Covering symmetric semi-monotone functions
نویسندگان
چکیده
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 augmentation problem. Our contribution is to provide a significantly simpler and shorter proof.
منابع مشابه
Fitzpatrick Functions and Continuous Linear Monotone Operators
The notion of a maximal monotone operator is crucial in optimization as it captures both the subdifferential operator of a convex, lower semicontinuous, and proper function and any (not necessarily symmetric) continuous linear positive operator. It was recently discovered that most fundamental results on maximal monotone operators allow simpler proofs utilizing Fitzpatrick functions. In this pa...
متن کاملCones of material response functions in 1D and anisotropic linear viscoelasticity
Viscoelastic materials have non-negative relaxation spectra. This property implies that viscoelastic response functions satisfy certain necessary and sufficient conditions. It is shown that these conditions can be expressed in terms of each viscoelastic response function ranging over a cone. The elements of each cone are completely characterized by an integral representation. The 1:1 correspond...
متن کاملLearning symmetric non-monotone submodular functions
We prove a new structural result for symmetric submodular functions. We use that result to obtain an efficient algorithm for approximately learning such functions in the passive, supervised learning setting. We also complement this result with a nearly matching lower bound. Our work provides the first results for learning a large class of non-monotone submodular functions under general distribu...
متن کاملOn limit cycles of monotone functions with symmetric connection graph
We study the length of the limit cycles of discrete monotone functions with symmetric connection graph. We construct a family of monotone functions such that the limit cycles are of maximum possible length, which is exponential in the number of variables. Furthermore, we prove for the class of monotone functions with more than two states and connection graph equal to a caterpillar that the leng...
متن کاملMonotonicity of Löwner operators and its applications to symmetric cone complementarity problems
We prove necessary and sufficient conditions for locally Lipschitz Löwner operators to be monotone, strictly monotone and strongly monotone. Utilizing our characterization of the strict monotonicity of Löwner operators, we generalize Mangasarian class of Nonlinear Complementarity Problem (NCP)-functions to the setting of symmetric cone complementarity problem. This affirmatively answers a quest...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Applied Mathematics
دوره 156 شماره
صفحات -
تاریخ انتشار 2008