y . Given a laminar family F , a demand function d : F → R+, and a monotone concave cost function F : RV+ → R+, we consider the problem of finding a minimum-cost x ∈ RV+ such that x(X) ≥ d(X) for all X ∈ F . Here we do not assume that the cost function F is differ...
متن کاملMaximizing a Submodular Set Function
Let f : 2 → R be a non-decreasing submodular set function, and let (N, I) be a matroid. We consider the problem maxS∈I f(S). It is known that the greedy algorithm yields a 1/2-approximation [9] for this problem. It is also known, via a reduction from the max-k-cover problem, that there is no (1− 1/e+ )-approximation for any constant > 0, unless P = NP [6]. In this paper, we improve the 1/2-appr...
متن کاملMinimizing a General Penalty Function on a Single Machine via Developing Approximation Algorithms and FPTASs
This paper addresses the Tardy/Lost penalty minimization on a single machine. According to this penalty criterion, if the tardiness of a job exceeds a predefined value, the job will be lost and penalized by a fixed value. Besides its application in real world problems, Tardy/Lost measure is a general form for popular objective functions like weighted tardiness, late work and tardiness with reje...
متن کاملSFO: A Toolbox for Submodular Function Optimization
In recent years, a fundamental problem structure has emerged as very useful in a variety of machine learning applications: Submodularity is an intuitive diminishing returns property, stating that adding an element to a smaller set helps more than adding it to a larger set. Similarly to convexity, submodularity allows one to efficiently find provably (near-) optimal solutions for large problems....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1999
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(99)00051-7