Longest Path Research Articles

An Alternative Method for Finding the Critical Path of the Network in Fuzzy Time Cost Trade off Problem

Background : The critical path approach is used to determine the network's longest path, according to historical records. This study examines a different approach to determining the construction network's longest path. Method: Here, the network is viewed as a directed acyclic graph, and the critical path of the network is found using the longest path algorithm of the network. To find the best answer for a building project, the longest path that was found was integrated into a linear programming issue. The triangle fuzzy variable defines all of the project's inputs. The 992 square foot building area is incorporated, and three project manager’s quotes are used as a triangular fuzzy variable. Findings : This work has the options of getting quotation from the project managers, convert them as the fuzzy variables such as triangular fuzzy variable, Trapezoidal fuzzy variable and pentagonal fuzzy variable. After the network is converted into a linear programming problem using the fully fuzzy mathematical model, the best possible solution is found. Novelty and applications : Alternative method for critical path of the network has been incorporated. It has been found that the proposed method reduces the time to find the critical path of the larger networks. Keywords: Directed Acyclic Graph, Longest Path Algorithm, Triangular Fuzzy Variable, Fuzzy Linear Programming Problem, Fully Fuzzy Mathematical Model

PathMap: a path-based mapping tool for long noisy reads with high sensitivity.

With the rapid development of single-molecule sequencing (SMS) technologies, the output read length is continuously increasing. Mapping such reads onto a reference genome is one of the most fundamental tasks in sequence analysis. Mapping sensitivity is becoming a major concern since high sensitivity can detect more aligned regions on the reference and obtain more aligned bases, which are useful for downstream analysis. In this study, we present pathMap, a novel k-mer graph-based mapper that is specifically designed for mapping SMS reads with high sensitivity. By viewing the alignment chain as a path containing as many anchors as possible in the matched k-mer graph, pathMap treats chaining as a path selection problem in the directed graph. pathMap iteratively searches the longest path in the remaining nodes; more candidate chains with high quality can be effectively detected and aligned. Compared to other state-of-the-art mapping methods such as minimap2 and Winnowmap2, experiment results on simulated and real-life datasets demonstrate that pathMap obtains the number of mapped chains at least 11.50% more than its closest competitor and increases the mapping sensitivity by 17.28% and 13.84% of bases over the next-best mapper for Pacific Biosciences and Oxford Nanopore sequencing data, respectively. In addition, pathMap is more robust to sequence errors and more sensitive to species- and strain-specific identification of pathogens using MinION reads.

Optimizing the integration of express bus services with micro-mobility: a case study

Considering a bus line, the problem of defining an express bus line consists in determining which stops of the original line will belong to the express line and the frequency of the new line. The objective of the optimization is a trade-off between the advantages of the passengers that benefit from the new service and the disadvantages of the passengers that cannot exploit the improved service. The advantages and disadvantages are measured in terms of total travel and waiting time.In this work we consider the introduction of micro-mobility, such as shared electric scooters or bikes, to mitigate the disadvantages and to increase the ridership of the express line. The contribution of the paper is twofold. On the one hand, we propose an improved mathematical model for defining an express bus line. The model is based on a longest path problem on an acyclic graph; thus, it is very efficient with respect to the other models in the literature. On the other hand, we consider the real case of two urban bus lines in the city of Milan and present the results computed on real passenger data. The results provide evidence that implementing an express line can improve total travel and waiting time. The time wasted by switching lines is in general higher than the time gained by the passengers. However, this can be compensated by the introduction of micro-mobility means of transportation.

Longest Path Selection Based on Path Identifiers

Longest Path Selection Based on Path Identifiers

LP-Star : Embedding Longest Paths into Star Networks with Large-Scale Missing Edges under an Emerging Assessment Model

LP-Star : Embedding Longest Paths into Star Networks with Large-Scale Missing Edges under an Emerging Assessment Model

DwMLCS: An Efficient MLCS Algorithm based on Dynamic and Weighted Directed Acyclic Graph.

