Coverage Problem Research Articles

From coordinate subspaces over finite fields to ideal multipartite uniform clutters

AbstractTake a prime power q, an integer $$n\ge 2$$ n ≥ 2 , and a coordinate subspace $$S\subseteq GF(q)^n$$ S ⊆ G F ( q ) n over the Galois field GF(q). One can associate with S an n-partite n-uniform clutter $$\mathcal {C}$$ C , where every part has size q and there is a bijection between the vectors in S and the members of $$\mathcal {C}$$ C . In this paper, we determine when the clutter $$\mathcal {C}$$ C is ideal, a property developed in connection to Packing and Covering problems in the areas of Integer Programming and Combinatorial Optimization. Interestingly, the characterization differs depending on whether q is 2, 4, a higher power of 2, or otherwise. Each characterization uses crucially that idealness is a minor-closed property: first the list of excluded minors is identified, and only then is the global structure determined. A key insight is that idealness of $$\mathcal {C}$$ C depends solely on the underlying matroid of S. Our theorems also extend from idealness to the stronger max-flow min-cut property. As a consequence, we prove the Replication and $$\tau =2$$ τ = 2 Conjectures for this class of clutters.

Fixed-Ratio Approximation Algorithm for the Minimum Cost Cover of a Digraph by Bounded Number of Cycles

We consider polynomial time approximation for the minimum cost cycle cover problem of an edge-weighted digraph, where feasible covers are restricted to have at most k disjoint cycles. In the literature this problem is referred to as Min-k-SCCP. The problem is closely related to classic Traveling Salesman Problem (TSP) and Vehicle Routing Problem (VRP) and has many important applications in algorithms design and operations research. Unlike its unconstrained variant, the Min-k-SCCP is strongly NP-hard even on undirected graphs and remains intractable in very specific settings. For any metric, the problem can be approximated in polynomial time within ratio 2, while in fixed-dimensional Euclidean spaces it admits Polynomial Time Approximation Schemes (PTAS). In the same time, approximation of the more general asymmetric Min-k-SCCP still remains weakly studied. In this paper, we propose the first fixed-ratio approximation algorithm for this problem, which extends the recent breakthrough Svensson-Tarnawski-Vegh and Traub-Vygen results for the Asymmetric Traveling Salesman Problem.

PangeBlocks: customized construction of pangenome graphs via maximal blocks

BackgroundThe construction of a pangenome graph is a fundamental task in pangenomics. A natural theoretical question is how to formalize the computational problem of building an optimal pangenome graph, making explicit the underlying optimization criterion and the set of feasible solutions. Current approaches build a pangenome graph with some heuristics, without assuming some explicit optimization criteria. Thus it is unclear how a specific optimization criterion affects the graph topology and downstream analysis, like read mapping and variant calling.ResultsIn this paper, by leveraging the notion of maximal block in a Multiple Sequence Alignment (MSA), we reframe the pangenome graph construction problem as an exact cover problem on blocks called Minimum Weighted Block Cover (MWBC). Then we propose an Integer Linear Programming (ILP) formulation for the MWBC problem that allows us to study the most natural objective functions for building a graph. We provide an implementation of the ILP approach for solving the MWBC and we evaluate it on SARS-CoV-2 complete genomes, showing how different objective functions lead to pangenome graphs that have different properties, hinting that the specific downstream task can drive the graph construction phase.ConclusionWe show that a customized construction of a pangenome graph based on selecting objective functions has a direct impact on the resulting graphs. In particular, our formalization of the MWBC problem, based on finding an optimal subset of blocks covering an MSA, paves the way to novel practical approaches to graph representations of an MSA where the user can guide the construction.

Fabrication of angle-gradient echelle grating on metallic glass using shaped vibration cutting with time-varying trajectory

In order to solve the problem of narrow band coverage of traditional infrared gratings, a new type of diffraction grating is invented and named as angle-gradient echelle grating. The blaze angle of the grating gradually changes along the direction of the grating grooves, which can be regarded as etching countless sub-gratings with different blaze angles on a grating, breaking the limitation of the number of blaze angles of traditional gratings. In addition, in order to solve the processing problem of angle-gradient echelle grating, a new processing method, shaped vibration cutting (SVC) with a time-varying trajectory is developed. By exploring the influence of different processing parameters on the grating processing results, a suitable processing plan was proposed. Eventually, angle-gradient echelle grating with blaze angles varying from 30° to 55° and surface roughness of as low as 20 nm was fabricated on metallic glass, a material that is difficult to machine.

