Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, October 08, 2024, 12:15 pm

Duration: 30 minutes

Location: OAT X 11 (floor 19)

Speaker: Rares Buhai

Semirandom Planted Clique and the Restricted Isometry Property

We give a simple, greedy O(n^{omega + 2.5})-time algorithm to list-decode planted cliques in a semirandom model introduced in [CSV17] following [FK01] that succeeds whenever the size of the planted clique is k >= O(sqrt{n} log^2 n). In the model, the edges touching the vertices in the planted k-clique are drawn independently with probability p = 1/2 while the edges not touching the planted clique are chosen by an adversary in response to the random choices. Our result shows that the computational threshold in the semirandom setting is within a O(log^2 n) factor of the information-theoretic one [Ste17] thus resolving an open question of Steinhard. This threshold also essentially matches the conjectured computational threshold for the well-studied special case of fully random planted clique.

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