The problem of finding the longest common subsequence (MLCS) for multiple sequences is a computationally intensive and challenging problem that has significant applications in various fields such as text comparison, pattern recognition, and gene diagnosis. Currently, the dominant point-based MLCS algorithms have become popular and extensively studied. Generally, they construct the directed acyclic graph (DAG) of matching points and convert the MLCS problem into a search for the longest paths in the DAG. Several improvements have been made, focusing on decreasing model size and reducing redundant computations. These include 1) hash methods for eliminating duplicated nodes, 2) dynamic structures for supporting smaller DAG and 3) path pruning strategy and so on. However, the algorithms are still too limited when facing large-scale MLCS problem due to 1) the dynamic structures are too time-consuming to maintain and 2) the path pruning relies heavily on the tightness of the lower and upper bound of the MLCS. These factors contribute to the large-scale MLCS problem remaining a challenge. We propose a novel algorithm for the large-scale MLCS problem, named dwMLCS. It is based on two models: one is a dynamic DAG model which is both space and time efficient. It can decrease the size of the DAG significantly. The other is a weighted DAG model with new successor strategies. With this model, we design the algorithm for finding a tighter lower bound of the MLCS. Then, the path pruning is conducted to further reduce the size of the DAG and eliminate redundant computation. Additionally, we propose an upper bound method for improving the efficiency of the path pruning strategy. The experimental results demonstrate that the effectiveness and efficiency of the models and algorithms proposed are better than state-of-the-art algorithms. The source codes of dwMLCS can be downloaded from web site https://github.com/BioLab310/dwMLCS.

A Three-Stage MCDM and Extended Longest Path Algorithm for the Satellite Image Acquisition Scheduling Problem

A Three-Stage MCDM and Extended Longest Path Algorithm for the Satellite Image Acquisition Scheduling Problem

Tight Bound on Treedepth in Terms of Pathwidth and Longest Path

Tight Bound on Treedepth in Terms of Pathwidth and Longest Path

Could Physics Teachers Also Have Misconceptions on Basic Kinematics?

The role of a physics teacher in learning is to facilitate student activities to construct correct conceptual understanding as that of a scientist. As the primary source of knowledge for students, a physics teacher is required to have the right concept, but this demand is not necessarily fully fulfilled. This study aims to determine the profile of physics teachers’ understanding of concepts on kinematics material detected by a four-tier misconception test. Participants in this study were 20 high school physics teachers in Surabaya. Based on the results of data analysis, it was found that the dominant misconceptions included: (1) Two objects that make the same displacement at the same time interval will have the same velocity, regardless of the type of movement of the two objects (2) Objects that move vertically straight up or down will always have the acceleration of motion equal to the acceleration of gravity which is directed downwards. (3) As long as the object’s position is at positive coordinates, it means the object is moving in the forward direction. (4) The graph of velocity against time, which has a positive gradient, means that the object always moves forward (5) In parabolic motion, the length of time an object is in the air only depends on the length of its path, the longest path will require the longest time. (6) In parabolic motion, the final speed of an object when it lands on the ground depends not only on its initial speed but also on its elevation angle. The findings of several misconceptions above show that even a physics teacher cannot escape misconceptions. Therefore, it is crucial for a teacher to be able to remedy the misconceptions he suffers so that these misconceptions are not transmitted to the students he teaches. This finding is the first step for researchers to detect misconceptions, followed by the application of certain learning methods to remedy misconceptions in future research.

Self-Test Library Generation for In-Field Test of Path Delay Faults

New semiconductor technologies for advanced applications are more prone to defects and imperfections related, among several different causes, to the manufacturing process, aging and cross-talks. These phenomena negatively affect the circuit’s timing and can be effectively modeled by means of the path delay fault (PDF) model. While path delay testing is currently supported by commercial Automatic Test Pattern Generation tools for scan designs, functional testing covering PDFs is not widely adopted, mainly because of the high cost for test generation. On the other side, functional test is already widely adopted for in-field test of stuck-at faults, which is often performed resorting to the execution of suitable test programs (Self Test Libraries, or STLs). This approach is attractive, since it can be performed at-speed with limited time constraints and high flexibility, making it a suitable in-field test solutions. Previous work assessed the feasibility and validity of functional approaches based on test programs targeting PDFs. In this work, we present the first systematic method for the development of very high fault coverage test programs for PDFs, which largely outperform test programs written for other fault models. Moreover, the proposed method allows the identification of functionally untestable faults. The effectiveness of the proposed approach was proven on an open-source RISC-V processor core, where 100% coverage of the functionally testable longest paths was achieved, compared with an initial coverage of 0.52% achieved with test programs targeting stuck-at faults. Results demonstrate that shorter paths are also effectively covered.

