Time Algorithm Research Articles

Computing Pareto-Optimal and Almost Envy-Free Allocations of Indivisible Goods

We study the problem of fair and efficient allocation of a set of indivisible goods to agents with additive valuations using the popular fairness notions of envy-freeness up to one good (EF1) and equitability up to one good (EQ1) in conjunction with Pareto-optimality (PO). There exists a pseudo-polynomial time algorithm to compute an EF1+PO allocation and a non-constructive proof of the existence of allocations that are both EF1 and fractionally Pareto-optimal (fPO), which is a stronger notion than PO. We present a pseudopolynomial time algorithm to compute an EF1+fPO allocation, thereby improving the earlier results. Our techniques also enable us to show that an EQ1+fPO allocation always exists when the values are positive and that it can be computed in pseudo-polynomial time. We also consider the class of k-ary instances where k is a constant, i.e., each agent has at most k different values for the goods. For such instances, we show that an EF1+fPO allocation can be computed in strongly polynomial time. When all values are positive, we show that an EQ1+fPO allocation for such instances can be computed in strongly polynomial time. Next, we consider instances where the number of agents is constant and show that an EF1+PO (likewise, an EQ1+PO) allocation can be computed in polynomial time. These results significantly extend the polynomial-time computability beyond the known cases of binary or identical valuations. We also design a polynomial-time algorithm that computes a Nash welfare maximizing allocation when there are constantly many agents with constant many different values for the goods. Finally, on the complexity side, we show that the problem of computing an EF1+fPO allocation lies in the complexity class PLS.

Sharp threshold for embedding balanced spanning trees in random geometric graphs

AbstractA rooted tree is balanced if the degree of a vertex depends only on its distance to the root. In this paper we determine the sharp threshold for the appearance of a large family of balanced spanning trees in the random geometric graph . In particular, we find the sharp threshold for balanced binary trees. More generally, we show that all sequences of balanced trees with uniformly bounded degrees and height tending to infinity appear above a sharp threshold, and none of these appears below the same value. Our results hold more generally for geometric graphs satisfying a mild condition on the distribution of their vertex set, and we provide a polynomial time algorithm to find such trees.

A linear time algorithm for linearizing quadratic and higher-order shortest path problems

AbstractAn instance of the NP-hard Quadratic Shortest Path Problem (QSPP) is called linearizable iff it is equivalent to an instance of the classic Shortest Path Problem (SPP) on the same input digraph. The linearization problem for the QSPP (LinQSPP) decides whether a given QSPP instance is linearizable and determines the corresponding SPP instance in the positive case. We provide a novel linear time algorithm for the LinQSPP on acyclic digraphs which runs considerably faster than the previously best algorithm. The algorithm is based on a new insight revealing that the linearizability of the QSPP for acyclic digraphs can be seen as a local property. Our approach extends to the more general higher-order shortest path problem.

A Theory of Alternating Paths and Blossoms from the Perspective of Minimum Length

The Micali–Vazirani (MV) algorithm for finding a maximum cardinality matching in general graphs, which was published in 1980, remains to this day the most efficient known algorithm for the problem. The current paper gives the first complete and correct proof of this algorithm. The MV algorithm resorts to finding minimum-length augmenting paths. However, such paths fail to satisfy an elementary property, called breadth first search honesty in this paper. In the absence of this property, an exponential time algorithm appears to be called for—just for finding one such path. On the other hand, the MV algorithm accomplishes this and additional tasks in linear time. The saving grace is the various “footholds” offered by the underlying structure, which the algorithm uses in order to perform its key tasks efficiently. The theory expounded in this paper elucidates this rich structure and yields a proof of correctness of the algorithm. It may also be of independent interest as a set of well-knit graph-theoretic facts. Funding: This work was supported in part by the National Science Foundation [Grant CCF-2230414].

SAR deep learning sea ice retrieval trained with airborne laser scanner measurements from the MOSAiC expedition

Abstract. Automated sea ice charting from synthetic aperture radar (SAR) has been researched for more than a decade, and we are still not close to unlocking the full potential of automated solutions in terms of resolution and accuracy. The central complications arise from ground truth data not being readily available in the polar regions. In this paper, we build a data set from 20 near-coincident x-band SAR acquisitions and as many airborne laser scanner (ALS) measurements from the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC), between October and May. This data set is then used to assess the accuracy and robustness of five machine-learning-based approaches by deriving classes from the freeboard, surface roughness (standard deviation at 0.5 m correlation length) and reflectance. It is shown that there is only a weak correlation between the radar backscatter and the sea ice topography. Accuracies between 44 % and 66 % and robustness between 71 % and 83 % give a realistic insight into the performance of modern convolutional neural network architectures across a range of ice conditions over 8 months. It also marks the first time algorithms have been trained entirely with labels from coincident measurements, allowing for a probabilistic class retrieval. The results show that segmentation models able to learn from the class distribution perform significantly better than pixel-wise classification approaches by nearly 20 % accuracy on average.

