Related papers: On Polynomial Kernels for Integer Linear Programs:…
For several decades the dominant techniques for integer linear programming have been branching and cutting planes. Recently, several authors have developed core point methods for solving symmetric integer linear programs (ILPs). An integer…
Enumerative kernelization is a recent promising at the intersection of parameterized complexity and enumeration algorithms, with two proposed models. The first, known as enum-kernels and due to Creignou et al., was too permissive, leading…
We propose a new exact approach for solving integer linear programming (ILP) problems which we will call projective splitting algorithms (PSAs). Unlike classical methods for solving ILP problems, PSAs conduct the search for the optimal…
We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…
We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability,…
This paper studies the kernelization complexity of graph coloring problems with respect to certain structural parameterizations of the input instances. We are interested in how well polynomial-time data reduction can provably shrink…
We introduce a new technique for proving kernelization lower bounds, called cross-composition. A classical problem L cross-composes into a parameterized problem Q if an instance of Q with polynomially bounded parameter value can express the…
We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability,…
We propose a preprocessing algorithm for the multiway cut problem that establishes its polynomial kernelizability when the difference between the parameter $k$ and the size of the smallest isolating cut is at most $log(k)$. To the best of…
Structural graph parameters play an important role in parameterized complexity, including in kernelization. Notably, vertex cover, neighborhood diversity, twin-cover, and modular-width have been studied extensively in the last few years.…
Object proposals are an ensemble of bounding boxes with high potential to contain objects. In order to determine a small set of proposals with a high recall, a common scheme is extracting multiple features followed by a ranking algorithm…
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.…
Voting problems are central in the area of social choice. In this article, we investigate various voting systems and types of control of elections. We present integer linear programming (ILP) formulations for a wide range of NP-hard control…
We investigate computational problems involving large weights through the lens of kernelization, which is a framework of polynomial-time preprocessing aimed at compressing the instance size. Our main focus is the weighted Clique problem,…
In the Vertex Cover problem we are given a graph $G=(V,E)$ and an integer $k$ and have to determine whether there is a set $X\subseteq V$ of size at most $k$ such that each edge in $E$ has at least one endpoint in $X$. The problem can be…
Covering problems are well-studied in the domain of Operations Research, and, more specifically, in Location Science. When the location space is a network, the most frequent assumption is to consider the candidate facility locations, the…
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,…
Enumeration kernelization for parameterized enumeration problems was defined by Creignou et al. [Theory Comput. Syst. 2017] and was later refined by Golovach et al. [J. Comput. Syst. Sci. 2022, STACS 2021] to polynomial-delay enumeration…
For a set of graphs $\mathcal{H}$, the \textsc{$\mathcal{H}$-free Edge Deletion} problem asks to find whether there exist at most $k$ edges in the input graph whose deletion results in a graph without any induced copy of $H\in\mathcal{H}$.…
We consider the problem of computing matrix polynomials $p(X)$, where $X$ is a large dense matrix, with as few matrix-matrix multiplications as possible. More precisely, let $\Pi_{2^{m}}^*$ represent the set of polynomials computable with…