Rank aggregation is a task of combining the rankings of items from multiple users into a single ranking that best represents the users' rankings. Alabi et al. (AAAI'22) presents differentially-private (DP) polynomial-time approximation schemes (PTASes) and 5-approximation algorithms with certain additive errors for the Kemeny rank aggregation problem in both central and local models. In this paper, we present improved DP PTASes with smaller additive error in the central model. Furthermore, we are first to study the footrule rank aggregation problem under DP. We give a near-optimal algorithm for this problem; as a corollary, this leads to 2-approximation algorithms with the same additive error as the 5-approximation algorithms of Alabi et al. for the Kemeny rank aggregation problem in both central and local models.

We present a method for privately publishing sparse vectors with communication and computation costs that scale linearly with the number of nonzero elements. The Poisson Private Representation (PPR) framework was introduced to compress any differentially private mechanism to achieve a communication cost of O(ϵ), where ϵ is the privacy budget. However, PPR and its variant, Chunk PPR, are not well suited for publishing sparse vectors under metric differential privacy: PPR incurs exponential computation cost, while Chunk PPR requires both execution and communication costs linear in the vector dimension. As a result, their guarantees are no stronger than those of non-compressed randomized response, which for a matrix with N users, n columns, and m nonzero elements, requires Ω(nN) communication—rendering it impractical for large-scale data.

The problem of counting subgraphs or graphlets under local differential privacy is an important challenge that has attracted significant attention from researchers. However, much of the existing work focuses on small graphlets like triangles or $k$-stars. In this paper, we propose a non-interactive, locally differentially private algorithm capable of counting graphlets of any size $k$. When $n$ is the number of nodes in the input graph, we show that the expected $\ell_2$ error of our algorithm is $O(n^{k - 1})$. Additionally, we prove that there exists a class of input graphs and graphlets of size $k$ for which any non-interactive counting algorithm incurs an expected $\ell_2$ error of $\Omega(n^{k - 1})$, demonstrating the optimality of our result. Furthermore, we establish that for certain input graphs and graphlets, any locally differentially private algorithm must have an expected $\ell_2$ error of $\Omega(n^{k - 1.5})$. Our experimental results show that our algorithm is more accurate than the classical randomized response method.

In our study, we present an algorithm for publishing the count of walks and Katz centrality under local differential privacy (LDP), complemented by a comprehensive theoretical analysis. While previous research in LDP has predominantly focused on counting subgraphs with a maximum of five nodes, our work extends this to larger subgraphs. The primary challenge in such an extension lies in managing the exponentially increasing noise associated with LDP as the size of the subgraph grows. Our solution involves an algorithm for publishing the count of walks originating from each node in the graph, which subsequently enables us to publish the Katz centrality of all nodes. This algorithm incorporates multiple communication rounds and employs a clipping technique. Through both theoretical and empirical evaluation, we demonstrate that our algorithm achieves has a relatively small bias and variance, showing significant improvements over both the randomized response method and non-clipping algorithms. Additionally, our approach to estimating Katz centrality successfully identifies up to 90% of the nodes with the highest centrality values.

This paper presents efficient algorithms, designed to leverage SIMD for performing additions and Montgomery reductions on integers larger than 512 bits. The existing algorithms encounter inefficiencies when parallelized using SIMD due to extensive dependencies in both operations, particularly noticeable in ARM’s SVE where SIMD operations are costly. To mitigate this problem, a novel addition algorithm is introduced that simulates the addition of large integers using a smaller addition, quickly producing the same set of carries. These carries are then utilized to perform parallel additions on large integers. For Montgomery reductions, serial multiplications are replaced with precomputations that can be effectively calculated using SIMD extensions. Experimental evidence demonstrates that these proposed algorithms substantially enhance the performance of state-of-the-art implementations of several post-quantum cryptography algorithms. Notably, they deliver a 30% speed-up from the latest CTIDH implementation, an 11% speed-up from the latest CSIDH implementation in AVX-512 processors, and a 7% speed-up from Microsoft’s standard PQCrypto-SIDH for SIKEp503 on A64FX.

This work presents a mechanism to debias polynomial functions computed from locally differentially private data. Local differential privacy is a widely used privacy notion where users add Laplacian noise to their information before submitting it to a central server. That, however, causes bias when we calculate non-linear functions based on those noisy information. Our proposed recursive algorithm debiases these functions, with a calculation time of O(r n log n), where r is the polynomial degree and n is the number of users. We evaluate our method on the problems of k-star counting and variance estimation, comparing results with state-of-the-art algorithms. The results show that our method not only eliminates bias, but also provides at least 100 times more accuracy than previous works.

Several works recently focus on monitoring air quality of critical areas using sensors attached to buses. They aim to monitor the maximum number of critical areas using a limited number of sensors. In practice, we may want to have information for all critical areas. We work on the problem of covering all the areas using the minimum number of sensors in this work. We show that, even when the bus routes are not pre-defined, the problem is NP-hard and is significantly harder than the problem of the previous works. Then, we develop two algorithms for the case that the routes are pre-defined. Those algorithms include a fixed parameter tractability and a 2-approximation algorithm for a special case of the problem. Our experiment results show that, although we usually give the similar number of sensors as the algorithm in the previous works, our algorithms have a shorter computation time than the classical greedy algorithm.