A multi-stage localization framework for accurate and precise docking of autonomous mobile robots (AMRs)

Abstract Autonomous navigation has been a long-standing research topic, and researchers have worked on many challenging problems in indoor and outdoor environments. One application area of navigation solutions is material handling in industrial environments. With Industry 4.0, the simple problem in traditional factories has evolved into the use of autonomous mobile robots within flexible production islands in a self-decision-making structure. Two main stages of such a navigation system are safe transportation of the vehicle from one point to another and reaching destinations at industrial standards. The main concern in the former is roughly determining the vehicle’s pose to follow the route, while the latter aims to reach the target with high accuracy and precision. Often, it may not be possible or require extra effort to satisfy requirements with a single localization method. Therefore, a multi-stage localization approach is proposed in this study. Particle filter-based large-scale localization approaches are utilized during the vehicle’s movement from one point to another, while scan-matching-based methods are used in the docking stage. The localization system enables the appropriate approach based on the vehicle’s status and task through a decision-making mechanism. The decision-making mechanism uses a similarity metric obtained through the correntropy criterion to decide when and how to switch from large-scale localization to precise localization. The feasibility and performance of the developed method are corroborated through field tests. These evaluations demonstrate that the proposed method accomplishes tasks with sub-centimeter and sub-degree accuracy and precision without affecting the operation of the navigation algorithms in real time.

Leaf sector covers with applications on circle graphs

Damian and Pemmaraju [J. Algorithms, 42 (2002), pp. 255–276] introduced leaf sector covers for circle graphs and presented an O(n2)-time algorithm to find this data structure. They subsequently employed it as an algorithmic tool, leading to the development of an 8-approximation algorithm for the dominating set problem, a (2+ε)-approximation scheme for the dominating set problem, and a (3+ε)-approximation scheme for the total dominating set problem.In this paper, we have improved the time complexity from O(n2) to O(n+m) for finding a leaf sector cover. Furthermore, we employed leaf sector covers as a powerful algorithmic tool to design a 10-approximation algorithm for the total dominating set problem and a 12-approximation algorithm for the paired-dominating set problem. Moreover, we also proposed a (2+ε)-approximation scheme for the total dominating set problem and a (4+ε)-approximation scheme for the paired-dominating set problem. The results presented above are currently the best algorithms for circle graphs.

Is the change deforestation? Using time-series analysis of satellite data to disentangle deforestation from other forest degradation causes

Protecting natural ecosystems requires monitoring approaches that work as early warning systems to avoid degradation and protect biodiversity. However, separating forest disturbance causes in change-detection pipelines is challenging due to the complex interplay of multiple drivers affecting vegetation. This study aims to detect deforestation in highly heterogeneous ecosystems. We used Landsat NDVI time-series data for testing three unsupervised change detection methods: 1) the non-parametric phenological anomaly detection (npphen), 2) the continuous change detection and classification (CCDC), and 3) the pruned exact linear time (PELT) algorithms. We used visual interpretation of Google Earth Pro high-resolution data (< 10 m) to depict deforestation, and natural-induced changes, like forest browning and fires, evaluating the performance of the unsupervised methods. Additionally, a Random Forest model trained with the outputs from detection algorithms together with elevation and radar vegetation index data were utilised to depict deforestation in a second step. While PELT slightly outperformed other methods for tracking general vegetation changes, with overall accuracies (OA) ranging from 0.78 to 0.99, depending on the vegetation type, it also showed the slowest deforestation tracking response. CCDC presented the fastest response and an OA between 0.78 and 0.95. Additionally, we observed a mean OA of only 0.47 when separating deforestation from other changes using only the unsupervised models. On the other hand, deforestation was accurately detected (OA = 0.93; kappa = 0.83) when using CCDC outputs within a secondary supervised classification, agreeing with selected citizen-based complaints from the Environmental Superintendence. The relatively fast response in deforestation tracking using CCDC makes it a viable alternative for near real-time monitoring. Commonly used unsupervised detection methods may be coupled with supervised techniques to depict vegetation change sources robustly. This application constitutes a step forward for managing and monitoring vegetation areas in highly complex and dynamic landscapes, like Mediterranean ecosystems.

