Optimal lower bounds for multiple recurrence

Some Lower Bounds for Estrada Index

Optimal Lower Bounds for Sketching Graph Cuts

We study the space complexity of sketching cuts and Laplacian quadratic forms of graphs. We show that any data structure which approximately stores the sizes of all cuts in an undirected graph on n vertices up to a 1 + ǫ error must use Ω(n logn/ǫ) bits of space in the worst case, improving the Ω(n/ǫ) bound of [ACK16] and matching the best known upper bound achieved by spectral sparsifiers [BSS1...

Optimal Lower Bounds for Anonymous Scheduling Mechanisms

We consider the problem of designing truthful mechanisms on m unrelated machines, to minimize some optimization goal. Nisan and Ronen (1999) consider the specific goal of makespan minimization, and show a lower bound of 2, and an upper bound of m. This large gap inspired many attempts that yielded positive results for several special cases, but very partial success for the general case: the low...

Optimal lower bounds for locality sensitive hashing

We study lower bounds for Locality Sensitive Hashing (LSH) in the strongest setting: point sets in {0, 1} under the Hamming distance. Recall that H is said to be an (r, cr, p, q)-sensitive hash family if all pairs x, y ∈ {0, 1} with dist(x, y) ≤ r have probability at least p of collision under a randomly chosen h ∈ H, whereas all pairs x, y ∈ {0, 1} with dist(x, y) ≥ cr have probability at most...

Upper and lower bounds for numerical radii of block shifts

For an n-by-n complex matrix A in a block form with the (possibly) nonzero blocks only on the diagonal above the main one, we consider two other matrices whose nonzero entries are along the diagonal above the main one and consist of the norms or minimum moduli of the diagonal blocks of A. In this paper, we obtain two inequalities relating the numeical radii of these matrices and also determine ...