A retrospective CT based comparative analysis of available screw pathways to determine optimal iliac screw trajectory

<b>Introduction:</b> The lumbo-sacral stabilization using iliac screw is gaining popularity in such cases of long multi segment lumbar constructs. Iliac screws help to achieve strong spinopelvic fixation, augments and protects sacral screws. However, there is a great variability found in literature for iliac screw fixation in terms of trajectory, screw length and screw diameter. Also, to the best of our knowledge, there is lacunae in current literature regarding the optimal pathway, screw length and screw diameter in the Indian population. Hence, we planned the study with the aim to analyze the available screw pathways to determine optimal iliac screw trajectory, screw length and diameter for the Indian population.<br /> <b>Material and methods:</b> This was a tertiary center-based retrospective study. One hundred pelvic CT scans of patients in 18-70 years age, who underwent abdominal CT on Siemens 256-slice dual source CT scanner for various indications were evaluated. Subsequently, 4 iliac screw trajectories were assessed by connecting the points given below using double oblique reformats on which the lengths and narrowest zones of these trajectories were measured. Path A: Posterior Superior Iliac Spine (PSIS) to Anterior Superior Iliac Spine (AIIS); Path B: point between PSIS and posterior inferior iliac spine (PIIS) to Anterior Inferior iliac spine  (AIIS); Path C: iliac crest intersection point (CLIC) point to Upper acetabulum; Path D: CLIC point to acetabular center.<br /> [p1] <b>[a2] Results:</b> Statistically significant difference was found in the lengths of various pathways. Path A (PSIS to AIIS) was found to be the longest (mean 13 cm). The second longest path in our study was path C (CLIC point to Upper acetabulum). The narrowest widths of each path were not found to have any statistically significant difference.<br /> <b>Conclusion:</b> Iliac screw fixation is of paramount importance for lumbosacral stabilization. Of the studied paths, trajectory from posterior-superior iliac spine to Antero-inferior iliac spine has the longest passage length and is the most optimal path for the Indian population. In case additional screws are required, the trajectory from CLIC point to Upper acetabulum provides the second largest screw passage.

Path eccentricity of graphs

Let G be a connected graph. The eccentricity of a path P, denoted by eccG(P), is the maximum distance from P to any vertex in G. In the Central path (CP) problem, our aim is to find a path of minimum eccentricity. This problem was introduced by Cockayne et al., in 1981, in the study of different centrality measures on graphs. They showed that CP can be solved in linear time in trees, but it is known to be NP-hard in many classes of graphs such as chordal bipartite graphs, planar 3-connected graphs, split graphs, etc. We investigate the path eccentricity of a connected graph G as a parameter. Let pe(G) denote the value of eccG(P) for a central path P of G. We obtain tight upper bounds for pe(G) in some graph classes. We show that pe(G)≤1 on biconvex graphs and design an algorithm that finds such a path in linear time. On the other hand, by investigating the longest paths of a graph, we obtain tight upper bounds for pe(G) on arbitrary graphs and k-connected graphs. Finally, we study the relation between a central path and a longest path in a graph. We show that, on bipartite permutation graphs, a longest path is also a central path. Furthermore, for any such class of graphs, we exhibit a superclass that does not satisfy this property.

Square Distance in Graphs

In this paper, we consider a simple connected graph having no loops and multiple edges. The order and size of are denoted by and respectively in graphs is a wide branch of graph theory having many scientific and real-life applications. There are various types of distances studied in the literature.The distance is the length of the shortest path between the vertices and in [2]. The detour distance is the length of the longest path between the vertices and in [3]. The concept of centrality widely applied in social network analysis. Degree centrality is the simplest centrality measure to compute centre. Betweenness centrality measures used for analyzed cancer network.