Optimizing DOCRs coordination when synergizing energy management with V2G using innovative optimization algorithms

This manuscript proposes an optimal coordination approach for directional overcurrent relays (DOCRs) within electric vehicle charging stations (EVCS), considering energy management and Vehicle-to-Grid (V2G) integration. The study focuses on maximizing efficiency and grid interaction in charging stations by addressing the challenge of DOCRs coordination. Three innovative optimization algorithms, namely the Hunger Games Search (HGS), Hunter Prey Optimization (HPO), and Sparrow Search algorithm (SSA), are employed to determine the optimal coordination for the DOCRs and get the time dial setting (TDS) and pickup current (IP) targeting minimum operating time for all DOCRs, considering factors such as load balancing, fault detection, and power quality in three different scenarios. EVSC has two types of charges DC and AC with two modes: V2G mode when EV is discharged into the grid, and G2V mode when EV is charged from the grid. Fast chargers are used to proceed as it can work in two modes V2G and G2V. Through extensive simulations and performance evaluations, the results demonstrate the effectiveness of the proposed approach. The three scenarios are simulated by using ETAP and MATLAB software according to fault location and to achieve voltage regulation and sufficient power for loads to achieved continuity of service for up to 1960.7 kW loads that kept fed. The proposed approach achieved the target of protecting the EVCS in minimum operating time of relays using the three algorithms and SSA introduces the best result more than other algorithms for the relay operating time with reduction up to 21 %.

Task scheduling using glowworm-based optimal heterogeneous earliest finish time algorithm for mobile grid

Task scheduling using glowworm-based optimal heterogeneous earliest finish time algorithm for mobile grid

Envy-free relaxations for goods, chores, and mixed items

In fair division problems, we are given a set S of m items and a set N of n agents with individual preferences, and the goal is to find an allocation of items among agents so that each agent finds the allocation fair. There are several established fairness concepts and envy-freeness is one of the most extensively studied ones. However envy-free allocations do not always exist when items are indivisible and this has motivated relaxations of envy-freeness: envy-freeness up to one item (EF1) and envy-freeness up to any item (EFX) are two well-studied relaxations. We consider the problem of finding EF1 and EFX allocations for utility functions that are not necessarily monotone, and propose four possible extensions of different strength to this setting.In particular, we present a polynomial time algorithm for finding an EF1 allocation for two agents with arbitrary utility functions. An example is given showing that EFX allocations need not exist for two agents with non-monotone, non-additive, identical utility functions. However, when all agents have monotone (not necessarily additive) identical utility functions, we give a pseudo-polynomial time algorithm that always finds an EFX allocation of chores. As a step toward understanding the general case, we discuss two subclasses of utility functions: Boolean utilities that are {0,+1}-valued functions, and negative Boolean utilities that are {0,−1}-valued functions. For the latter, we give a polynomial time algorithm that finds an EFX allocation when the utility functions are identical.

Cepstral coefficients effectiveness for gunshot classifying

This paper analyses the efficiency of various frequency cepstral coefficients (FCC) in a non-speech application, specifically in classifying acoustic impulse events-gunshots. There are various methods for such event identification available. The majority of these methods are based on time or frequency domain algorithms. However, both of these domains have their limitations and disadvantages. In this article, an FCC, combining the advantages of both frequency and time domains, is presented and analyzed. These originally speech features showed potential not only in speech-related applications but also in other acoustic applications. The comparison of the classification efficiency based on features obtained using four different FCC, namely mel-FCC (MFCC), inverse mel-frequency cepstral coefficients (IMFCC), linear-frequency cepstral coefficients (LFCC), and gammatone-frequency cepstral coefficients (GTCC) is presented. An optimal frame length for an FCC calculation is also explored. Various gunshots from short guns and rifle guns of different calibers and multiple acoustic impulse events, similar to the gunshots, to represent false alarms are used. More than 600 acoustic events records have been acquired and used for training and validation of two designed classifiers, support vector machine, and neural network. Accuracy, recall and Matthew’s correlation coefficient measure the classification success rate. The results reveal the superiority of GFCC to other analyzed methods.

The precision by the Face Arm Speech Time (FAST) algorithm in stroke capture, sex and age differences: a stroke registry study

BackgroundThe shift towards milder strokes and studies suggesting that stroke symptoms vary by age and sex may challenge the Face-Arm-Speech Time (FAST) coverage. We aimed to study the proportion of...

