Related papers: The Colourful Feasibility Problem
A recent line of research investigates how algorithms can be augmented with machine-learned predictions to overcome worst case lower bounds. This area has revealed interesting algorithmic insights into problems, with particular success in…
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…
In the Colored Bin Packing problem a sequence of items of sizes up to $1$ arrives to be packed into bins of unit capacity. Each item has one of $c\geq 2$ colors and an additional constraint is that we cannot pack two items of the same color…
Binary optimisation tasks are ubiquitous in areas ranging from logistics to cryptography. The exponential complexity of such problems means that the performance of traditional computational methods decreases rapidly with increasing problem…
We study the behavior of the Douglas-Rachford algorithm on the graph vertex-coloring problem. Given a graph and a number of colors, the goal is to find a coloring of the vertices so that all adjacent vertex pairs have different colors. In…
We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…
Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
We describe the integration of logical and uncertain reasoning methods to identify the likely source and location of software problems. To date, software engineers have had few tools for identifying the sources of error in complex software…
We consider the red-blue-yellow matching problem: given two natural numbers $k_R$, $k_B$ and a graph $G$ whose edges are colored red, blue or yellow, the goal is to find a matching of $G$ that contains exactly $k_R$ red edges and exactly…
Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…
In this paper, we study the generalized Douglas-Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas-Rachford algorithm and the alternating projection algorithm. Specifically,…
This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…
Nonlinear constrained optimization problems are encountered in many scientific fields. To utilize the huge calculation power of current computers, many mathematic models are also rebuilt as optimization problems. Most of them have…
General purpose language models (LMs) encounter difficulties when processing domain-specific jargon and terminology, which are frequently utilized in specialized fields such as medicine or industrial settings. Moreover, they often find it…
A recent work by Christiansen, Nowicki, and Rotenberg provides dynamic algorithms for coloring sparse graphs, concretely as a function of the arboricity alpha of the input graph. They give two randomized algorithms: O({alpha} log {alpha})…
The growing demand for large language models (LLMs) with tunable reasoning capabilities in many real-world applications highlights a critical need for methods that can efficiently produce a spectrum of models balancing reasoning depth and…
Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…
We consider two models of computation: centralized local algorithms and local distributed algorithms. Algorithms in one model are adapted to the other model to obtain improved algorithms. Distributed vertex coloring is employed to design…
In this paper, we prove results on the relationship between the complexity of the group and color isomorphism problems. The difficulty of color isomorphism problems is known to be closely linked to the the composition factors of the…