Related papers: Computational Complexity of Three Central Problems…
Model Interpretation aims at the extraction of insights from the internals of a trained model. A common approach to address this task is the characterization of relevant features internally encoded in the model that are critical for its…
The maximum graph bisection problem is a well known graph partition problem. The problem has been proven to be NP-hard. In the maximum graph bisection problem it is required that the set of vertices is divided into two partition with equal…
Minesweeper is an interesting single player game based on logic, memory and guessing. Solving Minesweeper has been shown to be an NP-hard task. Deterministic solvers are the best known approach for solving Minesweeper. This project proposes…
In this work, we prove the NP-completeness of two variants of tokenisation, defined as the problem of compressing a dataset to at most $\delta$ symbols by either finding a vocabulary directly (direct tokenisation), or selecting a sequence…
In this manuscript, we derive the principle of conservation of computational complexity. We measure computational complexity as the number of binary computations (decisions) required to solve a problem. Every problem then defines a unique…
Studying the computational complexity of problems is one of the - if not the - fundamental questions in computer science. Yet, surprisingly little is known about the computational complexity of many central problems in data mining. In this…
Let $G$ be a complete edge-weighted graph on $n$ vertices. To each subset of vertices of $G$ assign the cost of the minimum spanning tree of the subset as its weight. Suppose that $n$ is a multiple of some fixed positive integer $k$. The…
Convolutional neural networks (CNNs) have been successfully applied to many recognition and learning tasks using a universal recipe; training a deep model on a very large dataset of supervised examples. However, this approach is rather…
An unconstrained nonlinear binary optimization problem of selecting a maximum expected value subset of items is considered. Each item is associated with a profit and probability. Each of the items succeeds or fails independently with the…
The local and global interpretability of various ML models has been studied extensively in recent years. However, despite significant progress in the field, many known results remain informal or lack sufficient mathematical rigor. We…
The core is a quintessential solution concept for profit sharing in cooperative game theory. An imputation allocates the worth of the given game among its agents. The imputation lies in the core of the game if, for each sub-coalition, the…
This paper studies the sample complexity (aka number of comparisons) bounds for the active best-$k$ items selection from pairwise comparisons. From a given set of items, the learner can make pairwise comparisons on every pair of items, and…
The decoding problem is a ubiquitous algorithmic task in fault-tolerant quantum computing, and solving it efficiently is essential for scalable quantum computing. Here, we prove that minimum-weight decoding is NP-hard in three…
The hardness of finite domain Constraint Satisfaction Problems (CSPs) is a very important research area in Constraint Programming (CP) community. However, this problem has not yet attracted much attention from the researchers in the…
Ensuring the reproducibility of scientific work is crucial as it allows the consistent verification of scientific claims and facilitates the advancement of knowledge by providing a reliable foundation for future research. However,…
We introduce the subset assignment problem in which items of varying sizes are placed in a set of bins with limited capacity. Items can be replicated and placed in any subset of the bins. Each (item, subset) pair has an associated cost. Not…
Representing graphs by their homomorphism counts has led to the beautiful theory of homomorphism indistinguishability in recent years. Moreover, homomorphism counts have promising applications in database theory and machine learning, where…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
Mathematical optimization, although often leading to NP-hard models, is now capable of solving even large-scale instances within reasonable time. However, the primary focus is often placed solely on optimality. This implies that while…
In this work, we study diversity-aware clustering problems where the data points are associated with multiple attributes resulting in intersecting groups. A clustering solution needs to ensure that the number of chosen cluster centers from…