149 citations · 560 across the 62 of their papers we have counts for
6 papers · 1 filter
Abelian logic gates
Alexander E. Holroyd, Lionel Levine, Peter Winkler
An abelian processor is an automaton whose output is independent of the order of its inputs. Bond and Levine have proved that a network of abelian processors performs the same comp…
Constrained percolation in two dimensions
Alexander Holroyd, Zhongyang Li
We prove absence of infinite clusters and contours in a class of critical constrained percolation models on the square lattice. The percolation configuration is assumed to satisfy…
Representing Permutations with Few Moves
Sergey Bereg, Alexander E. Holroyd, Lev Nachmanson +1
Consider a finite sequence of permutations of the elements 1,...,n, with the property that each element changes its position by at most 1 from any permutation to the next. We call…
GraphMaps: Browsing Large Graphs as Interactive Maps
Lev Nachmanson, Roman Prutkin, Bongshin Lee +3
Algorithms for laying out large graphs have seen significant progress in the past decade. However, browsing large graphs remains a challenge. Rendering thousands of graphical eleme…
Games on Random Boards
Riddhipratim Basu, Alexander E. Holroyd, James B. Martin +1
We consider the following two-player game on a graph. A token is located at a vertex, and the players take turns to move it along an edge to a vertex that has not been visited befo…
Percolation games, probabilistic cellular automata, and the hard-core model
Alexander E. Holroyd, Irène Marcovici, James B. Martin
Let each site of the square lattice be independently assigned one of three states: a \textit{trap} with probability , a \textit{target} with probability , and…