Efficient Algorithm for Proportional Lumpability and Its Application to Selfish Mining in Public Blockchains

This paper explores the concept of proportional lumpability as an extension of the original definition of lumpability, addressing the challenges posed by the state space explosion problem in computing performance indices for large stochastic models. Lumpability traditionally relies on state aggregation techniques and is applicable to Markov chains demonstrating structural regularity. Proportional lumpability extends this idea, proposing that the transition rates of a Markov chain can be modified by certain factors, resulting in a lumpable new Markov chain. This concept facilitates the derivation of precise performance indices for the original process. This paper establishes the well-defined nature of the problem of computing the coarsest proportional lumpability that refines a given initial partition, ensuring a unique solution exists. Additionally, a polynomial time algorithm is introduced to solve this problem, offering valuable insights into both the concept of proportional lumpability and the broader realm of partition refinement techniques. The effectiveness of proportional lumpability is demonstrated through a case study that consists of designing a model to investigate selfish mining behaviors on public blockchains. This research contributes to a better understanding of efficient approaches for handling large stochastic models and highlights the practical applicability of proportional lumpability in deriving exact performance indices.

NXPH4 can be used as a biomarker for pan-cancer and promotes colon cancer progression.

NXPH4 promotes cancer proliferation and invasion. However, its specific role and mechanism in cancer remain unclear. Transcriptome and clinical data for pan-cancer were derived from the TCGA database. K-M survival curve and univariate Cox were used for prognostic analysis. CIBERSORT and TIMER algorithms were employed to calculate immune cell infiltration. Gene set enrichment analysis (GSEA) was employed for investigating the function of NXPH4. Western blot verified differential expression of NXPH4 in colon cancer. Functional assays (CCK-8, plate clonogenicity assay, wound healing assay, and Transwell assay) confirmed the impact of NXPH4 on proliferation, invasion, and migration of colon cancer cells. Dysregulation of NXPH4 in pan-cancer suggests its potential as a diagnostic and prognostic marker for certain cancers, including colon and liver cancer. High expression of NXPH4 in pan-cancer might be associated with the increase in copy number and hypomethylation. NXPH4 expression in pan-cancer is substantially linked to immune cell infiltration in the immune microenvironment. NXPH4 expression is associated with the susceptibility to immunotherapy and chemotherapy. Western blot further confirmed the higher expression of NXPH4 in colon cancer. Knockdown of NXPH4 significantly suppresses proliferation, invasion, and migration of colon cancer cell lines HT-29 and HCT116, as validated by functional assays.

Inverse design and optimization of an aperiodic multi-notch fiber Bragg grating using neural networks

Recent developments in the application of aperiodic fiber Bragg gratings (AFBGs) in astrophotonics, such as AFBG for astronomical near-infrared OH suppression and gas detection based on cross-correlation spectroscopy, have illuminated the problem that the optimization for AFBG with certain fabrication constraints has not been fully investigated and solved. Previous solutions will either sacrifice part of the spectral features or consume a significant amount of computation resources and time. Inspired by recently successful applications of artificial neural networks (ANNs) in photonics inverse design, we develop an AFBG optimization approach employing ANNs in conjunction with genetic algorithms (GAs) for the first time, to the best of our knowledge. The approach maintains the spectral notch depths and preserves the fourth-order super-Gaussian spectral features with improvements of interline loss by ∼100 times. We also implement, to our knowledge, the first inverse scattering neural network based on a tandem architecture for AFBG, using a first-order Gaussian notch profile. The neural network successfully converges but has a poor predictive capability for the phase part of the design. We discuss possible ways to overcome these limitations.

A comparative study of stereo-dependent SSVEP targets and their impact on VR-BCI performance.

Steady-state visual evoked potential brain-computer interfaces (SSVEP-BCI) have attracted significant attention due to their ease of deployment and high performance in terms of information transfer rate (ITR) and accuracy, making them a promising candidate for integration with consumer electronics devices. However, as SSVEP characteristics are directly associated with visual stimulus attributes, the influence of stereoscopic vision on SSVEP as a critical visual attribute has yet to be fully explored. Meanwhile, the promising combination of virtual reality (VR) devices and BCI applications is hampered by the significant disparity between VR environments and traditional 2D displays. This is not only due to the fact that screen-based SSVEP generally operates under static, stable conditions with simple and unvaried visual stimuli but also because conventional luminance-modulated stimuli can quickly induce visual fatigue. This study attempts to address these research gaps by designing SSVEP paradigms with stereo-related attributes and conducting a comparative analysis with the traditional 2D planar paradigm under the same VR environment. This study proposed two new paradigms: the 3D paradigm and the 3D-Blink paradigm. The 3D paradigm induces SSVEP by modulating the luminance of spherical targets, while the 3D-Blink paradigm employs modulation of the spheres' opacity instead. The results of offline 4-object selection experiments showed that the accuracy of 3D and 2D paradigm was 85.67 and 86.17% with canonical correlation analysis (CCA) and 86.17 and 91.73% with filter bank canonical correlation analysis (FBCCA), which is consistent with the reduction in the signal-to-noise ratio (SNR) of SSVEP harmonics for the 3D paradigm observed in the frequency-domain analysis. The 3D-Blink paradigm achieved 75.00% of detection accuracy and 27.02 bits/min of ITR with 0.8 seconds of stimulus time and task-related component analysis (TRCA) algorithm, demonstrating its effectiveness. These findings demonstrate that the 3D and 3D-Blink paradigms supported by VR can achieve improved user comfort and satisfactory performance, while further algorithmic optimization and feature analysis are required for the stereo-related paradigms. In conclusion, this study contributes to a deeper understanding of the impact of binocular stereoscopic vision mechanisms on SSVEP paradigms and promotes the application of SSVEP-BCI in diverse VR environments.

