Explicit expanders of every degree and size
WebFor every constant d ≥ 3 and ϵ > 0, we give a deterministic poly ( n) -time algorithm that … WebFeb 2, 2024 · We study the problem of constructing explicit sparse imbalanced bipartite unique-neighbor expanders. For large enough d_1 and d_2, we give a strongly explicit construction of an infinite family of (d_1,d_2)-biregular graph (assuming d_1 ≤ d_2) where all sets S with fewer than 1/d_1^3 fraction of vertices have Ω(d_1· S ) unique-neighbors.
Explicit expanders of every degree and size
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WebEntropy Waves, the Zig-Zag Graph Product, and New Constant-Degree Expanders and Extractors Omer Reingold Salil Vadhan Avi Wigderson February 23, 2001 Abstract Themaincontributiono
WebExpander graphs have also found some applications in various areas of pure mathematics [KR83, Lub94, Gro00, LP01]. Standard probabilistic arguments ([Pin73]) show that almost every constant-degree ( 3) graph is an expander. However, explicit and efficient construction of such graphs (which is required by most of the WebJan 1, 2011 · Explicit expanders of every degree and size. Preprint. Mar 2024; Noga Alon; ... This property is optimal and leads to the best known explicit expander graphs. The girth ofX is asymptotically ≧4/ ...
WebExplicit expanders of every degree and size Noga Alon ∗ Abstract An (n;d; )-graph is a … http://dimacs.rutgers.edu/TechnicalReports/abstracts/2001/2001-09.html
Web1. Introduction. Although there is no standard definition of life [1–7], the literature often states that a living system tends to reduce its entropy, defying the second law of thermodynamics to sustain its non-equilibrium (NEQ) existence.However, conforming to the second law of thermodynamics, adjudication between the entropy reduction and augmentation of an …
WebExplicit Expanders of Every Degree and Size. 01 February 2024. Noga Alon. The back-and-forth method and computability without delay. 01 October 2024. Alexander G. Melnikov & Keng Meng Ng. QuickXsort: A Fast Sorting Scheme in Theory and Practice. 22 October 2024. Stefan Edelkamp, Armin Weiß & Sebastian Wild. clifton funeral homeWebIt is known that random graphs are good expanders. It is easier to analyze bipartite expanders which are deflned as follows. Deflnition 3. A bipartite graph G on n+n vertices L[R is called a (d;fl)-expander, if the degrees in L are d and any set of vertices S ‰ L of size jSj • n=d has at least fljSj neighbors in R. Theorem 1. clifton from ready to love instagramWebStandard probabilistic arguments ([39]) show that almost every constant-degree ( 3) graph is an expander. ... 29, 33, 35] provided such highly explicit families of constant-degree expanders. All of these constructions are based on groups, and their analysis often appeals to ... fixed size expander “seed” graph , from which all others are ... clifton friends of the shelter clifton nj