33 research outputs found
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
Heuristics for the traveling repairman problem with profits
In the traveling repairman problem with profits, a repairman (also known as the server) visits a subset of nodes in order to collect time-dependent profits. The objective consists of maximizing the total collected revenue. We restrict our study to the case of a single server with nodes located in the Euclidean plane. We investigate properties of this problem, and we derive a mathematical model assuming that the number of visited nodes is known in advance. We describe a tabu search algorithm with multiple neighborhoods, and we test its performance by running it on instances based on TSPLIB. We conclude that the tabu search algorithm finds good-quality solutions fast, even for large instances
Dial a Ride from k-forest
The k-forest problem is a common generalization of both the k-MST and the
dense--subgraph problems. Formally, given a metric space on vertices
, with demand pairs and a ``target'' ,
the goal is to find a minimum cost subgraph that connects at least demand
pairs. In this paper, we give an -approximation
algorithm for -forest, improving on the previous best ratio of
by Segev & Segev.
We then apply our algorithm for k-forest to obtain approximation algorithms
for several Dial-a-Ride problems. The basic Dial-a-Ride problem is the
following: given an point metric space with objects each with its own
source and destination, and a vehicle capable of carrying at most objects
at any time, find the minimum length tour that uses this vehicle to move each
object from its source to destination. We prove that an -approximation
algorithm for the -forest problem implies an
-approximation algorithm for Dial-a-Ride. Using our
results for -forest, we get an -
approximation algorithm for Dial-a-Ride. The only previous result known for
Dial-a-Ride was an -approximation by Charikar &
Raghavachari; our results give a different proof of a similar approximation
guarantee--in fact, when the vehicle capacity is large, we give a slight
improvement on their results.Comment: Preliminary version in Proc. European Symposium on Algorithms, 200
DMVP: Foremost Waypoint Coverage of Time-Varying Graphs
We consider the Dynamic Map Visitation Problem (DMVP), in which a team of
agents must visit a collection of critical locations as quickly as possible, in
an environment that may change rapidly and unpredictably during the agents'
navigation. We apply recent formulations of time-varying graphs (TVGs) to DMVP,
shedding new light on the computational hierarchy of TVG classes by analyzing them in the
context of graph navigation. We provide hardness results for all three classes,
and for several restricted topologies, we show a separation between the classes
by showing severe inapproximability in , limited approximability
in , and tractability in . We also give topologies in
which DMVP in is fixed parameter tractable, which may serve as a
first step toward fully characterizing the features that make DMVP difficult.Comment: 24 pages. Full version of paper from Proceedings of WG 2014, LNCS,
Springer-Verla
The multi-depot k-traveling repairman problem
In this paper, we study the multi-depot k-traveling repairman problem. This problem extends the traditional traveling repairman problem to the multi-depot case. Its objective, similar to the single depot variant, is the minimization of the sum of the arrival times to customers. We propose two distinct formulations to model the problem, obtained on layered graphs. In order to find feasible solutions for the largest instances, we propose a hybrid genetic algorithm where initial solutions are built using a splitting heuristic and a local search is embedded into the genetic algorithm. The efficiency of the mathematical formulations and of the solution approach are investigated through computational experiments. The proposed models are scalable enough to solve instances up to 240 customers