Approximation Algorithm Research Articles

Core characteristics of sublingual veins analysis and its relationship with hypertension.

The sublingual vein (SV) is a specialized diagnostic method used in Traditional Chinese Medicine (TCM). Despite its ability to objectively reflect blood flow, SV is often overlooked in clinical practice. This study aims to analyze the core characteristics of SV and investigate the in-depth relationship between its digital characteristics and hypertension. The goal is to find a link between SV and hypertension and break out of the current situation. Modern digital analysis techniques were applied to the traditional SV diagnostic theory. In a controlled study with 204 participants, the digital characteristics of SV were documented using TFDA-1, and its color value was analyzed using TDAS. Morphological characteristics of SV, such as trunklength, width, and tortuosity, were examined by combining computer vision with expert interpretation. This involved the application of automatic ranging methods and a rectangular approximation algorithm, which are novel approaches in the field of TCM. The t-test and Mann-Whitney U test were used to analyze the digital characteristics of SV in hypertension. Binary logistic regression and neural network models were established using machine learning to explore the deep relationship between SV characteristics and hypertension. There was a significant difference of the tortuosity of SV between the two groups (Z=-2.629, p= 0.009). The results revealed thick width of SV (OR = 2.64, 95% CI: 1.02-6.79) was the risk factor for hypertension. Addition of SV characteristics improved overall percent correct for hypertension prediction to 80%. TCM method of diagnosis of SV has been greatly expanded in terms of technical means, and the close relationship between SV and hypertension has been found in clinical data.

Improved lower bound for differentially private facility location

We consider the differentially private (DP) facility location problem in the so called super-set output setting proposed by Gupta et al. [13]. The current best known expected approximation ratio for an ϵ-DP algorithm is O(log⁡nϵ) due to Cohen-Addad et al. [3] where n denote the size of the metric space, meanwhile the best known lower bound is Ω(1/ϵ)[8].In this short note, we give a lower bound of Ω˜(min⁡{log⁡n,log⁡nϵ}) on the expected approximation ratio of any ϵ-DP algorithm, which is the first evidence that the approximation ratio has to grow with the size of the metric space.

Multi-Connectivity for Multicast Video Streaming in Cellular Networks

The escalating demand for high-quality video streaming poses a major challenge for communication networks today. Catering to these bandwidth-hungry video streaming services places a huge burden on the limited spectral resources of communication networks, limiting the resources available for other services as well. Large volumes of video traffic can lead to severe network congestion, particularly during live streaming events, which require sending the same content to a large number of users simultaneously. For such applications, multicast transmission can effectively combat network congestion while meeting the demands of all the users by serving groups of users requesting the same content over shared spectral resources. Streaming services can further benefit from multi-connectivity, which allows users to receive content from multiple base stations simultaneously. Integrating multi-connectivity within multicast streaming can improve the system resource utilization while also providing seamless connectivity to multicast users. Toward this end, this work studied the impact of using multi-connectivity (MC) alongside wireless multicast for meeting the resource requirements of video streaming. Our findings show that MC substantially enhances the performance of multicast streaming, particularly benefiting cell-edge users who often experience poor channel conditions. We especially considered the number of users that can be simultaneously served by multi-connected multicast systems. It was observed that about 60% of the users that are left unserved under single-connectivity multicast are successfully served using the same resources by employing multi-connectivity in multicast transmissions. We prove that the optimal resource allocation problem for MC multicast is NP-hard. As a solution, we present a greedy approximation algorithm with an approximation factor of (1−1/e). Furthermore, we establish that no other polynomial-time algorithm can offer a superior approximation. To generate realistic video traffic patterns in our simulations, we made use of traces from actual videos. Our results clearly demonstrate that multi-connectivity leads to significant enhancements in the performance of multicast streaming.

Rectilinear convex hull of points in 3D and applications

AbstractLet P be a set of n points in $$\mathbb {R}^3$$ R 3 in general position, and let RCH(P) be the rectilinear convex hull of P. In this paper we obtain an optimal $$O(n\log n)$$ O ( n log n ) time and O(n) space algorithm to compute RCH(P). We also obtain an efficient $$O(n\log ^2 n)$$ O ( n log 2 n ) time and $$O(n\log n)$$ O ( n log n ) space algorithm to compute and maintain the set of vertices of the rectilinear convex hull of P as we rotate $${\mathbb {R}}^3$$ R 3 around the Z-axis. We study some combinatorial properties of the rectilinear convex hulls of point sets in $$\mathbb {R}^3$$ R 3 . Finally, as an application of the obtained results, we show an approximation algorithm to an optimization fitting problem in $$\mathbb {R}^3$$ R 3 .

