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This paper investigates several cost-sparsity induced optimal input selection problems for structured systems. Given are an autonomous system and a prescribed set of input links, where each input link has a non-negative cost. The problems…
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…
In parameterized algorithmics, the process of kernelization is defined as a polynomial time algorithm that transforms the instance of a given problem to an equivalent instance of a size that is limited by a function of the parameter. As,…
Structured output prediction problems (e.g., sequential tagging, hierarchical multi-class classification) often involve constraints over the output label space. These constraints interact with the learned models to filter infeasible…
We consider the following problem about dispersing points. Given a set of points in the plane, the task is to identify whether by moving a small number of points by small distance, we can obtain an arrangement of points such that no pair of…
We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general.…
A polynomial-time algorithm for 0-1 integer linear programmings has been proposed. This method continues the classic idea of solving ILP with its LP relaxation. The innovation is that every constraint in the LP is reconstructed into a…
The technique of kernelization consists in extracting, from an instance of a problem, an essentially equivalent instance whose size is bounded in a parameter k. Besides being the basis for efficient param-eterized algorithms, this method…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
The notion of treewidth plays an important role in theoretical and practical studies of graph problems. It has been recognized that, especially in practical environments, when computing the treewidth of a graph it is invaluable to first…
Low-rank approximation of kernels is a fundamental mathematical problem with widespread algorithmic applications. Often the kernel is restricted to an algebraic variety, e.g., in problems involving sparse or low-rank data. We show that…
We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…
An $\alpha$-approximate polynomial Turing kernelization is a polynomial-time algorithm that computes an $(\alpha c)$-approximate solution for a parameterized optimization problem when given access to an oracle that can compute…
A well-recognized limitation of kernel learning is the requirement to handle a kernel matrix, whose size is quadratic in the number of training examples. Many methods have been proposed to reduce this computational cost, mostly by using a…
We provide a number of algorithmic results for the following family of problems: For a given binary m\times n matrix A and integer k, decide whether there is a "simple" binary matrix B which differs from A in at most k entries. For an…
There are existing standard solvers for tackling discrete optimization problems. However, in practice, it is uncommon to apply them directly to the large input space typical of this class of problems. Rather, the input is preprocessed to…
This paper analyzes to what extent it is possible to efficiently reduce the number of clauses in NP-hard satisfiability problems, without changing the answer. Upper and lower bounds are established using the concept of kernelization.…
Integer Linear Programming (ILP) serves as a versatile framework for modeling a wide range of combinatorial optimization problems, typically addressed by sophisticated exact solvers or heuristics. While learning-based approaches have…
It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…
Kernelization algorithms in the context of Parameterized Complexity are often based on a combination of reduction rules and combinatorial insights. We will expose in this paper a similar strategy for obtaining polynomial-time approximation…