Online facility location with timed-requests and congestion

11/22/2022
โˆ™
by   Arghya Chakraborty, et al.
โˆ™
0
โˆ™

The classic online facility location problem deals with finding the optimal set of facilities in an online fashion when demand requests arrive one at a time and facilities need to be opened to service these requests. In this work, we study two variants of the online facility location problem; (1) timed requests and (2) congestion. Both of these variants are motivated by the applications to real life and the previously known results on online facility location cannot be directly adapted to analyse them. Timed requests : In this variant, each demand request is a pair (x,t) where the x is the standard location of the demand while t is the corresponding weight of the request. The cost of servicing request (x,t) at facility F is tยท d(x,F') where F' is the set of facilities available at the time of request (x,t). For this variant, we present an online algorithm attaining a competitive ratio of ๐’ช(log n) in the secretarial model for the timed requests and show that it is optimal. Congestion : The congestion variant considers the case when there is an additional congestion cost that grows with the number of requests served by each request. For this variant, when the congestion cost is a monomial, we show that there exists an algorithm attaining a constant competitive ratio. This constant is a function of the exponent of the monomial and the facility opening cost but independent of the number of requests.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
โˆ™ 05/17/2020

The Online Multi-Commodity Facility Location Problem

We consider a natural extension to the metric uncapacitated Facility Loc...
research
โˆ™ 07/20/2019

Dynamic Trip-Vehicle Dispatch with Scheduled and On-Demand Requests

Transportation service providers that dispatch drivers and vehicles to r...
research
โˆ™ 01/23/2017

Space-Time Graph Modeling of Ride Requests Based on Real-World Data

This paper focuses on modeling ride requests and their variations over l...
research
โˆ™ 03/12/2021

Tight Competitive Analyses of Online Car-sharing Problems

The car-sharing problem, proposed by Luo, Erlebach and Xu in 2018, mainl...
research
โˆ™ 01/03/2022

Orienteering problem with time-windows and updating delay

The Orienteering Problem with Time Window and Delay () is a variant of t...
research
โˆ™ 11/30/2021

Servicing Timed Requests on a Line

We consider an off-line optimisation problem where k robots must service...
research
โˆ™ 07/06/2020

Approximation algorithms for car-sharing problems

We consider several variants of a car-sharing problem. Given are a numbe...

Please sign up or login with your details

Forgot password? Click here to reset