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Electronic Colloquium on Computational Complexity

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Reports tagged with zig-zag product:
TR05-022 | 19th February 2005
Omer Reingold, Luca Trevisan, Salil Vadhan

Pseudorandom Walks in Biregular Graphs and the RL vs. L Problem

Motivated by Reingold's recent deterministic log-space algorithm for Undirected S-T Connectivity (ECCC TR 04-94), we revisit the general RL vs. L question, obtaining the following results.

1. We exhibit a new complete problem for RL: S-T Connectivity restricted to directed graphs for which the random walk is promised to have ... more >>>

TR05-092 | 23rd August 2005
Eyal Rozenman, Salil Vadhan

Derandomized Squaring of Graphs

We introduce a "derandomized" analogue of graph squaring. This
operation increases the connectivity of the graph (as measured by the
second eigenvalue) almost as well as squaring the graph does, yet only
increases the degree of the graph by a constant factor, instead of
squaring the degree.

One application of ... more >>>

TR24-013 | 26th January 2024
Oded Goldreich

On locally-characterized expander graphs (a survey)

Revisions: 1

We consider the notion of a local-characterization of an infinite family of unlabeled bounded-degree graphs.
Such a local-characterization is defined in terms of a finite set of (marked) graphs yielding a generalized notion of subgraph-freeness, which extends the standard notions of induced and non-induced subgraph freeness.

We survey the work ... more >>>

TR24-047 | 8th March 2024
Oded Goldreich

On the query complexity of testing local graph properties in the bounded-degree graph model

Revisions: 1

We consider the query complexity of testing local graph properties in the bounded-degree graph model.
A local property is defined in terms of forbidden subgraphs that are augmented by degree information, where the latter account also for neighbors that are not in the subgraph.
Indeed, this formulation yields a generalized ... more >>>

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