Year: 2015
Type: preprint
Abstract: We consider TSP with time windows and service time. In this problem we receive a sequence of requests for a service at nodes in a metric space and a time window for each request. The goal of the online algorithm is to maximize the number of requests served during their time window. The time to traverse an edge is the distance between the incident nodes of that edge. Serving a request requires unit time. We characterize the competitive ratio for each metric space separately. The competitive ratio depends on the relation between the minimum laxity (the minimum length of a time window) and the diameter of the metric space. Specifically, there is a constant competitive algorithm depending whether the laxity is larger or smaller than the diameter. In addition, we characterize the rate of convergence of the competitive ratio to $1$ as the laxity increases. Specifically, we provide a matching lower and upper bounds depending on the ratio between the laxity and the TSP of the metric space (the minimum distance to traverse all nodes). An application of our result improves the lower bound for colored packets with transition cost and matches the upper bound. In proving our lower bounds we use an interesting non-standard embedding with some special properties. This embedding may be interesting by its own.
Source: arXiv (Cornell University)
Authors: Azar, Yossi, Vardi, Adi
Institution: Tel Aviv University
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G7965623349
OpenAlex ID: W1631636247