Some lower bounds in dynamic networks with oblivious adversaries

Some Lower Bounds in Dynamic Networks with Oblivious Adversaries

This paper considers several closely-related problems in synchronous dynamic networks with oblivious adversaries, and proves novel Ω(d + poly(m)) lower bounds on their time complexity (in rounds). Here d is the dynamic diameter of the dynamic network and m is the total number of nodes. Before this work, the only known lower bounds on these problems under oblivious adversaries were the trivial Ω...

Information Spreading in Dynamic Networks Under Oblivious Adversaries

We study the problem of all-to-all information exchange, also known as gossip, in dynamic networks controlled by an adversary that can modify the network arbitrarily from one round to another, provided that the network is always connected. In the gossip problem, there are n tokens arbitrarily distributed among the n network nodes, and the goal is to disseminate all the n tokens to every node. O...

Some Lower Bounds for Estrada Index

Lower Bounds for Oblivious Subspace Embeddings

An oblivious subspace embedding (OSE) for some ε, δ ∈ (0, 1/3) and d ≤ m ≤ n is a distribution D over Rm×n such that for any linear subspace W ⊂ Rn of dimension d, P Π∼D (∀x ∈W, (1− ε)‖x‖2 ≤ ‖Πx‖2 ≤ (1 + ε)‖x‖2) ≥ 1− δ. We prove that any OSE with δ < 1/3 must have m = Ω((d + log(1/δ))/ε2), which is optimal. Furthermore, if every Π in the support of D is sparse, having at most s non-zero entries...

Lower bounds for Quantum Oblivious Transfer

Oblivious transfer is a fundamental primitive in cryptography. While perfect information theoretic security is impossible, quantum oblivious transfer protocols can limit the dishonest players’ cheating. Finding the optimal security parameters in such protocols is an important open question. In this paper we show that every 1-out-of-2 oblivious transfer protocol allows a dishonest party to cheat...