We consider the heavy-hitters and F_p moment estimation problems in the sliding window model. For F_p moment estimation with 1 < p ≤ 2, we show that it is possible to give a (1± ε) multiplicative approximation to the F_p moment with 2/3 probability on any given window of size n using Õ(1/(ε^p)log² n + 1/(ε²)log n) bits of space. We complement this result with a lower bound showing that our algorithm gives tight bounds up to factors of log log n and log1/(ε). As a consequence of our F₂ moment estimation algorithm, we show that the heavy-hitters problem can be solved on an arbitrary window using O(1/(ε²)log² n) space which is tight.

Recently differential privacy has been used for a number of streaming, data structure, and dynamic graph problems as a means of hiding the internal randomness of the data structure, so that multiple possibly adaptive queries can be made without sacrificing the correctness of the responses. Although these works use differential privacy to show that for some problems it is possible to tolerate $T$ queries using $\widetilde{O}(\sqrt{T})$ copies of a data structure, such results only apply to numerical estimation problems, and only return the cost of an optimization problem rather than the solution itself. In this paper we investigate the use of differential privacy for adaptive queries to search problems, which are significantly more challenging since the responses to queries can reveal much more about the internal randomness than a single numerical query. We focus on two classical search problems: nearest neighbor queries and regression with arbitrary turnstile updates. We identify key parameters to these problems, such as the number of $c$-approximate near neighbors and the matrix condition number, and use different differential privacy techniques to design algorithms returning the solution point or solution vector with memory and time depending on these parameters. We give algorithms for each of these problems that achieve similar tradeoffs.

The escalating complexity of networks due to advancements in cloud computing, IoT, and data centers necessitates a shift towards more adaptable and scalable network architectures. Software Defined Networking (SDN) has risen as a prominent solution, offering a separation of control and data planes to bolster flexibility and manageability. However, network failures remain an inherent risk, undermining the reliability of both traditional and SDN environments. This paper presents BioWarp, a novel SDN failure recovery scheme that integrates bio-mimetic optimization with a Weighted-Cost Multi-Path (WCMP) routing approach. BioWarp confronts the unique challenges of SDN, such as TCAM overflow and controller computation stress, by proposing a hybrid strategy that merges the strengths of proactive and reactive recovery methods. We introduce a flow label based aggregation method to alleviate the burden on flow tables and controller resources. The Coati Optimization Algorithm (COA), inspired by the behaviors of coatis, is adapted to optimize weight update in real-time, facilitating rapid and efficient recovery from network faults. Simulation experiments are conducted to substantiate the scheme’s efficacy, demonstrating improved recovery times and resource management without compromising network stability.