We study the problem of maximizing a function that is approximately submodular under a cardinality constraint. Approximate submodularity implicitly appears in a wide range of applications as in many cases errors in evaluation of a submodular function break submodularity. Say that F is ε-approximately submodular if there exists a submodular function f such that (1−ε)f(S) ≤ F (S) ≤ (1+ε)f(S) for ...

The reservoir flood control operation problem has the characteristics of multiconstraint, high-dimension, nonlinearity, and being difficult to solve. In order better solve this problem, paper proposes an improved bald eagle search algorithm (CABES) coupled with ε-constraint method (ε-CABES). test performance CABES algorithm, a typical function is used simulate verify CABES. results are compared...

We consider maximizing a monotone submodular function under a cardinality constraint or a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access to only a small fraction of the data stored in primary memory. We propose the following streaming algorithms taking O(ε) passes: 1. a (1 − e − ε)-approximation al...

An instance of the Constraint Satisfaction Problem (CSP) is given by a family of constraints on overlapping sets of variables, and the goal is to assign values from a fixed domain to the variables so that all constraints are satisfied. In the optimization version, the goal is to maximize the number of satisfied constraints. An approximation algorithm for CSP is called robust if it outputs an as...

We give a nonstandard variant of Jordan’s proof of the Jordan curve theorem which is free of the defects his contemporaries criticized and avoids the epsilontic burden of the classical proof. The proof is selfcontained, except for the Jordan theorem for polygons taken for granted.

We study the problem of maximizing a monotone submodular function subject to Multiple Knapsack constraint. The input is set I items, each has non-negative weight, and bins arbitrary capacities. Also, we are given submodular, f over subsets items. objective find packing subset items A⊆I in such that f(A) maximized. Our main result an almost optimal polynomial time (1−e−1−ε)-approximation algorit...

Addressing an integrated decision-making structure for planting and harvesting scheduling may lead to more realistic, accurate, and efficient decision in fresh product supply chain. This study aims to develop an integrated bi-objective tactical and operational planning model for producing and distributing fresh crops. The first objective of the model is to maximize total revenue of supply chain...

The mixed-order eigenvalue problem −δ∆u + ∆u + λu = 0 with δ > 0, modeling small amplitude vibrations of a thin plate, is analyzed in a bounded 2-D domain Ω that contains a single small hole of radius ε centered at some x0 ∈ Ω. Clamped conditions are imposed on the boundary of Ω and on the boundary of the small hole. In the limit ε → 0, and for δ = O(1), the limiting problem for u must satisfy ...

An instance of a constraint satisfaction problem (CSP) is variable k-consistent if any subinstance with at most k variables has a solution. For a fixed constraint language L, ρk(L) is the largest ratio such that any variable k-consistent instance has a solution that satisfies at least a fraction of ρk(L) of the constraints. We provide an expression for the limit ρ(L) := limk→∞ ρk(L), and show t...