Minimizing a monotone concave function with laminar covering constraints
نویسندگان
چکیده
منابع مشابه
Minimizing 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 کاملMonotone Covering Problems with an Additional Covering Constraint
We provide preliminary results regarding the existence of a polynomial time approximation scheme (PTAS) for minimizing a linear function over a 0/1 covering polytope which is integral, with one additional covering constraint. Our algorithm is based on extending the methods of Goemans and Ravi for the constrained minimum spanning tree problem and, in particular, implies the existence of a PTAS f...
متن کاملMonotone k-Submodular Function Maximization with Size Constraints
A k-submodular function is a generalization of a submodular function, where the input consists of k disjoint subsets, instead of a single subset, of the domain. Many machine learning problems, including influence maximization with k kinds of topics and sensor placement with k kinds of sensors, can be naturally modeled as the problem of maximizing monotone k-submodular functions. In this paper, ...
متن کاملCovering a Simple Polygon by Monotone Directions
In this paper we study the problem of finding a set of k directions for a given simple polygon P , such that for each point p ∈ P there is at least one direction in which the line through p intersects the polygon only once. For k = 1, this is the classical problem of finding directions in which the polygon is monotone, and all such directions can be found in linear time for a simple n-gon. For ...
متن کاملCovering symmetric semi-monotone functions
We define a new set of functions called semi-monotone, a subclass of skew-supermodular functions. We show that the problem of augmenting a given graph to cover a symmetric semi-monotone function is NP-complete if all the values of the function are in {0, 1} and we provide a minimax theorem if all the values of the function are different from 1. Our problem is equivalent to the node to area augm...
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: 2008
ISSN: 0166-218X
DOI: 10.1016/j.dam.2007.04.016