Mitigating false negatives in imbalanced datasets: An ensemble approach

Imbalanced datasets present a challenge in machine learning, especially in binary classification scenarios where one class significantly outweighs the other. This imbalance often leads to models favoring the majority class, resulting in inadequate predictions for the minority class, specifically in false negatives. In response to this issue, this work introduces the MinFNR ensemble algorithm, designed to minimize False Negative Rates (FNR) in imbalanced datasets. The new approach strategically combines data-level, algorithmic-level, and hybrid-level approaches to enhance overall predictive capabilities while minimizing computational resources using the Set Covering Problem (SCP) formulation. Through a comprehensive evaluation of diverse datasets, MinFNR consistently outperforms individual algorithms, showing its potential for applications where the cost of false negatives is substantial, such as fraud detection and medical diagnosis. This work also contributes to ongoing efforts to improve the reliability and effectiveness of machine learning algorithms in real imbalanced scenarios.

Activation of Ms 6.9 Milin Earthquake on Sedongpu Disaster Chain, China with Multi-Temporal Optical Images

In recent years, disaster chains caused by glacier movements have occurred frequently in the lower Yarlung Tsangpo River in southwest China. However, it is still unclear whether earthquakes significantly contribute to glacier movements and disaster chains. In addition, it is difficult to measure the high-frequency and large gradient displacement time series with optical remote sensing images due to cloud coverage. To this end, we take the Sedongpu disaster chain as an example, where the Milin earthquake, with an epicenter 11 km away, occurred on 18 November 2017. Firstly, to deal with the cloud coverage problem for single optical remote sensing analysis, we employed multiple platform optical images and conducted a cross-platform correlation technique to invert the two-dimensional displacement rate and the cumulative displacement time series of the Sedongpu glacier. To reveal the correlation between earthquakes and disaster chains, we divided the optical images into three classes according to the Milin earthquake event. Lastly, to increase the accuracy and reliability, we propose two strategies for displacement monitoring, that is, a four-quadrant block registration strategy and a multi-window fusion strategy. Results show that the RMSE reduction percentage of the proposed registration method reaches 80%, and the fusion method can retrieve the large magnitude displacements and complete displacement field. Secondly, the Milin earthquake accelerated the Sedongpu glacier movement, where the pre-seismic velocities were less than 0.5 m/day, the co-seismic velocities increased to 1 to 6 m/day, and the post-seismic velocities decreased to 0.5 to 3 m/day. Lastly, the earthquake had a triggering effect around 33 days on the Sedongpu disaster chain event on 21 December 2017. The failure pattern can be summarized as ice and rock collapse in the source area, large magnitude glacier displacement in the moraine area, and a large volume of sediment in the deposition area, causing a river blockage.

The Exact Subset MultiCover problem

In this paper, we study the Exact Subset MultiCover problem (or ESM), which can be seen as an extension of the well-known Set Cover problem. Let (U,f) be a multiset built from set U={e1,e2,…,em} and function f:U→N⁎. ESM is defined as follows: given (U,f) and a collection S={S1,S2,…,Sn} of n subsets of U, is it possible to find a multiset (S′,g) with S′={S1′,S2′,…,Sn′} and g:S′→N, such that (i) Si′⊆Si for every 1≤i≤n, and (ii) each element of U appears as many times in (U,f) as in (S′,g)? We study this problem under an algorithmic viewpoint and provide diverse complexity results such as polynomial cases, NP-hardness proofs and FPT algorithms. We also study two variants of ESM: (i) Exclusive Exact Subset MultiCover (EESM), which asks that each element of U appears in exactly one subset Si′ of S′; (ii) Maximum Exclusive Exact Subset MultiCover (Max-EESM), an optimization version of EESM, which asks that a maximum number of elements of U appear in exactly one subset Si′ of S′. For both variants, we provide several complexity results; in particular we present a 2-approximation algorithm for Max-EESM, that we prove to be tight. For these three problems, we also provide an Integer Linear Programming (ILP) formulation.

