In this paper, we consider the problem of maximizing a monotone submodular function subject to a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access only to a small fraction of the data stored in primary memory. For this problem, we propose a (0.363− ε)-approximation algorithm, requiring only a single p...

For the spherical model with nearest-neighbour interactions, the microcanonical entropy s(ε,m) is computed analytically in the thermodynamic limit for all accessible values of the energy ε and the magnetization m per spin. The entropy is found to be a concave function, implying that the microcanonical and the canonical ensemble are equivalent, despite the long-range nature of the spherical cons...

This paper presents a filter-based artificial fish swarm algorithm for solving nonconvex constrained global optimization problems. Convergence to an ε-global minimizer is guaranteed. At each iteration k, the algorithm requires a (ρ(k),ε(k))-global minimizer of a bound constrained bi-objective subproblem, where as k→ ∞, ρ(k)→ 0 gives the constraint violation tolerance and ε(k)→ ε is the error bo...

We consider the rooted orienteering problem: Given a set P of n points in the plane, a starting point r ∈ P , and a length constraint B, one needs to find a path starting from r that visits as many points of P as possible and of length not exceeding B. We present a (1 − ε)-approximation algorithm for this problem that runs in nO(1/ε) time; the computed path visits at least (1 − ε)kopt points of...

We propose a novel idea of regression – balancing the distances from a regression function to all examples. We created a method, called balanced support vector regression (balanced SVR) in which we incorporated this idea to support vector regression (SVR) by adding an equality constraint to the SVR optimization problem. We implemented our method for two versions of SVR: ε-insensitive support ve...

In this paper, we improve a result by Arora, Khot, Kolla, Steurer, Tulsiani, and Vishnoi on solving the Unique Games problem on expanders. Given a (1−ε)-satisfiable instance of Unique Games with the constraint graph G, our algorithm finds an assignment satisfying at least a 1 − Cε/hG fraction of all constraints if ε < cλG where hG is the edge expansion of G, λG is the second smallest eigenvalue...

We consider an optimization problem of minimization of a linear function subject to the chance constraint Prob{G(x, ξ) ∈ C} ≥ 1 − ε, where C is a convex set, G(x, ξ) is bi-affine mapping and ξ is a vector of random perturbations with known distribution. When C is multi-dimensional and ε is small, like 10−6 or 10−10, this problem is, generically, a problem of minimizing under a nonconvex and dif...

We consider the questions of efficient mixing and un-mixing by incompressible flows which satisfy periodic, no-flow, or no-slip boundary conditions on a square. Under the uniform-in-time constraint ‖∇u(·, t)‖p ≤ 1 we show that any function can be mixed to scale ε in time O(| log ε|1+νp), with νp = 0 for p < 3+ √ 5 2 and νp ≤ 13 for p ≥ 3+ √ 5 2 . Known lower bounds show that this rate is optima...

We present approximation algorithms for balanced partitioning problems. These problems are notoriously hard and we present new bicriteria approximation algorithms, that approximate the optimal cost and relax the balance constraint. In the first scenario, we consider Min-Max k-Partitioning, the problem of dividing a graph into k equal-sized parts while minimizing the maximum cost of edges cut by...