A Lower Bound on the Competitive Ratio of the Permutation Algorithm for Online Facility Assignment on a Line

In the online facility assignment on a line (OFAL) with a set $S$ of $k$ servers and a capacity $c:S\to\mathbb{N}$, each server $s\in S$ with a capacity $c(s)$ is placed on a line and a request arrives on a line one-by-one. The task of an online algorithm is to irrevocably assign a current request to one of the servers with vacancies before the next request arrives. An algorithm can assign up to $c(s)$ requests to each server $s\in S$. In this paper, we show that the competitive ratio of the permutation algorithm is at least $k+1$ for OFAL where the servers are evenly placed on a line. This disproves the result that the permutation algorithm is $k$-competitive by Ahmed et al..Comment: 5 page

Competitive Analysis for Two Variants of Online Metric Matching Problem

In this paper, we study two variants of the online metric matching problem. The first problem is the online metric matching problem where all the servers are placed at one of two positions in the metric space. We show that a simple greedy algorithm achieves the competitive ratio of 3 and give a matching lower bound. The second problem is the online facility assignment problem on a line, where servers have capacities, servers and requests are placed on 1-dimensional line, and the distances between any two consecutive servers are the same. We show lower bounds $1+ \sqrt{6}$ $(> 3.44948)$, $\frac{4+\sqrt{73}}{3}$ $(>4.18133)$ and $\frac{13}{3}$ $(>4.33333)$ on the competitive ratio when the numbers of servers are 3, 4 and 5, respectively.Comment: 12 pages. Update from the 1st version: The first author was added and Theorems 3, 4 and 5 were improve

Competitive Analysis for Two Variants of Online Metric Matching Problem

14th International Conference, COCOA 2020, Dallas, TX, USA, December 11–13, 2020

Online Facility Assignment

We consider the online facility assignment problem, with a set of facilities F of equal capacity l in metric space and customers arriving one by one in an online manner. We must assign customer c(i) to facility f(j) before the next customer c(i+1) arrives. The cost of this assignment is the distance between ci and fj. The total number of customers is at most vertical bar F vertical bar l and each customer must be assigned to a facility. The objective is to minimize the sum of all assignment costs. We first consider the case where facilities are placed on a line so that the distance between adjacent facilities is the same and customers appear anywhere on the line. We describe a greedy algorithm with competitive ratio 4 vertical bar F vertical bar and another one with competitive ratio vertical bar F vertical bar. Finally, we consider a variant in which the facilities are placed on the vertices of a graph and two algorithms in that setting.NSF [CCF-AF 1712119]12 month embargo; published online: 31 January 2018This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Online Facility Assignment for General Layout of Servers on a Line

identifier:oai:t2r2.star.titech.ac.jp:5068282