Reinforcement Learning Approaches for Exploring Discrepancy Variations: Implications for Supply Chain Optimization

Combinatorics discrepancy theory studies the ways in which a given state deviates from the ideal. A set system's disparity in its classical form has been shown to be bound in certain situations. Though they may not hold for other types of discrepancy, no mathematician has been able to produce an example that defies these limits as of yet. Due to the large number of set systems (kmn for m sets and n elements, each choosing one of k possible values), it is not viable to use traditional techniques, such as human reasoning or computer brute forcing, to identify the few set systems with a significant discrepancy. However, in a 2021 preprint, Adam Zsolt Wagner shows how the deep cross-entropy method—a popular Neural Network (NNs)-based Reinforcement-Learning (RL) technique—could effectively find examples that disprove open conjectures in two other combinatorial subfields: pattern avoidance and graph theory. Therefore, in light of these encouraging findings, we wondered if Wagner's method could help us find examples that defy the upper bound of discrepancy variations. To start answering this question, we examined whether Wagner's approach might be extended to find set systems that exhibit significant inconsistencies, either as classical or variant (prefix and fractional in our instance) systems. Our findings could help approximation algorithms, which employ discrepancy theory to tackle certain problems, as well as discrepancy theory itself.

A 3-Approximation Algorithm for Uniform Capacitated Facility Location Problem with Penalties

We introduce an algorithm based on local search for “Uniform Capacitated Facility Location Problem with Penalties (UCFLPP)” and analyze the same. The algorithm is same as given by Korupolu et al. for the “Uniform Capacitated Facility Location Problem (UCFLP)”. Aggarwal et al. in their work proved that the algorithm given by Korupolu et al. is a 3-factor approximation algorithm for UCFLP. We extend idea of Aggarwal et al. to show that the same algorithm works for the problem with penalty incorporated. It has the same approximation guarantee for UCFLPP, as given by them. This improves upon the current best of 5.732 factor for the problem, which is an LP based algorithm by Lv and Wu.

Iterative layerwise training for the quantum approximate optimization algorithm

Iterative layerwise training for the quantum approximate optimization algorithm

Memory and Communication Efficient Federated Kernel k-Means.

A federated kernel k -means (FedKKM) algorithm is developed in this article to conduct distributed clustering with low memory consumption on user devices. In FedKKM, a federated eigenvector approximation (FEA) algorithm is designed to iteratively determine the low-dimensional approximate vectors of the transformed feature vectors, using only low-dimensional random feature vectors. To maintain high communication efficiency in each iteration of FEA, a communication-efficient Lanczos algorithm (CELA) is further designed in FEA to reduce the communication cost. Based on the low-dimensional approximate vectors, the clustering result is obtained by leveraging a distributed linear k -means algorithm. A theoretical analysis shows that: 1) FEA has a convergence rate of O(1/T) , where T is the number of iterations; 2) the scalability of FedKKM is not affected by the dataset size since the communication cost of FedKKM is independent of the number of users' data; and 3) FedKKM is a (1+ϵ) approximation algorithm. The experimental results show that FedKKM achieves the comparable clustering quality to that of a centralized kernel k -means. Compared with state-of-the-art schemes, FedKKM reduces the memory consumption on user devices by up to 94% and also reduces the communication cost by more than 40%.

Combinatorial Benders decomposition for single machine scheduling in additive manufacturing with two-dimensional packing constraints

This paper addresses a single-machine scheduling problem in additive manufacturing (AM). We focus on the direct metal laser sintering (DMLS) technology of an AM process, where parts can be produced simultaneously in a batch. In this problem, we consider simultaneously the assignment of parts to batches and the packing of parts onto two-dimensional surfaces of the build chamber to minimize the makespan objective. To solve this problem, a mixed integer linear programming model is formulated, and an approximation algorithm is proposed, followed by an exact algorithm based on combinatorial Benders decomposition method with various Benders cuts and acceleration strategies (Algorithm CBD). Finally, we conduct a comprehensive computational study to verify the efficiency of our proposed Algorithm CBD. The computational results show that our proposed Algorithm CBD can effectively solve the test instances with different sizes.

