8 research outputs found
Maximizing Revenues for Online-Dial-a-Ride
In the classic Dial-a-Ride Problem, a server travels in some metric space to
serve requests for rides. Each request has a source, destination, and release
time. We study a variation of this problem where each request also has a
revenue that is earned if the request is satisfied. The goal is to serve
requests within a time limit such that the total revenue is maximized. We first
prove that the version of this problem where edges in the input graph have
varying weights is NP-complete. We also prove that no algorithm can be
competitive for this problem. We therefore consider the version where edges in
the graph have unit weight and develop a 2-competitive algorithm for this
problem
Online k-server routing problems
In an online k-server routing problem, a crew of k servers has to visit points in a metric space as they arrive in real time. Possible objective functions include minimizing the makespan (k-Traveling Salesman Problem) and minimizing the sum of completion times (k-Traveling Repairman Problem). We give competitive algorithms, resource augmentation results and lower bounds for k-server routing problems in a wide class of metric spaces. In some cases the competitive ratio is dramatically better than that of the corresponding single server problem. Namely, we give a 1+O((log¿k)/k)-competitive algorithm for the k-Traveling Salesman Problem and the k-Traveling Repairman Problem when the underlying metric space is the real line. We also prove that a similar result cannot hold for the Euclidean plane
The on-line asymmetric traveling salesman problem
We consider two on-line versions of the asymmetric traveling salesman problem with triangle inequality. For the homing version, in which the salesman is required to return in the city where it started from, we give a 3+√5/2-competitive algorithm and prove that this is best possible. For the nomadic version, the on-line analogue of the shortest asymmetric hamiltonian path problem, we show that the competitive ratio of any on-line algorithm has to depend on the amount of asymmetry of the space in which the salesman moves. We also give bounds on the competitive ratio of on-line algorithms that are zealous, that is, in which the salesman cannot stay idle when some city can be served. © Springer-Verlag Berlin Heidelberg 2005
The on-line asymmetric traveling salesman problem
We consider two on-line versions of the asymmetric traveling salesman problem with triangle inequality. For the homing version, in which the salesman is required to return in the city where it started from, we give a frac(3 + sqrt(5), 2)-competitive algorithm and prove that this is best possible. For the nomadic version, the on-line analogue of the shortest asymmetric Hamiltonian path problem, we show that the competitive ratio of any on-line algorithm depends on the amount of asymmetry of the space in which the salesman moves. We also give bounds on the competitive ratio of on-line algorithms that are zealous, that is, in which the salesman cannot stay idle when some city can be served. © 2007 Elsevier B.V. All rights reserved
The On-line Asymmetric Traveling Salesman Problem 1
We consider two on-line versions of the asymmetric traveling salesman problem with triangle inequality. For the homing version, in which the salesman is required to return in the city where it started from, we give a 3+√5 2-competitive algorithm and prove that this is best possible. For the nomadic version, the on-line analogue of the shortest asymmetric hamiltonian path problem, we show that the competitive ratio of any on-line algorithm depends on the amount of asymmetry of the space in which the salesman moves. We also give bounds on the competitive ratio of on-line algorithms that are zealous, that is, in which the salesman cannot stay idle when some city can be served. Key words: On-line algorithms, competitive analysis, real time vehicle routing, asymmetric traveling salesman problem