The land-use optimization involves divisions of land into subregions to obtain spatial configuration of compact subregions and desired connections among them. Computational geometry-based algorithms, such as Voronoi diagram, are known to be efficient and suitable for iterative design processes to achieve land-use optimization. However, such algorithms assume that generating point positions are given as inputs, while we usually do not know the positions in advance. In this study, we propose a method to automatically calculate the suitable point positions. The method uses (1) semidefinite programming to approximate locations while maintaining relative positions among locations; and (2) gradient descent to iteratively update locations subject to area constraints. We apply the proposed framework to a practical case at Chiang Mai University and compare its performance with a benchmark, the differential genetic algorithm. The results show that the proposed method is 28 times faster than the differential genetic algorithm, while the resulting land allocation error is slightly larger than that of the benchmark but still acceptable. Additionally, the output does not contain disconnected areas, as found in all evolutionary computations, and the compactness is almost equal to the maximum possible value.

Using graph clustering, we improve accuracy of Kronecker social networks which are protected by differential privacy. Ensuring the differential privacy implicates addition of marginal changes to the network and publishing the modified network data. In many cases, it induces a large gap between the original network and the modified graph statistics, such that very little useful information can be inferred from the published graph. We use the fact that network structures in all graph clusters are similar, to improve the utility of the publication methods based on Kronecker graphs. Instead of anonymizing the social network as a whole, we anonymize each cluster of the network separately, and combine the sanitized results thereafter. We justify why this idea provides an anonymized social network with high utility and also prove that our output social network ensures rigorous differential privacy guarantees. Our experimental results show that our mechanism exhibits good agreement of the structural properties with the real graphs, and outperforms the existing anonymization techniques for certain utility measures.

In this paper, we present a Branch and Bound algorithm called QuickBB for computing the treewidth of an undirected graph. This algorithm performs a search in the space of perfect elimination ordering of vertices of the graph. The algorithm uses novel pruning and propagation techniques which are derived from the theory of graph minors and graph isomorphism. We present a new algorithm called minor-min-width for computing a lower bound on treewidth that is used within the branch and bound algorithm and which improves over earlier available lower bounds. Empirical evaluation of QuickBB on randomly generated graphs and benchmarks in Graph Coloring and Bayesian Networks shows that it is consistently better than complete algorithms like QuickTree [Shoikhet and Geiger, 1997] in terms of cpu time. QuickBB also has good anytime performance, being able to generate a better upper bound on treewidth of some graphs whose optimal treewidth could not be computed up to now.

Segment Routed Traffic Engineering is emerging as an important application for network operators to manage resource utilization by using segment routing paths as candidates for route selection. In order to facilitate the network operator demands, a traffic engineering program should be fast and efficient. These two characteristics are very essential since the traffic engineering program must be invoked periodically in short intervals. The segment routing paths can be constructed by concatenating the shortest paths between two nodes such that there is a path from source to destination. We are interested in the problem to find intermediate nodes to construct segment routing paths minimizing the maximum link utilization. However, the existing approaches have the shortcomings that either they require a substantial amount of time to find a solution or they must sacrifice a considerable amount of link utilization. To address these issues, we propose to limit the number of intermediate node candidates by using a bounded stretch constraint relative to the shortest path of the source-destination pair. Then, we evaluate the computation time and link utilization against the existing work. We show that the bounded stretch constraint helps reduce the computation time while a near optimal link utilization can be achieved.

We aim to decrease a communication cost of a network that uses compressive sensing, a technique that allows us to recover global information of sparse data by using only a small set of samples. Despite efficiency of the technique, collecting information from all samples is usually costly. Because the samples from previous works usually spread around the network, setting up a number of base stations does not help reducing the cost. In this paper, we propose a method that can utilize the base stations, while aiming to minimize the recovery error of compressive sensing. Based on Theorem 1 in [1] by Xu et al., which is for cost-aware compressive sensing, we derive a mathematical program that aims to maximize the preciseness in the setting. Then, we approximate the program by a convex quadratic program and prove that the approximation ratio is 0.63. Our simulation results show that, by using the coverage, the sampling error is decreased by at most thirty times.

Recently, many algorithms are proposed to find a communication flow that is robust against k-edges failures. That flow can be weaker, if attackers can obtain forwarding information in each router. In this paper, we propose an algorithm that find a forwarding algorithm maximizing the remaining flow in that situation. We show that Kishimoto's multiroute flow is a (k + 1)-approximation algorithm for the problem, when the route number is k + 1. When the route number is optimally chosen, we show that the multiroute flow is a 2-approximation algorithm for most of randomly generated graphs. Our experimental results show that our algorithm has 15%-37% better performance than max-flow algorithm.

This paper presents a new analytical model to analyze the performance of a probabilistic caching scheme with various cache replacement policies in content-centric networks. The cache replacement policies include Random Replacement (RR), First In First Out (FIFO), and Least Recently Used (LRU). This analytical model is based on Markov chains under Independent Reference Model (IRM) and Zero Download Delay (ZDD) assumption. A closed-form expression of the stationary distribution of cache state is derived and is used to compute the hit rates of caching systems. Moreover, we use this model to establish several important properties of the probabilistic caching scheme as well as the guidelines on effectively using it. Results of computer simulations show that the proposed analytical solution can model the probabilistic caching scheme very accurately.

Scheduling sensors to prolong the lifetime of covering targets in the field is one of the central problems in wireless sensor networks. This problem, called the maximum lifetime coverage problem (MLCP), can be formulated as a linear programming problem with exponential size, and has a constant-factor approximation algorithm. In reality, however, batteries of sensors have recovery effects, which is a phenomenon that the deliverable energy in batteries can be replenished by itself if it is left idling for sufficient duration. Thanks to that effects, we can obtain much longer lifetime of sensors if each sensor is forced to take a sleep at some interval. In this paper, we introduce two models that extend the MLCP, incorporating battery recovery effects. The first model represents battery recovery effects in a deterministic way, while the second one uses a probabilistic model to imitate the effects. We then propose efficient algorithms that work for both models by extending approximation algorithms for the original MLCP. Numerical experiments show that the lifetime of our schedule is 10–40% longer than one without battery recovery effects.