Related papers: Kernelization of Counting Problems
We give an algebraic, determinant-based algorithm for the K-Cycle problem, i.e., the problem of finding a cycle through a set of specified elements. Our approach gives a simple FPT algorithm for the problem, matching the $O^*(2^{|K|})$…
Existing neural networks are memory-consuming and computationally intensive, making deploying them challenging in resource-constrained environments. However, there are various methods to improve their efficiency. Two such methods are…
Parallel fixed-parameter tractability studies how parameterized problems can be solved in parallel. A surprisingly large number of parameterized problems admit a high level of parallelization, but this does not mean that we can also…
Enumeration kernelization was first proposed by Creignou et al. [TOCS 2017] and was later refined by Golovach et al. [JCSS 2022] into two different variants: fully-polynomial enumeration kernelization and polynomial-delay enumeration…
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…
Parameterized complexity theory offers a framework for a refined analysis of hard algorithmic problems. Instead of expressing the running time of an algorithm as a function of the input size only, running times are expressed with respect to…
Answer Set Programming with Quantifiers (ASP(Q)) has been introduced to provide a natural extension of ASP modeling to problems in the polynomial hierarchy (PH). However, ASP(Q) lacks a method for encoding in an elegant and compact way…
Kernelization is a theoretical formalization of efficient preprocessing for NP-hard problems. Empirically, preprocessing is highly successful in practice, for example in state-of-the-art ILP-solvers like CPLEX. Motivated by this, previous…
The framework of Bodlaender et al. (ICALP 2008) and Fortnow and Santhanam (STOC 2008) allows us to exclude the existence of polynomial kernels for a range of problems under reasonable complexity-theoretical assumptions. However, there are…
Despite their high accuracy, complex neural networks demand significant computational resources, posing challenges for deployment on resource constrained devices such as mobile phones and embedded systems. Compression algorithms have been…
The state-of-the-art performance for several real-world problems is currently reached by convolutional neural networks (CNN). Such learning models exploit recent results in the field of deep learning, typically leading to highly performing,…
We prove that, for many parameterized problems in the class FPT, the existence of polynomial kernels implies the collapse of the W-hierarchy (i.e., W[P] = FPT). The collapsing results are also extended to assumed exponential kernels for…
Deep Neural Networks have achieved remarkable success relying on the developing availability of GPUs and large-scale datasets with increasing network depth and width. However, due to the expensive computation and intensive memory,…
Quantization neural networks (QNNs) are very attractive to the industry because their extremely cheap calculation and storage overhead, but their performance is still worse than that of networks with full-precision parameters. Most of…
In recent years, compression of large language models (LLMs) has emerged as an important problem to enable language model deployment on resource-constrained devices, reduce computational costs, and mitigate the environmental footprint of…
The knapsack problem (KP) is a very famous NP-hard problem in combinatorial optimization. Also its generalization to multiple dimensions named d-dimensional knapsack problem (d-KP) and to multiple knapsacks named multiple knapsack problem…
A polynomial Turing compression (PTC) for a parameterized problem $L$ is a polynomial time Turing machine that has access to an oracle for a problem $L'$ such that a polynomial in the input parameter bounds each query. Meanwhile, a…
This paper presents a general framework to integrate prior knowledge in the form of logic constraints among a set of task functions into kernel machines. The logic propositions provide a partial representation of the environment, in which…
Deep learning models have achieved tremendous success in most of the industries in recent years. The evolution of these models has also led to an increase in the model size and energy requirement, making it difficult to deploy in production…
A decision problem is called parameterized if its input is a pair of strings. One of these strings is referred to as a parameter. The problem: given a propositional logic program P and a non-negative integer k, decide whether P has a stable…