An Infinite Pebble Game and Applications

An Infinite Pebble Game and Applications

An analysis of Bennett's pebble game

Bennett's pebble game 1, 2] was introduced to obtain better time/space tradeoos in the simulation of standard Turing machines by reversible ones. So far only upper bounds for the tradeoo based on the pebble game have been published. Here we give a recursion for the time optimal solution of the pebble game given a space bound. We analyze the recursion to obtain an explicit asymptotic expression ...

Pebble game algorithms and sparse graphs

A multi-graph G on n vertices is (k, l)-sparse if every subset of n ≤ n vertices spans at most kn − l edges. G is tight if, in addition, it has exactly kn − l edges. For integer values k and l ∈ [0, 2k), we characterize the (k, l)-sparse graphs via a family of simple, elegant and efficient algorithms called the (k, l)-pebble games.

Sparse Hypergraphs and Pebble Game Algorithms

A hypergraph G = (V, E) is (k, `)-sparse if no subset V ′ ⊂ V spans more than k|V ′|−` hyperedges. We characterize (k, `)-sparse hypergraphs in terms of graph theoretic, matroidal and algorithmic properties. We extend several well-known theorems of Haas, Lovász, Nash-Williams, Tutte, and White and Whiteley, linking arboricity of graphs to certain counts on the number of edges. We also address t...

An Algorithm for Two-Dimensional Rigidity Percolation: The Pebble Game

Many important macroscopic properties of materials depend upon the number of microscopic degrees of freedom. The task of counting the number of such degrees of freedom can be computationally very expensive. We describe a new approach for this calculation which is appropriate for twodimensional, glass-like networks, building upon recent work in graph rigidity. This purely combinatorial algorithm...