Analysing Tortuosity for Solid Oxide Fuel Cell Anode Material: Experiments and Modeling

Solid oxide fuel cells (SOFCs) directly convert chemical energy to electricity with high electrical efficiency. It involves gas transport through the porous electrode to the three-phase boundaries (TPB). The tortuosity of gas transport relates the bulk diffusion of gas in free space to the effective diffusion coefficient of gas migrating through a porous material. Therefore, determining the tortuosity is of great importance. This paper tests button SOFCs with NiO-YSZ as anode material followed by dual beam-focused ion beam scanning electron microscopy (FIB-SEM) to obtain 2D serial slice images. Based on processed 2D images and reconstructed 3D microstructure, the tortuosity is calculated using three approaches i.e., porosity-tortuosity correlations, voxel-based, and path-length-based approaches. The test results show that a decrease in Ni content in the anode greatly decreases the cell performance due to a decreased percolated electronic phase. The sample with low performance has high tortuosity. Different approaches vary regarding the tortuosity value and computational time. The path-length-based approach can achieve reasonable accuracy in a relatively short time but is only valid for using the longest path length.

Design and Implementation of High QoS 3D-NoC using Modified Double Particle Swarm Optimization on FPGA

One technique to overcome the exponential growth bottleneck is to increase the number of cores on a processor, although having too many cores might cause issues including chip overheating and communication blockage. The problem of the communication bottleneck on the chip is presently effectively resolved by networks-on-chip (NoC). A 3D stack of chips is now possible, thanks to recent developments in IC manufacturing techniques, enabling to reduce of chip area while increasing chip throughput and reducing power consumption. The automated process associated with mapping applications to form three-dimensional NoC architectures is a significant new path in 3D NoC research. This work proposes a 3D NoC partitioning approach that can identify the 3D NoC region that has to be mapped. A double particle swarm optimization (DPSO) inspired algorithmic technique, which may combine the characteristics having neighbourhood search and genetic architectures, also addresses the challenge of a particle swarm algorithm descending into local optimal solutions. Experimental evidence supports the claim that this hybrid optimization algorithm based on Double Particle Swarm Optimisation outperforms the conventional heuristic technique in terms of output rate and loss in energy. The findings demonstrate that in a network of the same size, the newly introduced router delivers the lowest loss on the longest path. Three factors, namely energy, latency or delay, and throughput, are compared between the suggested 3D mesh ONoC and its 2D version. When comparing power consumption between 3D ONoC and its electronic and 2D equivalents, which both have 512 IP cores, it may save roughly 79.9% of the energy used by the electronic counterpart and 24.3% of the energy used by the latter. The network efficiency of the 3D mesh ONoC is simulated by DPSO in a variety of configurations. The outcomes also demonstrate an increase in performance over the 2D ONoC. As a flexible communication solution, Network-On-Chips (NoCs) have been frequently employed in the development of multiprocessor system-on-chips (MPSoCs). By outsourcing their communication activities, NoCs permit on-chip Intellectual Property (IP) cores to communicate with one another and function at a better level. The important components in assigning application duties, distributing the work to the IPs, and coordinating communication among them are mapping and scheduling methods. This study aims to present an entirely advanced form of research in the area of 3D NoC mapping and scheduling applications, grouping the results according to various parameters and offering several suggestions for further research.

Detour Polynomial of Theta Graph

Let be any connected graph with vertices set and edges set . For any two distinct vertices and , the detour distance between and which is denoted by is a longest path between and in a graph . The detour polynomial of a connected graph is denoted by ; and is defined by . In this paper, the detour polynomial of the theta graph and the uniform theta graph will be computed.

