Related papers: Optimal Threshold Padlock Systems
We study the problems of covering or partitioning a polygon $P$ (possibly with holes) using a minimum number of small pieces, where a small piece is a connected sub-polygon contained in an axis-aligned unit square. For covering, we seek to…
We consider the Bilevel Knapsack with Interdiction Constraints, an extension of the classic 0-1 knapsack problem formulated as a Stackelberg game with two agents, a leader and a follower, that choose items from a common set and hold their…
Given a reference set $R$ of $n$ points and a query set $Q$ of $m$ points in a metric space, this paper studies an important problem of finding $k$-nearest neighbors of every point $q \in Q$ in the set $R$ in a near-linear time. In the…
We consider a memory allocation problem that can be modeled as a version of bin packing where items may be split, but each bin may contain at most two (parts of) items. A 3/2-approximation algorithm and an NP-hardness proof for this problem…
We investigate the problem of maintaining an encoded distributed storage system when some nodes contain adversarial errors. Using the error-correction capabilities that are built into the existing redundancy of the system, we propose a…
This note analyses one of the existing space efficient secret sharing schemes and suggests vulnerabilities in its design. We observe that the said algorithm fails for certain choices of the set of secrets and there is no reason for…
Motivated by emerging resource allocation and data placement problems such as web caches and peer-to-peer systems, we consider and study a class of resource allocation problems over a network of agents (nodes). In this model, nodes can…
We consider the problem of estimating the value of MAX-CUT in a graph in the streaming model of computation. At one extreme, there is a trivial $2$-approximation for this problem that uses only $O(\log n)$ space, namely, count the number of…
We study the complexity of lattice problems in a world where algorithms, reductions, and protocols can run in superpolynomial time, revisiting four foundational results: two worst-case to average-case reductions and two protocols. We also…
We introduce the problem of minimal actuator placement in a linear control system so that a bound on the minimum control effort for a given state transfer is satisfied while controllability is ensured. We first show that this is an NP-hard…
We study the properties of secret sharing schemes, where a random secret value is transformed into shares distributed among several participants in such a way that only the qualified groups of participants can recover the secret value. We…
The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local…
The $k$-Minimum Values (\kmv) data sketch algorithm stores the $k$ least hash keys generated by hashing the items in a dataset. We show that compression based on ordering the keys and encoding successive differences can offer $O(\log n)$…
We critically analyze the results and claims in [Physics Letters A 373 (2009) 901-904]. We show that the strong security leak appeared in the simulations is only an artifact and not caused by "multiple reflections". Since no wave modes…
In the study of differential privacy, composition theorems (starting with the original paper of Dwork, McSherry, Nissim, and Smith (TCC'06)) bound the degradation of privacy when composing several differentially private algorithms. Kairouz,…
Consider a region that requires to be protected from unauthorized penetrations. The border of the region, modeled as a unit line segment, consists of high priority segments that require the highest level of protection separated by low…
A Quantum Key Distribution (QKD) protocol describes how two remote parties can establish a secret key by communicating over a quantum and a public classical channel that both can be accessed by an eavesdropper. QKD protocols using…
We consider a cooperative wireless network in the presence of one of more eavesdroppers, and exploit node cooperation for achieving physical (PHY) layer based security. Two different cooperation schemes are considered. In the first scheme,…
Let $S$ be a pool of $s$ parties and Alice be the dealer. In this paper, we propose a scheme that allows the dealer to encrypt messages in such a way that only one authorized coalition of parties (which the dealer chooses depending on the…
Large-scale multi-agent cooperative control problems have materially enjoyed the scalability, adaptivity, and flexibility of decentralized optimization. However, due to the mandatory iterative communications between the agents and the…