Predictive Service Provisioning With Online Learning in Wireless Edge Networks

Mobile Edge Computing (MEC) technology can be implemented at cellular base stations, enabling flexible and configurable provisions of services for mobile users to access. Nevertheless, the conventional solutions mainly focus on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">statical</i> service provisioning, which ignores the dynamic nature of the arriving service requests. In this work, we first conduct comprehensive data-driven observations on over 4 million service requests throughout 9,800 base stations. Our key findings suggest that users' demands intrinsically exhibit spatial and temporal patterns, which inevitably lead to performance degradation in statical service provisioning. Motivated by that, we design and implement MobiEdge, a predictive service provisioning system with online learning in wireless edge networks. We propose a graph embedding learning-based model for representation learning, thus to achieve accurate request prediction at different base stations. Then, based on the prediction of incoming service requests, we study the service provisioning reconfiguration problem, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , how to jointly optimize service placement and corresponding request scheduling across dual timescales, under constraints of network resources and the total budget. By leveraging the submodular technique, we transform the research issue into a submodular function maximization problem under the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> -independence system constraint, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> is a positive constant related to the ratio of coefficients in constraint conditions. On this basis, we propose a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1/(1+q)$</tex-math></inline-formula> approximation algorithm with rigorous theoretical analysis on the bounded maximum utility. Extensive trace-driven evaluations are conducted over networks of different scales, and MobiEdge shows remarkable performance enhancements by achieving the accuracy of up to 98% in service prediction and an average utility of 92.9% to the optimal solution in service provisioning.

Impacts of capacity redundancy and process flexibility on risk mitigation in e-waste recycling supply chain management

Recently Waste Electrical and Electronic equipment (WEEE) has become urgent environmental issues around the world. Generally, the e-waste recycling reverse supply chain (RSC) features higher uncertainties and complicated network structures, making the operation more difficult. Since the study on impact of hybrid uncertainty mitigation strategy in RSC is rare, we study the coupling effect of two strategies —— capacity redundancy and process flexibility through the design of two hybrid strategies. A distributionally robust optimization model is proposed to handle both waste returns and resource yields uncertainties, and solved by a proposed Outer Approximation (OA) algorithm after an adaptive robust formulation. With numerical experiments based on real data implemented, our research finds conflict situation of using capacity redundancy and process flexibility strategies together. We also give guidelines for the use of hybrid strategies in RSC. We find that the optimal strategy changes as required service level increases. We also suggest moderate investment in capacity redundancy with long chain flexibility and resource centralization when applying hybrid strategy with optimal flexibility.

Designing a Bayesian adaptive clinical trial to evaluate novel mechanical ventilation strategies in acute respiratory failure using integrated nested Laplace approximations

BackgroundAdaptive trials usually require simulations to determine values for design parameters, demonstrate error rates, and establish the sample size. We designed a Bayesian adaptive trial comparing ventilation strategies for patients with acute hypoxemic respiratory failure using simulations. The complexity of the analysis would usually require computationally expensive Markov Chain Monte Carlo methods but this barrier to simulation was overcome using the Integrated Nested Laplace Approximations (INLA) algorithm to provide fast, approximate Bayesian inference. MethodsWe simulated two-arm Bayesian adaptive trials with equal randomization that stratified participants into two disease severity states. The analysis used a proportional odds model, fit using INLA. Trials were stopped based on pre-specified posterior probability thresholds for superiority or futility, separately for each state. We calculated the type I error and power across 64 scenarios that varied the probability thresholds and the initial minimum sample size before commencing adaptive analyses. Two designs that maintained a type I error below 5%, a power above 80%, and a feasible mean sample size were evaluated further to determine the optimal design. ResultsPower generally increased as the initial sample size and the futility threshold increased. The chosen design had an initial recruitment of 500 and a superiority threshold of 0.9925, and futility threshold of 0.95. It maintained high power and was likely to reach a conclusion before exceeding a feasible sample size. ConclusionsWe designed a Bayesian adaptive trial to evaluate novel strategies for ventilation using the INLA algorithm to efficiently evaluate a wide range of designs through simulation.