Coverage optimization for IoT-based network using Monarch Butterfly Optimization with greedy strategy and self-adaptive crossover operator

In the dynamic development of technology, the Internet of Things (IoT) stands as a driving force of innovation and opening new frontiers. Data collection and processing in IoT systems provide services to decision making in various fields including home automation, disaster management, healthcare, and so on. In such services, the IoT has certain limitations to perform the required tasks and it can cause extreme consequences in the network. One of the main challenge in IoT is to ensure maximum coverage by optimally placing the sensors. To address the coverage problem, a meta-heuristic algorithm Monarch Butterfly Optimization with greedy strategy and self-adaptive crossover operator (GCMBO) is proposed for Optimal Sensor Placement (OSP) in 3D monitoring region. The performance of proposed algorithm is evaluated by a series of simulation and it provide efficient results when compared to other similar existing optimization algorithms. Additionally, a statistical analysis (ANOVA and LSD post-hoc) is exhibited from the comparative results.

Background-Free Imaging of Food Freshness Using Curcumin-Functionalized Upconversion Reversible Hydrogel Patch.

Functionalized upconversion nanomaterials can overcome the drawbacks faced of strong background interference, photodamage, and spectral overlap by conventional optical labeling. Here, curcumin-functionalized upconversion hydrogel patch is designed with background-free and reversible for food freshness monitoring by ultra-sensitive response to biogenic amines. By loading the probes onto hydrogel patch, utilizing the good ductility to solve the problem of non-smooth surface coverage, thus accurately capturing biogenic amines. The presence of biogenic amines leads to the conversion of the diketone group on the probe to enolate ions, which triggers fluorescence resonance energy transfer (FRET) and ultimately causes the upconverted fluorescence to gradually change from green to red. The probe exhibits good detection capability for biogenic amines with a low limit of detection (LOD) of 2.73 µm. Interestingly, the patch can be restored to its initial state after water rinsing, realizing reversible detection of biogenic amines. Additionally, combining the color recognition system of smartphone can convert the imaging signal into a data signal to achieve quantitative analysis and show a reliable assessment comparable to the results of high performance liquid chromatography (HPLC). This study demonstrates the practical applicability in real-time monitoring of freshness, suggests great potential in developing optical nano-sensing strategy to ensure food safety.

Approximation algorithms for minimum ply covering of points with unit squares and unit disks

Given a set P of points and a set U of geometric objects in the Euclidean plane, a minimum ply cover of P with U is a subset of U that covers P and minimizes the number of objects that share a common intersection, called the minimum ply cover number of P with U. Biedl et al. (2021) [9] showed that for both unit squares and unit disks, determining the minimum ply cover number for a set of points is NP-hard. They gave polynomial-time 2-approximation algorithms for the special case when the minimum ply cover number is constant, and asked whether there exists polynomial-time O(1)-approximation algorithms for these problems. In this paper, we settle the question posed by Biedl et al. by providing polynomial-time O(1)-approximation algorithms for the minimum ply cover problem for both unit squares and unit disks.

DETERMINING THE OPTIMAL TEMPORARY WASTE DISPOSAL SITES IN THE ALANG-ALANG LEBAR SUB-DISTRICT PALEMBANG USING THE P-CENTRE LOCATION PROBLEM AND P-MEDIAN PROBLEM MODELS

The rapid development of Palembang City comes with an increase in population and a proportionate increase in waste. Providing Temporary Waste Disposal Sites (TWDS) with ideal locations is one way to address the waste problem in Palembang City. The location of the existing TWDS could be more regular and optimal. The problem of determining the optimal TWDS location can be solved by optimization science, as classified in the Set Covering Problem (SCP) model. The SCP model is divided into the -Center Location Problem and -Median Problem models. This study aims to determine the optimal locations for TWDS in the Alang-Alang Lebar Sub-District, Palembang City, by comparing the results of the p-Center Location Problem and p-Median Problem models. Initially, the Alang-Alang Lebar Sub-District had 33 TWDS. After formulating the Set Covering Location Problem and Maximal Covering Location Problem models, we obtain the optimal solution, which we then solve using the -Center Location Problem and -Median Problem models. Based on the results and discussion, the optimal TWDS can meet the demand of each village in the Alang-Alang Lebar Sub-District. The -Center Location Problem and -Median Problem models produce the same optimal TWDS, namely TWDS Pramuka 2 Street and around, TWDS Colonel Sulaiman Amin Street, TWDS Talang Kelapa Ujung, and TWDS Beside Soekarno Hatta Street. This study recommends using both models to determine the optimal TWDS.

