Related papers: Kernelization of Counting Problems

We examine a parameterized complexity class for randomized computation where only the error bound and not the full runtime is allowed to depend more than polynomially on the parameter, based on a proposal by Kwisthout in [15,16]. We prove…

In the context of kernel machines, polynomial and Fourier features are commonly used to provide a nonlinear extension to linear models by mapping the data to a higher-dimensional space. Unless one considers the dual formulation of the…

It has been observed in many places that constant-factor approximable problems often admit polynomial or even linear problem kernels for their decision versions, e.g., Vertex Cover, Feedback Vertex Set, and Triangle Packing. While there…

We extend the notion of lossy kernelization, introduced by Lokshtanov et al. [STOC 2017], to approximate Turing kernelization. An $\alpha$-approximate Turing kernel for a parameterized optimization problem is a polynomial-time algorithm…

The standard formalization of preprocessing in parameterized complexity is given by kernelization. In this work, we depart from this paradigm and study a different type of preprocessing for problems without polynomial kernels, still aiming…

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…

In the framework of computational complexity and in an effort to define a more natural reduction for problems of equivalence, we investigate the recently introduced kernel reduction, a reduction that operates on each element of a pair…

In this work, we study the $k$-median clustering problem with an additional equal-size constraint on the clusters, from the perspective of parameterized preprocessing. Our main result is the first lossy ($2$-approximate) polynomial kernel…

Compression is a key step to deploy large neural networks on resource-constrained platforms. As a popular compression technique, quantization constrains the number of distinct weight values and thus reducing the number of bits required to…

We investigate preprocessing for vertex-subset problems on graphs. While the notion of kernelization, originating in parameterized complexity theory, is a formalization of provably effective preprocessing aimed at reducing the total…

The usefulness of parameterized algorithmics has often depended on what Niedermeier has called, "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of…

In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution, even if the compilation is…

Weighted counting problems are a natural generalization of counting problems where a weight is associated with every computational path of polynomial-time non-deterministic Turing machines and the goal is to compute the sum of the weights…

This work proposes kernel transform learning. The idea of dictionary learning is well known; it is a synthesis formulation where a basis is learnt along with the coefficients so as to generate or synthesize the data. Transform learning is…

ML-powered code generation aims to assist developers to write code in a more productive manner, by intelligently generating code blocks based on natural language prompts. Recently, large pretrained deep learning models have substantially…

Representations that can compactly and effectively capture temporal evolution of semantic content are important to machine learning algorithms that operate on multi-variate time-series data. We investigate such representations motivated by…

Quantization is a widely used technique to compress and accelerate deep neural networks. However, conventional quantization methods use the same bit-width for all (or most of) the layers, which often suffer significant accuracy degradation…

Deep Neural Networks reached state-of-the-art performance across numerous domains, but this progress has come at the cost of increasingly large and over-parameterized models, posing serious challenges for deployment on resource-constrained…

A permutation $\pi$ contains a permutation $\sigma$ as a pattern if it contains a subsequence of length $|\sigma|$ whose elements are in the same relative order as in the permutation $\sigma$. This notion plays a major role in enumerative…

Flum and Grohe define a parameter (parameterization) as a function $\kappa$ which maps words over a given alphabet to natural numbers. They require such functions to be polynomial-time computable. We show how this technical restriction can…