The algorithm relies heavily on the zigzag product. In 2005 Omer Reingold introduced an algorithm that solves the undirected st-connectivity problem, the problem of testing whether there is a path between two given vertices in an undirected graph, using only logarithmic space. Solving the undirected s-t connectivity problem in logarithmic space
This process continues, yielding arbitrarily large expanders.įrom the properties of the zigzag product mentioned above, we see that the product of a large graph with a small graph, inherits a size similar to the large graph, and degree similar to the small graph, while preserving its expansion properties from both, thus enabling to increase the size of the expander without deleterious effects. In each iteration the zigzag product is used in order to generate another graph whose size is increased but its degree and expansion remains unchanged. The construction is iterative, and needs as a basic building block a single, expander of constant size. In 2002 Omer Reingold, Salil Vadhan, and Avi Wigderson gave a simple, explicit combinatorial construction of constant-degree expander graphs. In graph theory, the zig-zag product of regular graphs G, H ).Īpplications Construction of constant degree expanders
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