Related papers: Computing the Coverage of an Opaque Forest

A mobile robot represented by a point moving in the plane has to explore an unknown terrain with obstacles. Both the terrain and the obstacles are modeled as arbitrary polygons. We consider two scenarios: the unlimited vision, when the…

New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…

This paper addresses the problem of finding a representation of a subtree distance, which is an extension of the tree metric. We show that a minimal representation is uniquely determined by a given subtree distance, and give a linear time…

Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of…

The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when the local minima that are a…

Graph isomorphism, subgraph isomorphism, and maximum common subgraphs are classical well-investigated objects. Their (parameterized) complexity and efficiently tractable cases have been studied. In the present paper, for a given set of…

Matchings and coverings are central topics in graph theory. The close relationship between these two has been key to many fundamental algorithmic and polyhedral results. For mixed graphs, the notion of matching forest was proposed as a…

The increasing recognition of the association between adverse human health conditions and many environmental substances as well as processes has led to the need to monitor them. An important problem that arises in environmental statistics…

We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its…

Random forests are decision tree ensembles that can be used to solve a variety of machine learning problems. However, as the number of trees and their individual size can be large, their decision making process is often incomprehensible. In…

We consider the problem of exploring an unknown tree with a team of $k$ initially colocated mobile agents. Each agent has limited energy and cannot, as a result, traverse more than $B$ edges. The goal is to maximize the number of nodes…

We show the first conditionally optimal deterministic algorithm for $3$-coloring forests in the low-space massively parallel computation (MPC) model. Our algorithm runs in $O(\log \log n)$ rounds and uses optimal global space. The best…

We consider methods for finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of points in the plane. Both problems are known to be NP-hard; at the center of the recent CG Challenge, practical…

Real-time occlusion handling is a major problem in outdoor mixed reality system because it requires great computational cost mainly due to the complexity of the scene. Using only segmentation, it is difficult to accurately render a virtual…

The notion of the cover is a generalization of a period of a string, and there are linear time algorithms for finding the shortest cover. The seed is a more complicated generalization of periodicity, it is a cover of a superstring of a…

When applying optimization method to a real-world problem, the possession of prior knowledge and preliminary analysis on the landscape of a global optimization problem can give us an insight into the complexity of the problem. This…

Covering a network with the minimum possible number of boxes can reveal interesting features for the network structure, especially in terms of self-similar or fractal characteristics. Considerable attention has been recently devoted to this…

We consider the computational aspects of lossy data compression problem, where the compression error is determined by a cover of the data space. We propose an algorithm which reduces the number of partitions needed to find the entropy with…

Research on fractal networks is a dynamically growing field of network science. A central issue is to analyze fractality with the so-called box-covering method. As this problem is known to be NP-hard, a plethora of approximating algorithms…

The production of thematic maps depicting land cover is one of the most common applications of remote sensing. To this end, several semantic segmentation approaches, based on deep learning, have been proposed in the literature, but land…