Related papers: Recognizing the Tractability in Big Data Computing

Length generalization, the ability to solve problems of longer sequences than those observed during training, poses a core challenge of Transformer-based large language models (LLM). Although existing studies have predominantly focused on…

A classic result of Lenstra [Math.~Oper.~Res.~1983] says that an integer linear program can be solved in fixed-parameter tractable (FPT) time for the parameter being the number of variables. We extend this result by incorporating…

We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…

This work addresses the challenge of using a deep learning model to prune graphs and the ability of this method to integrate explainability into spatio-temporal problems through a new approach. Instead of applying explainability to the…

Large pre-trained models have been vital in recent advancements in domains like language and vision, making model training for individual downstream tasks more efficient and provide superior performance. However, tackling time-series…

The applicability of Large Language Models (LLMs) in temporal reasoning tasks over data that is not present during training is still a field that remains to be explored. In this paper we work on this topic, focusing on structured and…

By algorithmic metatheorems for a model checking problem P over infinite-state systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a…

Recently a strong connection has been shown between the tractability of integer programming (IP) with bounded coefficients on the one side and the structure of its constraint matrix on the other side. To that end, integer linear programming…

Test-time scaling (TTS) -- the dynamic allocation of compute during inference -- is a promising direction for improving reasoning in large language models (LLMs). However, a systematic comparison of well-known TTS strategies under identical…

Decision trees (DTs) epitomize what have become to be known as interpretable machine learning (ML) models. This is informally motivated by paths in DTs being often much smaller than the total number of features. This paper shows that in…

Parallel machine scheduling has been extensively studied in the past decades, with applications ranging from production planning to job processing in large computing clusters. In this work we study some of these fundamental optimization…

We propose logical characterizations of problems solvable in deterministic polylogarithmic time (PolylogTime) and polylogarithmic space (PolylogSpace). We introduce a novel two-sorted logic that separates the elements of the input domain…

Deep learning's success has been attributed to the training of large, overparameterized models on massive amounts of data. As this trend continues, model training has become prohibitively costly, requiring access to powerful computing…

This paper presents a new abstract method for proving lower bounds in computational complexity. Based on the notion of topological and measurable entropy for dynamical systems, it is shown to generalise three previous lower bounds results…

There is a subset of computational problems that are computable in polynomial time for which an existing algorithm may not complete due to a lack of high performance technology on a mission field. We define a subclass of deterministic…

In this work we revisit the elementary scheduling problem $1||\sum p_j U_j$. The goal is to select, among $n$ jobs with processing times and due dates, a subset of jobs with maximum total processing time that can be scheduled in sequence…

Tree Regular Model Checking (TRMC) is the name of a family of techniques for analyzing infinite-state systems in which states are represented by terms, and sets of states by Tree Automata (TA). The central problem in TRMC is to decide…

Magnetic tapes are often considered as an outdated storage technology, yet they are still used to store huge amounts of data. Their main interests are a large capacity and a low price per gigabyte, which come at the cost of a much larger…

Large Language Models (LLMs), typified by OpenAI's GPT, have marked a significant advancement in artificial intelligence. Trained on vast amounts of text data, LLMs are capable of understanding and generating human-like text across a…

In the paper we define three new complexity classes for Turing Machine undecidable problems inspired by the famous Cook/Levin's NP-complete complexity class for intractable problems. These are U-complete (Universal complete), D-complete…