Related papers: Approximation Algorithms for Generalized MST and T…
We develop a general framework for designing polynomial-time approximation schemes (PTASs) for various vehicle routing problems in trees. In these problems, the goal is to optimally route a fleet of vehicles, originating at a depot, to…
The graph invariant EPT-sum has cropped up in several unrelated fields in later years: As an objective function for hierarchical clustering, as a more fine-grained version of the classical edge ranking problem, and, specifically when the…
In the context of algorithm theory, various studies have been conducted on spanning trees with desirable properties. In this paper, we consider the \textsc{Minimum Cover Spanning Tree} problem (MCST for short). Given a graph $G$ and a…
We study the NP-hard problem of approximating a Minimum Routing Cost Spanning Tree in the message passing model with limited bandwidth (CONGEST model). In this problem one tries to find a spanning tree of a graph $G$ over $n$ nodes that…
In this lecture we will consider the minimum weight spanning tree (MST) problem, i.e., one of the simplest and most vital combinatorial optimization problems. We will discuss a particular greedy algorithm that allows to compute a MST for…
The Prize-Collecting Steiner Tree (PCST) problem is a generalization of the Steiner Tree problem that has applications in network design, content distribution networks, and many more. There are a few centralized approximation algorithms…
In the Asymmetric Traveling Salesperson Problem (ATSP) the goal is to find a closed walk of minimum cost in a directed graph visiting every vertex. We consider the approximability of ATSP on topologically restricted graphs. It has been…
The Colored Points Traveling Salesman Problem (Colored Points TSP) is introduced in this work as a novel variation of the traditional Traveling Salesman Problem (TSP) in which the set of points is partitioned into multiple classes, each of…
Due to its broad applications in practice, the minimum spanning tree problem and its all kinds of variations have been studied extensively during the last decades, for which a host of efficient exact and heuristic algorithms have been…
With applications in distribution systems and communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The…
The Travelling Salesman Problem (TSP) is a classical combinatorial optimisation problem. Deep learning has been successfully extended to meta-learning, where previous solving efforts assist in learning how to optimise future optimisation…
We present a polynomial-time approximation scheme (PTAS) for the min-max multiple TSP problem in Euclidean space, where multiple traveling salesmen are tasked with visiting a set of $n$ points and the objective is to minimize the maximum…
In this paper we consider the Recoverable Traveling Salesman Problem (TSP). Here the task is to find two tours simultaneously, such that the intersection between the tours is at least a given minimum size, while the sum of travel distances…
An important variant of the classic Traveling Salesman Problem (TSP) is the Dynamic TSP, in which a system with dynamic constraints is tasked with visiting a set of n target locations (in any order) in the shortest amount of time. Such…
We consider a multistage framework introduced recently where, given a time horizon t=1,2,...,T, the input is a sequence of instances of a (static) combinatorial optimization problem I_1,I_2,...,I_T, (one for each time step), and the goal is…
Randomized Greedy Algorithms (RGAs) are interesting approaches to solve problems whose structures are not well understood as well as problems in combinatorial optimization which incorporate the random processes and the greedy algorithms.…
Uniform cost-distance Steiner trees minimize the sum of the total length and weighted path lengths from a dedicated root to the other terminals. They are applied when the tree is intended for signal transmission, e.g. in chip design or…
We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem (ATSP). Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured…
In the minimum spanning tree (MST) interdiction problem, we are given a graph $G=(V,E)$ with edge weights, and want to find some $X\subseteq E$ satisfying a knapsack constraint such that the MST weight in $(V,E\setminus X)$ is maximized.…
In this paper, we reduce Prize-Collecting Steiner TSP (PCTSP), Prize-Collecting Stroll (PCS), Prize-Collecting Steiner Tree (PCST), Prize-Collecting Steiner Forest (PCSF) and more generally Submodular Prize-Collecting Steiner Forest (SPCSF)…