Approximating the k-traveling repairman problem with repairtimes
نویسندگان
چکیده
Given an undirected graph G= (V,E) and a source vertex s ∈ V , the k-traveling repairman (KTR) problem, also known as the minimum latency problem, asks for k tours, each starting at s and together covering all the vertices (customers) such that the sum of the latencies experienced by the customers is minimum. Latency of a customer p is defined to be the distance traveled (time elapsed) before visiting p for the first time. Previous literature on the KTR problem has considered the version of the problem in which the repairtime of a customer is assumed to be zero for latency calculations. We consider a generalization of the problem in which each customer has an associated repairtime. For a fixed k, we present a (β + 2)-approximation algorithm for this problem, where β is the best achievable approximation ratio for the KTR problem with zero repairtimes (currently β = 6). For arbitrary k, we obtain a ( 2β + 2 )-approximation ratio. When the repairtimes of all the customers are the same, we present an approximation algorithm with better ratio.2 We also introduce the bounded-latency problem, a complementary version of the KTR problem, in which we are given a latency bound L and are asked to find the minimum number of repairmen required to service all the customers such that the latency of no customer is more than L. For this problem, we present a simple bicriteria approximation algorithm that finds a solution with at most 2/ρ times the number of repairmen required by an optimal solution, with the latency of no customer exceeding (1 + ρ)L, ρ > 0. © 2006 Published by Elsevier B.V.
منابع مشابه
A Review on Traveling Repairman Problem
Suppose G=(V,A) be an undirected graph with n nodes and a source vertex s Є V. Each node has a problem that must be solved by the repairman that has send. We are given the time required by the repairman to travel among nodes. The objective is to find a tour that minimizes the total waiting time of all the problems that are waiting to be solved. Traveling Repairman problem (TRP) is also known as...
متن کاملEfficient GRASP+VND and GRASP+VNS metaheuristics for the traveling repairman problem
The traveling repairman problem is a customer-centric routing problem, in which the total waiting time of the customers is minimized, rather than the total travel time of a vehicle. To date, research on this problem has focused on exact algorithms and approximation methods. This paper presents the first metaheuristic approach for the traveling repairman problem.
متن کاملSpeedup in the Traveling Repairman Problem with Unit Time Windows
The input to the unrooted traveling repairman problem is an undirected metric graph and a subset of nodes, each of which has a time window of unit length. Given that a repairman can start at any location, the goal is to plan a route that visits as many nodes as possible during their respective time windows. A polynomial-time bicriteria approximation algorithm is presented for this problem, gain...
متن کاملSolving the Traveling Repairman Problem with Differentiated Waiting times through Lagrangian Relaxation
In this paper we present a formulation of the traveling repairman problem with differentiated waiting times that is derived from the extended disaggregated flow formulation for the asymmetric traveling salesman problem. We focus on the usage of the Lagrangian approach as a mechanism of speeding up the solution of the linear relaxation by a simplex method. We show some computational results.
متن کاملمدلی جدید برای حل مسئله تعمیرکار سیار بر پایه برنامهریزی عدد صحیح آمیخته
The Traveling Repairman Problem is a customer-oriented routing problem in which a repairman is visiting a set of geographically distributed customers. The objective function is to minimize the total waiting times of all customers. The importance of this problem can be found in its applications in the following areas: blood distributing, manufacturing systems, and transportation and logistics. A...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Discrete Algorithms
دوره 5 شماره
صفحات -
تاریخ انتشار 2007