Asymptotically Optimal Online Page Migration on Three Points

This paper addresses the page migration problem: given online requests from nodes on a network for accessing a page stored in a node, output online migrations of the page. Serving a request costs the distance between the request and the page, and migrating the page costs the migration distance multiplied by the page size D≥1. The objective is to minimize the total sum of service costs and migration costs. Black and Sleator conjectured that there exists a 3-competitive deterministic algorithm for every graph. Although the conjecture was disproved for the case D=1, whether or not an asymptotically (with respect to D) 3-competitive deterministic algorithm exists for every graph is still open. In fact, we did not know if there exists a 3-competitive deterministic algorithm for an extreme case of three nodes with D≥2. As the first step toward an asymptotic version of the Black and Sleator conjecture, we present 3- and (3+1/D)-competitive algorithms on three nodes with D=2 and D≥3, respectively, and a lower bound of 3+Ω(1/D) that is greater than 3 for every D≥3. In addition to the results on three nodes, we also derive ρ-competitiveness on complete graphs with edge-weights between 1 and 2-2/ρ for any ρ≥3, extending the previous 3-competitive algorithm on uniform networks. © 2013 Springer Science+Business Media New York

Dynamic Beats Fixed: On Phase-Based Algorithms for File Migration

In this paper, we construct a deterministic 4-competitive algorithm for the online file migration problem, beating the currently best 20-year old, 4.086-competitive MTLM algorithm by Bartal et al. (SODA 1997). Like MTLM, our algorithm also operates in phases, but it adapts their lengths dynamically depending on the geometry of requests seen so far. The improvement was obtained by carefully analyzing a linear model (factor-revealing LP) of a single phase of the algorithm. We also show that if an online algorithm operates in phases of fixed length and the adversary is able to modify the graph between phases, no algorithm can beat the competitive ratio of 4.086

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

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