Multi-Embedding of Metric Spaces

Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion as a function of its size. Using probabilistic metric embeddings, the bound on the distortion reduces to logarithmic in the size. We make a step in the direction of bypassing the lower bound on the distortion in terms of the size of the metric. We define "multi-embeddings" of metric spaces in which a point is mapped onto a set of points, while keeping the target metric of polynomial size and preserving the distortion of paths. The distortion obtained with such multi-embeddings into ultrametrics is at most O(log Delta loglog Delta) where Delta is the aspect ratio of the metric. In particular, for expander graphs, we are able to obtain constant distortion embeddings into trees in contrast with the Omega(log n) lower bound for all previous notions of embeddings. We demonstrate the algorithmic application of the new embeddings for two optimization problems: group Steiner tree and metrical task systems

オンライン予測の手法を用いたオンライン意思決定に関する研究

Tohoku University瀧本 英

Nested convex bodies are chaseable

In the Convex Body Chasing problem, we are given an initial point v0 2 Rd and an online sequence of n convex bodies F1; : : : ; Fn. When we receive Fi, we are required to move inside Fi. Our goal is to minimize the total distance traveled. This fundamental online problem was first studied by Friedman and Linial (DCG 1993). They proved an ( p d) lower bound on the competitive ratio, and conjectured that a competitive ratio depending only on d is possible. However, despite much interest in the problem, the conjecture remains wide open. We consider the setting in which the convex bodies are nested: F1 : : : Fn. The nested setting is closely related to extending the online LP framework of Buchbinder and Naor (ESA 2005) to arbitrary linear constraints. Moreover, this setting retains much of the difficulty of the general setting and captures an essential obstacle in resolving Friedman and Linial's conjecture. In this work, we give a f(d)competitive algorithm for chasing nested convex bodies in Rd

Analyzing the Flow of Information from Initial Publishing to Wikipedia

This thesis covers my efforts at researching the factors that lead to a research paper being cited by Wikipedia. Wikipedia is one of the most popular websites on the internet for quickly learning about a specific topic. It achieved this by being able to back up its claims with cited sources, many of which are research papers. I wanted to see exactly how those papers were found by Wikipedia’s editors when they write the articles. To do this, I gathered thousands of computer science research papers from arXiv.org, as well as a selection of papers that were cited by Wikipedia, so that I could examine those papers and see what made them visible and attractive to the Wikipedia editors. After I gathered the information on how and when these papers are cited, I ran a series of tests on them to learn as much as I could about what causes a paper to be cited by Wikipedia. I discovered that papers that are cited by Wikipedia tend to be more popular than papers which are not cited by Wikipedia even before they are cited but getting cited by Wikipedia can result in a boost in popularity. Wikipedia editors also tend to choose papers that either showcase a creation of the author(s) or give a general overview on a topic. I also discovered one paper that was likely added to Wikipedia by the author in an attempt at increased visibility

Ramsey-type theorems for metric spaces with applications to online problems

A nearly logarithmic lower bound on the randomized competitive ratio for the metrical task systems problem is presented. This implies a similar lower bound for the extensively studied k-server problem. The proof is based on Ramsey-type theorems for metric spaces, that state that every metric space contains a large subspace which is approximately a hierarchically well-separated tree (and in particular an ultrametric). These Ramsey-type theorems may be of independent interest.Comment: Fix an error in the metadata. 31 pages, 0 figures. Preliminary version in FOCS '01. To be published in J. Comput. System Sc