ECCC-Report TR23-089https://eccc.weizmann.ac.il/report/2023/089Comments and Revisions published for TR23-089en-usTue, 09 Jan 2024 06:37:22 +0200
Revision 1
| New Explicit Constant-Degree Lossless Expanders |
Louis Golowich
https://eccc.weizmann.ac.il/report/2023/089#revision1 We present a new explicit construction of onesided bipartite lossless expanders of constant degree, with arbitrary constant ratio between the sizes of the two vertex sets. Our construction is simpler to state and analyze than the only prior construction of Capalbo, Reingold, Vadhan, and Wigderson (2002), and achieves improvements in some parameters.
We construct our lossless expanders by imposing the structure of a constant-sized lossless expander "gadget" within the neighborhoods of a large bipartite spectral expander; similar constructions were previously used to obtain the weaker notion of unique-neighbor expansion. Our analysis simply consists of elementary counting arguments and an application of the expander mixing lemma.Tue, 09 Jan 2024 06:37:22 +0200https://eccc.weizmann.ac.il/report/2023/089#revision1
Paper TR23-089
| New Explicit Constant-Degree Lossless Expanders |
Louis Golowich
https://eccc.weizmann.ac.il/report/2023/089 We present a new explicit construction of onesided bipartite lossless expanders of constant degree, with arbitrary constant ratio between the sizes of the two vertex sets. Our construction is simpler to state and analyze than the prior construction of Capalbo, Reingold, Vadhan, and Wigderson (2002).
We construct our lossless expanders by imposing the structure of a constant-sized lossless expander "gadget" within the neighborhoods of a large bipartite spectral expander; similar constructions were previously used to obtain the weaker notion of unique-neighbor expansion. Our analysis simply consists of elementary counting arguments and an application of the expander mixing lemma.Thu, 15 Jun 2023 09:20:23 +0300https://eccc.weizmann.ac.il/report/2023/089