Distributionally Robust Chance-Constrained p-Hub Center Problem

The p-hub center problem is a fundamental model for the strategic design of hub location. It aims at constructing p fully interconnected hubs and links from nodes to hubs so that the longest path between any two nodes is minimized. Existing literature on the p-hub center problem under uncertainty often assumes a joint distribution of travel times, which is difficult (if not impossible) to elicit precisely. In this paper, we bridge the gap by investigating two distributionally robust chance-constrained models that cover, respectively, an existing stochastic one under independent normal distribution and one that is based on the sample average approximation approach as a special case. We derive deterministic reformulations as a mixed-integer program wherein a large number of constraints can be dynamically added via a constraint-generation approach to accelerate computation. Counterparts of our models in the emerging robust satisficing framework are also discussed. Extensive numerical experiments demonstrate the encouraging out-of-sample performance of our proposed models as well as the effectiveness of the constraint-generation approach. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work is partially supported by the National Natural Science Foundation of China [Grants 72101187 and 72021002] and Early Career Scheme from the Hong Kong Research Grants Council General Research Fund [Grant 9043424] and NSFC/RGC Joint Research Scheme N_CityU105/21. Y. Zhao is supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 grant call [Grant MOE-2019-T3-1-010]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0113 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0113 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Optimal Embedding of Graphs with Nonconcurrent Longest Paths in Archimedean Tessellations

Optimal graph embeddings represent graphs in a lower dimensional space in a way that preserves the structure and properties of the original graph. These techniques have wide applications in fields such as machine learning, data mining, and network analysis. Do we have small (if possible minimal) k -connected graphs with the property that for any j vertices there is a longest path avoiding all of them? This question of Zamfirescu (1972) was the first variant of Gallai’s question (1966): Do all longest paths in a connected graph share a common vertex? Several good examples answering Zamfirescu’s question are known. In 2001, he asked to investigate the family of geometrical lattices with respect to this property. In 2017, Chang and Yuan proved the existence of such graphs in Archimedean tiling. Here, we prove that the graphs presented by Chang and Yuan are not optimal by constructing such graphs of sufficiently smaller orders. The problem of finding nonconcurrent longest paths in Archimedean tessellations refers to finding paths in a lattice such that the paths do not overlap or intersect with each other and are as long as possible. The complexity of embedding graph is still unknown. This problem can be challenging because it requires finding paths that are both long and do not intersect, which can be difficult due to the constraints of the lattice structure.

Variable Ordering in Binary Decision Diagram Using Spider Monkey Optimization for Node and Path Length Optimization

Binary Decision Diagrams (BDDs) are an important data structure for the design of digital circuits using VLSI CAD tools. The ordering of variables affects the total number of nodes and path length in the BDDs. Finding a good variable ordering is an optimization problem and previously many optimization approaches have been implemented for BDDs in a number of research works. In this paper, an optimization approach based on Spider Monkey Optimization (SMO) algorithm is proposed for the BDD variable ordering problem targeting number of nodes and longest path length. SMO is a well-known swarm intelligence-based optimization approach based on spider monkeys foraging behavior. The proposed work has been compared with other latest BDD reordering approaches using Particle Swarm Optimization (PSO) algorithm. The results obtained show significant improvement over the Particle Swarm Optimization method. The proposed SMO-based method is applied to different benchmark digital circuits having different levels of complexities. The node count and longest path length for the maximum number of tested circuits are found to be better in SMO than PSO.

UC Secure Private Branching Program and Decision Tree Evaluation

Branching program (BP) is a DAG-based non-uniform computational model for L&#x002F;poly class. It has been widely used in formal verification, logic synthesis, and data analysis. As a special BP, a decision tree is a popular machine learning classifier for its effectiveness and simplicity. In this work, we propose a UC-secure efficient 3-party computation platform for outsourced branching program and&#x002F;or decision tree evaluation. We construct a constant-round protocol and a linear-round protocol. In particular, the overall (online &#x002B; offline) communication cost of our linear-round protocol is <inline-formula><tex-math notation="LaTeX">$O( {d( {\ell + log m + log n} )} )$</tex-math></inline-formula> and its round complexity is 2<i>d</i>-1, where <i>m</i> is the DAG size, n is the number of features, <inline-formula><tex-math notation="LaTeX">$\ell $</tex-math></inline-formula> is the feature length, and <i>d</i> is the longest path length. To enable efficient oblivious hopping among the DAG nodes, we propose a lightweight 1-out-of-<i>N</i> shared OT protocol with logarithmic communication in both online and offline phase. This partial result may be of independent interest to some other cryptographic protocols. Our benchmark shows, compared with the state-of-the-arts, the proposed constant-round protocol is up to 10X faster in the WAN setting, while the proposed linear-round protocol is up to 15X faster in the LAN setting.