Turmeric Topical Application: An effective solution for reducing breast milk secretion delays in new mothers

Background: The problem of low coverage of exclusive breastfeeding is partly influenced by insufficient breast milk production. The percentage of exclusive breastfeeding in infants under six months of age in Central Kalimantan in 2020 was 52.98%. This percentage was among the lowest nationally. In 2021, the coverage of exclusive breastfeeding in infants under six months of age reached 56.8%, and in 2022 it did 60.5%. The figure in 2022 exceeded the set target, but several regencies/cities still had low coverage. Insufficient breast milk supply impacts on the nutritional status of the child. Low breast milk production also arises due to several other factors during breastfeeding, namely late initiation of breastfeeding, long breastfeeding time, sore nipples, breast pain and swelling, and inverted nipples. Aims: The study sought to measure the level of success of turmeric topical application in shortening the time it takes to initiate breast milk secretion. Methods: The study uses a true experimental posttest-only control group design. A subject of 50 mothers having full-term spontaneous deliveries and with normal breasts was used in the study. The sample was divided into two groups: control and intervention groups. The sample was selected using a matching process based on age, parity, and early initiation of breastfeeding. Subjects who met the inclusion criteria were offered whether they were willing to be given turmeric compresses after the delivery process. Subjects who were willing were included in the intervention group and those who were not willing were included in the control group. Age and parity in the intervention group were all taken, while the control group was selected to match the intervention group. The intervention group was given a treatment with a turmeric compress on the breasts for six hours. All participants were then observed for time of breast milk secretion initiation. In this experiment, we didn't perform blinding, but we managed it by having the midwife administer the turmeric compress just once during the delivery process before sending the client home. Following this, we recorded the results, specifically the initial breast milk release in both the intervention and the control group. Results: The average time periods it took to initiate breast milk secretion in the intervention and control groups were 509.96 minutes (8.5 hours) and 1573.76 minutes (26.2 hours), respectively. There was a significant difference (p = 0.023) in the time of breast milk secretion initiation of 1063.8 minutes or 17.73 hours between both groups. Conclusion: Applying a turmeric compress on the breasts of postpartum mothers may shorten the time it takes to initiate breast milk secretion. Received: 05 August 2024, Reviewed: 23 August 2024, Revised: 21 September 2024, Accepted: 13 October 2024.

Using Online Algorithms to Solve NP-Hard Problems

This paper explores the application of online algorithms to tackle NP-hard problems, a class of computational challenges characterized by their intractability and wide-ranging real-world implications. Unlike traditional offline algorithms that have access to complete input data, online algorithms make decisions sequentially, often under constraints of incomplete information. We investigate various strategies, including greedy approaches, randomization, and competitive analysis, to assess their effectiveness in solving NP-hard problems such as the Traveling Salesman Problem, the Knapsack Problem, and the Set Cover Problem. Our analysis highlights the trade-offs between solution quality and computational efficiency, emphasizing the significance of the competitive ratio in evaluating algorithm performance. Additionally, we discuss the practical applications of online algorithms in dynamic environments, such as real-time systems and streaming data processing. Through a comprehensive review of existing literature and novel algorithmic designs, we aim to provide insights into the viability of online algorithms as a robust framework for addressing NP-hard problems in scenarios where immediate decision-making is crucial. The findings underscore the potential for future research to enhance these algorithms, making them increasingly applicable in complex, real-world contexts.

Some Covering and Packing Problems for Mixed Triples

Some Covering and Packing Problems for Mixed Triples

Algorithm for Target Coverage Problem Based on Deep Learning in Wireless Sensor Networks

Aiming at the uncertain mechanism of node activation strategies and redundancy of feasible solution sets in the process of solving target coverage problem in wireless sensor networks, we proposed a deep learning based target coverage algorithm to learn the scheduling strategies of nodes in wireless sensor networks. Firstly , the algorithm abstracted the construction of feasible solution sets into Markov decision process, and intelligently selected activated sensor nodes as discrete actions according to the network environment. Secondly, a reward function evaluated the performance of the intelligent agent in selecting actions based on the coverage capacity and its residual energy of the active node. The simulation experiment result shows that the algorithm is effective in different network environments, and the network lifecycle is superior to the three greedy algorithms, the maximum lifetime coverage algorithm and the adaptive learning automaton algorithm.

