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We revisit the traveling salesman problem with neighborhoods (TSPN) and present the first constant-ratio approximation for disks in the plane: Given a set of $n$ disks in the plane, a TSP tour whose length is at most $O(1)$ times the…
We study some variants of the $k$-\textsc{Watchman Routes} problem, the cooperative version of the classic \textsc{Watchman Routes} problem in a simple polygon. The watchmen may be required to see the whole polygon, or some pre-determined…
The Travelling Salesman Problem is one the most fundamental and most studied problems in approximation algorithms. For more than 30 years, the best algorithm known for general metrics has been Christofides's algorithm with approximation…
The famous Travelling Salesman Problem (TSP) is an important category of optimization problems that is mostly encountered in various areas of science and engineering. Studying optimization problems motivates to develop advanced techniques…
We present a black-box reduction from the path version of the Traveling Salesman Problem (Path TSP) to the classical tour version (TSP). More precisely, we show that given an $\alpha$-approximation algorithm for TSP, then, for any $\epsilon…
Orienteering is the following optimization problem: given an edge-weighted graph (directed or undirected), two nodes s,t and a time limit T, find an s-t walk of total length at most T that maximizes the number of distinct nodes visited by…
Yatsenko gives a polynomial-time algorithm for solving the traveling salesman problem. We examine the correctness of the algorithm and its construction. We also comment on Yatsenko's evaluation of the algorithm.
We consider several variants of a car-sharing problem. Given are a number of requests each consisting of a pick-up location and a drop-off location, a number of cars, and nonnegative, symmetric travel times that satisfy the triangle…
We consider here the MultiBot problem for the scheduling and the resource parametrization of jobs related to the production or the transportation of different products inside a given time horizon. Those jobs must meet known in advance…
TSP (Traveling Salesman Problem), a classic NP-complete problem in combinatorial optimization, is of great significance in multiple fields. Exact algorithms for TSP are not practical due to their exponential time cost. Thus, approximate…
With applications to many disciplines, the traveling salesman problem (TSP) is a classical computer science optimization problem with applications to industrial engineering, theoretical computer science, bioinformatics, and several other…
Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy…
We propose a simple and exact method for the Traveling Salesman Problem with Time Windows and Makespan objective (\TSPTW-M) that solves all instances of the classical benchmark with $50$ or more customers in less than ten seconds each.…
Given facilities with capacities and clients with penalties and demands, the transportation problem with market choice consists in finding the minimum-cost way to partition the clients into unserved clients, paying the penalties, and into…
We give a 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem.
The Orienteering Problem with Time Window and Delay (\OPTiWinD) is a variant of the online orienteering problem. A series of requests appear in various locations while a vehicle moves within the territory to serve them. Each request has a…
Proposed initially from a practical circumstance, the traveling salesman problem caught the attention of numerous economists, computer scientists, and mathematicians. These theorists were instead intrigued by seeking a systemic way to find…
We study the variant of the Euclidean Traveling Salesman problem where instead of a set of points, we are given a set of lines as input, and the goal is to find the shortest tour that visits each line. The best known upper and lower bounds…
The traveling salesman problem is a fundamental combinatorial optimization problem with strong exact algorithms. However, as problems scale up, these exact algorithms fail to provide a solution in a reasonable time. To resolve this, current…
Many real-world problems can be formulated as a constrained Traveling Salesman Problem (TSP). However, the constraints are always complex and numerous, making the TSPs challenging to solve. When the number of complicated constraints grows,…