相关论文: Maximal Closed Set and Half-Space Separations in F…

We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on…

Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…

We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…

Computing the size of maximum independent sets is a NP-hard problem for fixed graphs. Characterizing and designing efficient algorithms to estimate this independence number for random graphs are notoriously difficult and still largely open…

The seminar assignment problem is a variant of the generalized assignment problem in which items have unit size and the amount of space allowed in each bin is restricted to an arbitrary set of values. The problem has been shown to be…

Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…

In this paper, we propose and study a new semi-random model for graph partitioning problems. We believe that it captures many properties of real--world instances. The model is more flexible than the semi-random model of Feige and Kilian and…

A dominating set D in a graph G is a subset of its vertices such that every vertex of the graph which does not belong to set D is adjacent to at least one vertex from set D. A set of vertices of graph G is a global dominating set if it is a…

We consider linear systems arising from the use of the finite element method for solving scalar linear elliptic problems. Our main result is that these linear systems, which are symmetric and positive semidefinite, are well approximated by…

Sensor placement optimization methods have been studied extensively. They can be applied to a wide range of applications, including surveillance of known environments, optimal locations for 5G towers, and placement of missile defense…

The graph theoretic concept of maximal independent set arises in several practical problems in computer science as well as in game theory. A maximal independent set is defined by the set of occupied nodes that satisfy some packing and…

We propose a way to transform synchronous distributed algorithms solving locally greedy and mendable problems into self-stabilizing algorithms in anonymous networks. Mendable problems are a generalization of greedy problems where any…

The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…

In this paper, we concentrate on generating cutting planes for the unsplittable capacitated network design problem. We use the unsplittable flow arc-set polyhedron of the considered problem as a substructure and generate cutting planes by…

The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range…

A common technique for checking properties of complex state machines is to build a finite abstraction then check the property on the abstract system -- where a passing check on the abstract system is only transferred to the original system…

Nonlinear kernels can be approximated using finite-dimensional feature maps for efficient risk minimization. Due to the inherent trade-off between the dimension of the (mapped) feature space and the approximation accuracy, the key problem…

Finding the ground state of spin glasses is a challenging problem with broad implications. Many hard optimization problems, including NP-complete problems, can be mapped, for instance, to the Ising spin glass model. We present a graph-based…

We study the problem of selecting a subset of vectors from a large set, to obtain the best signal representation over a family of functions. Although greedy methods have been widely used for tackling this problem and many of those have been…

Partitioning a graph using graph separators, and particularly clique separators, are well-known techniques to decompose a graph into smaller units which can be treated independently. It was previously known that the treewidth was bounded…