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8 papers · 1 filter
Rigid Components of Random Graphs
Louis Theran
The planar rigidity problem asks, given a set of m pairwise distances among a set P of n unknown points, whether it is possible to reconstruct P, up to a finite set of possibilitie…
The arithmetic of trees
Adriano Bruno, Dan Yasaki
The arithmetic of the natural numbers can be extended to arithmetic operations on planar binary trees. This gives rise to a non-commutative arithmetic theory. In this exposition, w…
Sparsity-certifying Graph Decompositions
Ileana Streinu, Louis Theran
We describe a new algorithm, the -pebble game with colors, and use it obtain a characterization of the family of -sparse graphs and algorithmic solutions to a f…
Sparse Hypergraphs and Pebble Game Algorithms
Ileana Streinu, Louis Theran
A hypergraph is -sparse if no subset spans more than hyperedges. We characterize -sparse hypergraphs in terms of graph theo…
Pebble Game Algorithms and Sparse Graphs
Audrey Lee, Ileana Streinu
A multi-graph on vertices is -sparse if every subset of vertices spans at most edges. is {\em tight} if, in addition, it has exactly $k…
A Reciprocity Theorem for Monomer-Dimer Coverings
N. Anzalone, J. Baldwin, I. Bronshtein +1
The problem of counting monomer-dimer coverings of a lattice is a longstanding problem in statistical mechanics. It has only been exactly solved for the special case of dimer cover…