Related papers: Random Shortest Paths: Non-Euclidean Instances for…
The Euclidean k-means problem is arguably the most widely-studied clustering problem in machine learning. While the k-means objective is NP-hard in the worst-case, practitioners have enjoyed remarkable success in applying heuristics like…
Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R^d. We study the convergence of the shortest path distance in such graphs as the sample size…
Many distributed optimization algorithms achieve existentially-optimal running times, meaning that there exists some pathological worst-case topology on which no algorithm can do better. Still, most networks of interest allow for…
The 2-Opt heuristic is one of the simplest algorithms for finding good solutions to the metric Traveling Salesman Problem. It is the key ingredient to the well-known Lin-Kernighan algorithm and often used in practice. So far, only upper and…
As a first contribution the mTSP is solved using an exact method and two heuristics, where the number of nodes per route is balanced. The first heuristic uses a nearest node approach and the second assigns the closest vehicle (salesman). A…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
Parameterized runtime analysis seeks to understand the influence of problem structure on algorithmic runtime. In this paper, we contribute to the theoretical understanding of evolutionary algorithms and carry out a parameterized analysis of…
In this paper, we present a new algorithm that extends RRT* and RT-RRT* for online path planning in complex, dynamic environments. Sampling-based approaches often perform poorly in environments with narrow passages, a feature common to many…
This paper reports about the development of two provably correct approximate algorithms which calculate the Euclidean shortest path (ESP) within a given cube-curve with arbitrary accuracy, defined by $\epsilon >0$, and in time complexity…
We consider some generalizations of the Asymmetric Traveling Salesman Path problem. Suppose we have an asymmetric metric G = (V,A) with two distinguished nodes s,t. We are also given a positive integer k. The goal is to find k paths of…
The shortest path problem is among the most fundamental combinatorial optimization problems to answer reachability queries. It is hard to deter-mine which vertices or edges are visited during shortest path traversals. In this paper, we…
Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…
Optimal paths connecting randomly selected network nodes and fixed routers are studied analytically in the presence of non-linear overlap cost that penalizes congestion. Routing becomes increasingly more difficult as the number of selected…
This work elaborates on the important problem of (1) designing optimal randomized routing policies for reaching a target node t from a source note s on a weighted directed graph G and (2) defining distance measures between nodes…
This paper discusses the shortest path problem in a general directed graph with $n$ nodes and $K$ cost scenarios (objectives). In order to choose a solution, the min-max criterion is applied. The min-max version of the problem is hard to…
We study augmenting a plane Euclidean network with a segment, called a shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Problems of this type have received considerable attention…
We study geodesically convex (g-convex) problems that can be written as a difference of Euclidean convex functions. This structure arises in several optimization problems in statistics and machine learning, e.g., for matrix scaling,…
The Traveling Thief Problem (TTP) is a multi-component optimization problem that captures the interplay between routing and packing decisions by combining the classical Traveling Salesperson Problem (TSP) and the Knapsack Problem (KP). The…
We provide exact and approximation methods for solving a geometric relaxation of the Traveling Salesman Problem (TSP) that occurs in curve reconstruction: for a given set of vertices in the plane, the problem Minimum Perimeter Polygon (MPP)…
We develop an adaptive-metric framework for norm-minimization-based outer approximation algorithms in bounded convex vector optimization. The key idea is to let the scalarization metric vary across iterations while measuring approximation…