Farzam Ebrahimnejad

University of Washington Seattle | UW · Department of Computer Science and Engineering

We present an $O((\log n)^2)$-competitive algorithm for metrical task systems (MTS) on any $n$-point metric space that is also $1$-competitive for service costs. This matches the competitive ratio achieved by Bubeck, Cohen, Lee, and Lee (2019) and the refined competitive ratios obtained by Coester and Lee (2019). Those algorithms work by first rand...

Consider an infinite planar graph with uniform polynomial growth of degree d>2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d > 2$$\end{document}. Many examples of su...

Benjamini and Papasoglou (2011) showed that planar graphs with uniform polynomial volume growth admit $1$-dimensional annular separators: The vertices at graph distance $R$ from any vertex can be separated from those at distance $2R$ by removing at most $O(R)$ vertices. They asked whether geometric $d$-dimensional graphs with uniform polynomial vol...

Consider an infinite planar graph with uniform polynomial growth of degree d > 2. Many examples of such graphs exhibit similar geometric and spectral properties, and it has been conjectured that this is necessary. We present a family of counterexamples. In particular, we show that for every rational d > 2, there is a planar graph with uniform polyn...

A deterministic finite automaton (DFA) separates two strings w and x if it accepts w and rejects x. The minimum number of states required for a DFA to separate w and x is denoted by sep(w,x). The present paper shows that the difference |sep(w,x)-sep(wR,xR)| is unbounded for a binary alphabet; here wR stands for the mirror image of w. This solves an...

The function $sep(w,x)$ is defined as the size of the smallest DFA that accepts $w$ and rejects $x$. It has remained unsolved until now that whether the difference $| sep(w,x) - sep(w^R, x^R)|$ is bounded or not. In this paper, we prove by construction that this difference is unbounded.