Related papers: Random Shortest Paths: Non-Euclidean Instances for…
In this article, we study the Euclidean minimum spanning tree problem in an imprecise setup. The problem is known as the \emph{Minimum Spanning Tree Problem with Neighborhoods} in the literature. We study the problem where the neighborhoods…
The numerical quantification of the statistics of rare events in stochastic processes is a challenging computational problem. We present a sampling method that constructs an ensemble of stochastic trajectories that are constrained to have…
When traveling through a graph with an accessible deterministic path to a target, is it ever preferable to resort to stochastic node-to-node transitions instead? And if so, what are the conditions guaranteeing that such a stochastic optimal…
We propose a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organizing processes often found in nature. The method, called Extremal Optimization, successively eliminates extremely…
We investigate how the complexity of Euclidean TSP for point sets $P$ inside the strip $(-\infty,+\infty)\times [0,\delta]$ depends on the strip width $\delta$. We obtain two main results. First, for the case where the points have distinct…
The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate…
A solution of the $k$ shortest paths problem may output paths that are identical up to a single edge. On the other hand, a solution of the $k$ independent shortest paths problem consists of paths that share neither an edge nor an…
We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges in order to make a given graph Eulerian, whereas our approach also allows for the removal of…
Given an undirected graph, $G$, and vertices, $s$ and $t$ in $G$, the tracking paths problem is that of finding the smallest subset of vertices in $G$ whose intersection with any $s$-$t$ path results in a unique sequence. This problem is…
Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal…
Considering a graph with unknown weights, can we find the shortest path for a pair of nodes if we know the minimal Steiner trees associated with some subset of nodes? That is, with respect to a fixed latent decision-making system (e.g., a…
Using prototype methods to reduce the size of training datasets can drastically reduce the computational cost of classification with instance-based learning algorithms like the k-Nearest Neighbour classifier. The number and distribution of…
The Euclidean $k$-means problem is a classical problem that has been extensively studied in the theoretical computer science, machine learning and the computational geometry communities. In this problem, we are given a set of $n$ points in…
The problem of finding the longest simple cycle in a directed graph is NP-hard, with critical applications in computational biology, scheduling, and network analysis. Existing approaches include exact algorithms with exponential runtimes,…
This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…
In this paper, we propose a novel sampling-based planner for multi-goal path planning among obstacles, where the objective is to visit predefined target locations while minimizing the travel costs. The order of visiting the targets is often…
We consider the problem of traveling among random points in Euclidean space, when only a random fraction of the pairs are joined by traversable connections. In particular, we show a threshold for a pair of points to be connected by a…
Motion planning can be cast as a trajectory optimisation problem where a cost is minimised as a function of the trajectory being generated. In complex environments with several obstacles and complicated geometry, this optimisation problem…
The problem of finding multiple simple shortest paths in a weighted directed graph $G=(V,E)$ has many applications, and is considerably more difficult than the corresponding problem when cycles are allowed in the paths. Even for a single…
We propose an efficient probabilistic method to solve a deterministic problem -- we present a randomized optimization approach that drastically reduces the enormous computational cost of optimizing designs under many load cases for both…