A polyhedral approximation algorithm for recession cones of spectrahedral shadows

A polyhedral approximation algorithm for recession cones of spectrahedral shadows

An Efficient Homomorphic Argmax Approximation for Privacy-Preserving Neural Networks

An Efficient Homomorphic Argmax Approximation for Privacy-Preserving Neural Networks

Constructing Embedded Lattice-Based Algorithms for Multivariate Function Approximation with a Composite Number of Points

Constructing Embedded Lattice-Based Algorithms for Multivariate Function Approximation with a Composite Number of Points

On λ $\lambda $‐backbone coloring of cliques with tree backbones in linear time

AbstractA ‐backbone coloring of a graph with its subgraph (also called a backbone) is a function ensuring that is a proper coloring of and for each it holds that . In this paper we propose a way to color cliques with tree and forest backbones in linear time that the largest color does not exceed . This result improves on the previously existing approximation algorithms as it is ‐absolutely approximate, that is, with an additive error over the optimum. We also present an infinite family of trees with for which the coloring of cliques with backbones requires at least colors for close to . The construction draws on the theory of Fibonacci numbers, particularly on Zeckendorf representations.

Exact and approximation algorithms for covering timeline in temporal graphs

AbstractWe consider a variant of vertex cover on temporal graphs that has been recently defined for summarization of timeline activities in temporal graphs. The problem has been proved to be NP-hard, even for several restrictions of the time domain and vertex degree. We present novel algorithmic contributions for the problem and we give an approximation algorithm of factor $$O(T \log {n})$$ O ( T log n ) , on a temporal graph of T timestamps and n vertices. We focus then on the NP-hard restriction of the problem, where at most one temporal edge is defined in each timestamp. For this restriction we present a $$4(T-1)$$ 4 ( T - 1 ) approximation algorithm and a parameterized algorithm (a reduction to kernel) for parameter the cost, called span, of the solution.

On the atypical solutions of the symmetric binary perceptron

We study the random binary symmetric perceptron problem, focusing on the behavior of rare high-margin solutions. While most solutions are isolated, we demonstrate that these rare solutions are part of clusters of extensive entropy, heuristically corresponding to non-trivial fixed points of an approximate message-passing algorithm. We enumerate these clusters via a local entropy, defined as a Franz–Parisi potential, which we rigorously evaluate using the first and second moment methods in the limit of a small constraint density α (corresponding to vanishing margin κ ) under a certain assumption on the concentration of the entropy. This examination unveils several intriguing phenomena: (i) we demonstrate that these clusters have an entropic barrier in the sense that the entropy as a function of the distance from the reference high-margin solution is non-monotone when κ⩽1.429−α/log⁡α , while it is monotone otherwise, and that they have an energetic barrier in the sense that there are no solutions at an intermediate distance from the reference solution when κ⩽1.239−α/log⁡α . The critical scaling of the margin κ in −α/log⁡α corresponds to the one obtained from the earlier work of Gamarnik et al (2022 (arXiv:2203.15667)) for the overlap-gap property, a phenomenon known to present a barrier to certain efficient algorithms. (ii) We establish using the replica method that the complexity (the logarithm of the number of clusters of such solutions) versus entropy (the logarithm of the number of solutions in the clusters) curves are partly non-concave and correspond to very large values of the Parisi parameter, with the equilibrium being reached when the Parisi parameter diverges.

Approximation algorithm for the minimum partial connected Roman dominating set problem

Approximation algorithm for the minimum partial connected Roman dominating set problem

Coordinated risk-averse distributionally robust optimization for maintenance and generation schedules of offshore wind farm cluster

The coordinated optimization of maintenance and generation schedules of multiple offshore wind farms (OWFs) bring great benefits in reducing the maintenance and operation cost of OWF cluster. Firstly, a two-stage coordinated risk-averse distributionally robust optimization (CRDRO) model for maintenance and generation schedules of wind turbines (WTs) in OWF cluster is proposed. This model takes into account uncertainties related to the prediction errors in WTs’ maximum available active power outputs, the travel time of maintenance vessels, and the high operational cost risks associated with these uncertainties. A feasible route generating algorithm is designed to obtain all feasible maintenance combinations for WTs and the corresponding routes of maintenance vessels for the CRDRO model. The risk-averse term, which is a weighted sum of expected operation costs and GlueVaR value, is used to measure the tail risk of the worst probability distribution. To solve the two-stage CRDRO model, the risk-averse term is simplified into the form of expected value calculation, which can be further transformed into the tractable form by using the strong duality theorem. Finally, the two-stage CRDRO model is solved by the column-and-constraint generation algorithm, with the nonconvex sub-problem being addressed by the outer approximation algorithm. Case studies on an real-world cluster comprising three OWFs verify the correctness and efficiency of the proposed method, and demonstrate that the CRDRO model enhances the overall economic efficiency and reduces the high operational cost risk under extreme scenarios.