Joint promotional effort and assortment optimization under the multinomial logit model

AbstractPromotional effort is a common strategy to induce sales and broaden the market scope by enhancing the products' utility to customers. In this article, we incorporate promotional effort into the customer choice model and study the joint promotional effort and assortment optimization problems, where the customer's choice behavior follows the widely used multinomial‐logit (MNL) model. Motivated by various marketing scenarios, we introduce two distinct models that address the allocation of promotional effort: (1) differentiated promotional effort—the retailer can arbitrarily allocate promotional resources to each offered product; (2) uniform promotional effort—the retailer can determine a promotional level, and the promotional effort is equally distributed to each offered product. In the first model, the revenue‐ordered assortment strategy is optimal, and we can efficiently determine the optimal promotional effort level. In the second model, the revenue‐ordered assortment is no longer optimal. We develop a polynomial time algorithm to solve the joint optimization problem under this model. Using the algorithmic results, we conduct comparative analyses between the assortment optimization problem under the proposed models and the classic MNL model, which does not exert any promotional effort. We show that the assortment size shrinks when the retailer makes the promotional effort in the decision, which indicates that product variety and promotional effort are strategic substitutes. Moreover, the retailer and customers can be better off in the presence of promotional efforts, irrespective of the format. Additionally, we conduct extensive numerical experiments to demonstrate our analytical results and gain more managerial insights.

Multi-objective optimization of parameters design based on genetic algorithm in annulus aerated dual gradient drilling

AbstractThe optimization of drilling parameters is crucial for resolving the drilling problems in low-pressure and leaky formations using the annulus aerated dual gradient drilling technology. However, the previous studies have mostly focused on engineering applications and wellbore fluid flow models, with less emphasis on parameter optimization. This paper combines the wellbore multiphase flow model with genetic algorithms for the first time, proposing a key parameter optimization method for annulus aerated dual gradient drilling based on genetic algorithms. The study investigates the impact of selection operators on the performance of genetic algorithms and compares genetic algorithms with PSO algorithm and SAA. The results indicate that the convergence and stability of genetic algorithms can be improved by enhancing the selection operators. Compared to the gas–liquid ratio parameter optimization method, the IRSGA optimization method reduces the cost coefficient by 36.46%. Through comparative analysis of different optimization methods, the IRSGA demonstrates over 95% accuracy in large-scale computations. The research findings contribute to the optimization of parameters design under low-cost conditions and are of significant importance for promoting the use of this technology to address the serious issue of lost circulation in drilling technology.

How to Hide a Clique?

AbstractIn the well known planted clique problem, a clique (or alternatively, an independent set) of size k is planted at random in an Erdos-Renyi random G(n, p) graph, and the goal is to design an algorithm that finds the maximum clique (or independent set) in the resulting graph. We introduce a variation on this problem, where instead of planting the clique at random, the clique is planted by an adversary who attempts to make it difficult to find the maximum clique in the resulting graph. We show that for the standard setting of the parameters of the problem, namely, a clique of size $$k = \sqrt{n}$$ k = n planted in a random $$G(n, \frac{1}{2})$$ G ( n , 1 2 ) graph, the known polynomial time algorithms can be extended (in a non-trivial way) to work also in the adversarial setting. In contrast, we show that for other natural settings of the parameters, such as planting an independent set of size $$k=\frac{n}{2}$$ k = n 2 in a G(n, p) graph with $$p = n^{-\frac{1}{2}}$$ p = n - 1 2 , there is no polynomial time algorithm that finds an independent set of size k, unless NP has randomized polynomial time algorithms.