We study the problem of maximizing a non-negative monotone k-submodular function f under knapsack constraint, where is natural generalization submodular to k dimensions. present deterministic (12?12e)-approximation algorithm that evaluates O(n4k3) times, based on result Sviridenko (2004) maximization.

Revenue maximization (RM) is one of the most important problems on online social networks (OSNs), which attempts to find a small subset users in OSNs that makes expected revenue maximized. It has been researched intensively before. However, exsiting literatures were based non-adaptive seeding strategy and simple information diffusion model, such as IC/LT-model. considered single influenced user...

We study two mixed robust/average-case submodular partitioning problems that we collectively call Submodular Partitioning. These problems generalize both purely robust instances of the problem (namely max-min submodular fair allocation (SFA) Golovin (2005) and min-max submodular load balancing (SLB) Svitkina and Fleischer (2008)) and also generalize average-case instances (that is the submodula...

Let (L;⊓,⊔) be a finite lattice and let n be a positive integer. A function f : L → R is said to be submodular if f(a ⊓ b) + f(a ⊔ b) ≤ f(a)+f(b) for all a, b ∈ L. In this paper we study submodular functions when L is a diamond. Given oracle access to f we are interested in finding x ∈ L such that f(x) = miny∈Ln f(y) as efficiently as possible. We establish • a min–max theorem, which states tha...

Empirical risk minimization frequently employs convex surrogates to underlying discrete loss functions in order to achieve computational tractability during optimization. However, classical convex surrogates can only tightly bound modular loss functions, submodular functions or supermodular functions separately while maintaining polynomial time computation. In this work, a novel generic convex ...

Motivation: Submodular optimization, a discrete analogue to continuous convex optimization, has been used with great success in many fields but is not yet widely used in biology. We apply submodular optimization to the problem of removing redundancy in protein sequence data sets. This is a common step in many bioinformatics and structural biology workflows, including creation of non-redundant t...

Many combinatorial optimization problems have underlying goal functions that are submodular. The classical goal is to find a good solution for a given submodular function f under a given set of constraints. In this paper, we investigate the runtime of a simple single objective evolutionary algorithm called (1 + 1) EA and a multiobjective evolutionary algorithm called GSEMO until they have obtai...

Given a finite ground set N and a value vector a ∈ R , we consider optimization problems involving maximization of a submodular set utility function of the form h(S) = f (∑ i∈S ai ) , S ⊆ N , where f is a strictly concave, increasing, differentiable function. This function appears frequently in combinatorial optimization problems when modeling risk aversion and decreasing marginal preferences, ...

Submodular functions are well-studied in combinatorial optimization, game theory and economics. The natural diminishing returns property makes them suitable for many applications. We study an extension of monotone submodular functions, which we call proportionally submodular functions. Our extension includes some (mildly) supermodular functions. We show that several natural functions belong to ...

We investigate the systematic mechanism for designing fast mixing Markov chain Monte Carlo algorithms to sample from discrete point processes under the Dobrushin uniqueness condition for Gibbs measures. Discrete point processes are defined as probability distributions μ(S) ∝ exp(βf(S)) over all subsets S ∈ 2 of a finite set V through a bounded set function f : 2 → R and a parameter β > 0. A sub...