15 research outputs found
Cost thresholds for dynamic resource location
AbstractThe traditional dynamic resource location problem attempts to minimize the cost of servicing a number of sequential requests, given foreknowledge of a limited number of requests. One artificial constraint of this problem is the presumption that resource relocation and remote servicing of requests have identical costs. Parameterizing the ratio of relocation cost to service cost leads to two extreme behaviors in terms of dynamic optimizability. The threshold at which a specific graph transitions between these behaviors reveals certain characteristics of the graph's decomposability into cycles
Approximation Algorithms for Clustering with Dynamic Points
In many classic clustering problems, we seek to sketch a massive data set of
points in a metric space, by segmenting them into categories or
clusters, each cluster represented concisely by a single point in the metric
space. Two notable examples are the -center/-supplier problem and the
-median problem. In practical applications of clustering, the data set may
evolve over time, reflecting an evolution of the underlying clustering model.
In this paper, we initiate the study of a dynamic version of clustering
problems that aims to capture these considerations. In this version there are
time steps, and in each time step , the set of clients
needed to be clustered may change, and we can move the facilities between
time steps. More specifically, we study two concrete problems in this
framework: the Dynamic Ordered -Median and the Dynamic -Supplier problem.
We first consider the Dynamic Ordered -Median problem, where the objective
is to minimize the weighted sum of ordered distances over all time steps, plus
the total cost of moving the facilities between time steps. We present one
constant-factor approximation algorithm for and another approximation
algorithm for fixed . Then we consider the Dynamic -Supplier
problem, where the objective is to minimize the maximum distance from any
client to its facility, subject to the constraint that between time steps the
maximum distance moved by any facility is no more than a given threshold. When
the number of time steps is 2, we present a simple constant factor
approximation algorithm and a bi-criteria constant factor approximation
algorithm for the outlier version, where some of the clients can be discarded.
We also show that it is NP-hard to approximate the problem with any factor for
.Comment: To be published in the Proceedings of the 28th Annual European
Symposium on Algorithms (ESA 2020
Online Algorithms with Randomly Infused Advice
We introduce a novel method for the rigorous quantitative evaluation of online algorithms that relaxes the "radical worst-case" perspective of classic competitive analysis. In contrast to prior work, our method, referred to as randomly infused advice (RIA), does not make any assumptions about the input sequence and does not rely on the development of designated online algorithms. Rather, it can be applied to existing online randomized algorithms, introducing a means to evaluate their performance in scenarios that lie outside the radical worst-case regime.
More concretely, an online algorithm ALG with RIA benefits from pieces of advice generated by an omniscient but not entirely reliable oracle. The crux of the new method is that the advice is provided to ALG by writing it into the buffer ? from which ALG normally reads its random bits, hence allowing us to augment it through a very simple and non-intrusive interface. The (un)reliability of the oracle is captured via a parameter 0 ? ? ? 1 that determines the probability (per round) that the advice is successfully infused by the oracle; if the advice is not infused, which occurs with probability 1 - ?, then the buffer ? contains fresh random bits (as in the classic online setting).
The applicability of the new RIA method is demonstrated by applying it to three extensively studied online problems: paging, uniform metrical task systems, and online set cover. For these problems, we establish new upper bounds on the competitive ratio of classic online algorithms that improve as the infusion parameter ? increases. These are complemented with (often tight) lower bounds on the competitive ratio of online algorithms with RIA for the three problems
Design of Efficient Online Algorithms for Server Problems on Networks
13301甲第4735号博士(学術)金沢大学博士論文要旨Abstract 以下に掲載:Algorithms 9(3) pp.57/1-7 2016. MDPI AG. 共著者:Amanj Khorramian, Akira Matsubayash
Bucket Game with Applications to Set Multicover and Dynamic Page Migration
We present a simple two-person Bucket Game, based on throwing balls into buckets, and we discuss possible players’ strategies. We use these strategies to create an approximation algorithm for a generalization of the well known Set Cover problem, where we need to cover each element by at least k sets. Furthermore, we apply these strategies to construct a randomized algorithm for Dynamic Page Migration problem achieving the optimal competitive ratio against an oblivious adversary
Uniform page migration problem in Euclidean space
金沢大学理工研究域電子情報学系The page migration problem in Euclidean space is revisited. In this problem, online requests occur at any location to access a single page located at a server. Every request must be served, and the server has the choice to migrate from its current location to a new location in space. Each service costs the Euclidean distance between the server and request. A migration costs the distance between the former and the new server location, multiplied by the page size. We study the problem in the uniform model, in which the page has size D = 1. All request locations are not known in advance; however, they are sequentially presented in an online fashion. We design a 2.75-competitive online algorithm that improves the current best upper bound for the problem with the unit page size. We also provide a lower bound of 2.732 for our algorithm. It was already known that 2.5 is a lower bound for this problem. © 2016 by the authors; licensee MDPI, Basel, Switzerland