Related papers: Revisiting the Majority Problem: Average-Case Anal…
Using the Minority Game model we study a broad spectrum of problems of market mechanism. We study the role of different types of agents: producers, speculators as well as noise traders. The central issue here is the information flow :…
It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches…
Evaluating performance across optimization algorithms on many problems presents a complex challenge due to the diversity of numerical scales involved. Traditional data processing methods, such as hypothesis testing and Bayesian inference,…
The present work has been designed for students in secondary school and their teachers in mathematics. We will show how with the help of our knowledge of number systems we can solve problems from other fields of mathematics for example in…
We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high…
A high number of discrete optimization problems, including Vertex Cover, Set Cover or Feedback Vertex Set, can be unified into the class of covering problems. Several of them were shown to be inapproximable by deterministic algorithms. This…
In this paper, we present a new approach which qualifies or not a solution found by a heuristic as a potential optimal solution. Our approach is based on the following observation: for a minimization problem, the number of admissible…
The halting problem is undecidable --- but can it be solved for "most" inputs? This natural question was considered in a number of papers, in different settings. We revisit their results and show that most of them can be easily proven in a…
In this work the properties of minority games containing agents which try to winning all the time are studied by means of computational simulations. We have considered several ways of introducing above the rules clever players using…
Suppose one desires to randomly sample a pair of objects such as socks, hoping to get a matching pair. Even in the simplest situation for sampling, which is sampling with replacement, the innocent phrase "the distribution of the color of a…
The problem of vertex coloring in random graphs is studied using methods of statistical physics and probability. Our analytical results are compared to those obtained by exact enumeration and Monte-Carlo simulations. We critically discuss…
The study of fair algorithms has become mainstream in machine learning and artificial intelligence due to its increasing demand in dealing with biases and discrimination. Along this line, researchers have considered fair versions of…
Computational aesthetics is an emerging field of research which has attracted different research groups in the last few years. In this field, one of the main approaches to evaluate the aesthetic quality of paintings and photographs is a…
Optimisation algorithms are commonly compared on benchmarks to get insight into performance differences. However, it is not clear how closely benchmarks match the properties of real-world problems because these properties are largely…
While color harmony has long been studied in art and design, a clear consensus remains elusive, as most models are grounded in qualitative insights or limited datasets. In this work, we present a quantitative, data-driven study of color…
We study the problem of approximately counting the number of list packings of a graph. The analogous problem for usual vertex coloring and list coloring has attracted a lot of attention. For list packing the setup is similar but we seek a…
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…
Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods,…
The research area of algorithms with predictions has seen recent success showing how to incorporate machine learning into algorithm design to improve performance when the predictions are correct, while retaining worst-case guarantees when…
Quality assurance remains a key topic in human computation research. Prior work indicates that majority voting is effective for low difficulty tasks, but has limitations for harder tasks. This paper explores two methods of addressing this…