Efficient Algorithm for Generating Optimal Inequality Candidates for MILP Modeling of Boolean Functions

Mixed-Integer Linear Programming (MILP) modeling has become an important tool for both the analysis and the design of symmetric cryptographic primitives. The bit-wise modeling of their nonlinear components, especially the S-boxes, is of particular interest since it allows more informative analysis compared to word-oriented models focusing on counting active S-boxes. At the same time, the size of these models, especially in terms of the number of required inequalities, tends to significantly influence and ultimately limit the applicability of this method to real-world ciphers, especially for larger number of rounds. It is therefore of great cryptographic significance to study optimal linear inequality descriptions for Boolean functions. The pioneering works of Abdelkhalek et al. (FSE 2017), Boura and Coggia (FSE 2020) and Li and Sun (FSE 2023) provided various heuristic techniques for this computationally hard problem, decomposing it into two algorithmic steps, coined Problem 1 and Problem 2, with the latter being identical to the well-known NP-hard set cover problem, for which there are many heuristic and exact algorithms in the literature. In this paper, we introduce a novel and efficient branch-and-bound algorithm for generating all minimal, non-redundant candidate inequalities that satisfy a given Boolean function, therefore solving Problem 1 in an optimal manner without relying on heuristics. We furthermore prove that our algorithm correctly computes optimal solutions. Using a number of dedicated optimizations, it provides significantly improved runtimes compared to previous approaches and allows the optimal modeling of the difference distribution tables (DDT) and linear approximation tables (LAT) of many practically used S-boxes. The source code for our algorithm is publicly available as a tool for researchers and practitioners in symmetric cryptography.

The Kinomatics Australian Film Production Dataset: A Curated Dataset Describing Australian Feature Film Titles and Personnel 1975–2022

Abstract This article presents a novel, extensive, and thoroughly documented dataset describing Australian feature films and the personnel filling ten key production roles on those films. The dataset is curated from public information in multiple sources and draws on further supplemental resources to verify, validate and consolidate this information. In total, the data describes 22,720 roles filled by 9,397 distinct people across 1,877 films, covering an important 47-year period in the Australian film industry. The authors outline how the dataset solves several problems for scholars interested in data that provides a historical record of the collaborative filmmaking process. In particular, to address concerns about known coverage problems with popular sources such as the Internet Movie Database, this dataset has undergone extensive manual checking to ensure that it is reliable as a source of information on a national film industry. Moreover, the authors have carefully and manually linked each person appearing in the dataset, which allows the dataset to provide a rich source of information for exploring the relationality of filmmaking collaborations. The inclusion of ten key filmmaking roles further expands the utility of the dataset beyond existing datasets which tend to focus on actors and/or directors, writers and producers.

A Cost-Effective RISs Deployment to Abate the Coverage Problem in B5G Networks

A Cost-Effective RISs Deployment to Abate the Coverage Problem in B5G Networks

Approximation algorithms for solving the trip-constrained vehicle routing cover problems

Approximation algorithms for solving the trip-constrained vehicle routing cover problems

Equilibrium seeking of higher-order networks under facet cover constraints.

Agent intelligence involves specific requirements for social attributes. Intelligent agents make their decisions based on the groups they are part of, tend to satisfy co-members, and enlarge their own benefits. A fundamental question is whether this form of subgroup decision-making accommodate each individual's preferences. In this paper, we examine the evolution of an anticoordination game on a higher-order network in the form of a simplicial complex in relation to the facet cover problem, which ensures that each subgroup yields a positive benefit. We introduce and apply the facet update rule to regulate nodes' group-based interactions. We identify the payoff parameter condition that a strict Nash equilibrium (SNE) satisfies a facet cover. The proposed facet update rule enables the activated facet to reach a facet equilibrium, and all nodes would converge to an SNE with no more than 2m strategy switches, where m is the number of nodes in the simplicial complex. Additionally, we analyze the convergence of the asynchronous update rule, which can be seen as a special case of the facet update rule. Our simulations and extensive examples reveal that the SNE achieved by the facet update rule, on average, covers fewer nodes compared to the asynchronous update rule.