Hull Number Research Articles

Perbandingan Produktivitas dan Biaya Bongkar Overburden pada Excavator PC2000 Bucket Standart dengan Modifikasi pada Pertambangan Batubara: Studi Kasus PT. Putra Perkasa Abadi Job Site Bukit Asam

A company requires productivity to achieve predetermined goals. Productivity is an important aspect for a company in determining its future business because productivity is the effective and efficient use of resources to produce or increase the output of goods or services. PT. Putra Perkasa Abadi is targeting overburden productivity on its PC2000 excavator to be 820bcm/hour, but the company wants to increase or increase production by modifying the PC2000 excavator from the standard size of only 12m³ to 14m³ without changing other components in order to get better results. more without increasing operational costs and costs for removing soil layers. The modified tool is PC2000 with hull number EX2045 bucket 14m³ by comparing the standard tool PC2000 with hull number EX2044 bucket 12m³, the picking test was carried out on 16 December 2023 shift 1. The EX2045 data results obtained a productivity of 914bcm with operational costs of 18.270.000 and costs for removing soil layers of 2,176 /bcm while EX2044's productivity is 823bcm with operational costs of 18.210.000 with a land demolition price of 2,418/bcm, so EX2045 is 11% more efficient than EX2044 and provides productivity of 11.4% of the company's target provided that it must minimize obstacles in the field that hinder the production process so that production can run optimally as expected.

Computing the hull and interval numbers in the weakly toll convexity

A walk u0u1…uk−1uk of a graph G is a weakly toll walk if u0uk∉E(G), u0ui∈E(G) implies ui=u1, and ujuk∈E(G) implies uj=uk−1. The weakly toll interval of a set S⊆V(G), denoted by I(S), is formed by S and the vertices belonging to some weakly toll walk between two vertices of S. Set S is weakly toll convex if I(S)=S. The weakly toll convex hull of S, denote by H(S), is the minimum weakly toll convex set containing S. The weakly toll interval number of G is the minimum cardinality of a set S⊆V(G) such that I(S)=V(G); and the weakly toll hull number of G is the minimum cardinality of a set S⊆V(G) such that H(S)=V(G). In this work, we show how to compute the weakly toll interval and the weakly toll hull numbers of a graph in polynomial time. In contrast, we show that determining the weakly toll convexity number of a graph G (the size of a maximum weakly toll convex set different from V(G)) is NP-hard.

On the monophonic convexity in complementary prisms

A set S of vertices of a graph G is monophonic convex if S contains all the vertices belonging to any induced path connecting two vertices of S. The cardinality of a maximum proper monophonically convex set of G is called the monophonic convexity number of G. The monophonic interval of a set S of vertices of G is the set S together with every vertex belonging to any induced path connecting two vertices of S. The cardinality of a minimum set S⊆V(G) whose monophonic interval is V(G) is called the monophonic interval number of G. The monophonic convex hull of a set S of vertices of G is the smallest monophonically convex set containing S in G. The cardinality of a minimum set S⊆V(G) whose monophonic convex hull is V(G) is called the monophonic hull number of G. The complementary prismGG¯ of G is obtained from the disjoint union of G and its complement G¯ by adding the edges of a perfect matching between them. In this work, we show that the corresponding decision problem to the monophonic convexity number is NP-complete even for complementary prisms. On the other hand, we show that the monophonic interval number and the monophonic hull number can be determined in linear time for the complementary prisms of all graphs.

On the hull number on cycle convexity of graphs

In this work, we study the parameter hull number in a recently defined graph convexity called Cycle Convexity, whose definition is motivated by related notions in Knot Theory.For a graph G=(V,E), define the interval function in the Cycle Convexity as Icc(S)=S∪{v∈V(G)|there is a cycle C in G such that V(C)∖S={v}}, for every S⊆V(G). We say that S⊆V(G) is convex if Icc(S)=S. The convex hull of S⊆V(G), denoted by Hull(S), is the inclusion-wise minimal convex set S′ such that S⊆S′. A set S⊆V(G) is called a hull set if Hull(S)=V(G). The hull number of G in the cycle convexity, denoted by hncc(G), is the cardinality of a smallest hull set of G.We first focus on the class of planar graphs, as the main motivation for the definition of hncc(G) stems from Knot Theory and occurs when G is a 4-regular planar graph. We prove that: the hull number of a 4-regular planar graph is at most half of its number of vertices and that such bound is tight; and that deciding whether hncc(G)≤k, provided a positive integer k and a planar graph G, is an NP-complete problem.On the positive side, we present polynomial-time algorithms to compute the hull number in the cycle convexity of chordal graphs, P4-sparse graphs, and grids.

Automatic vessel plate number recognition for surface unmanned vehicles with marine applications.

In the practical application scenarios of USVs, it is necessary to identify a vessel in order to accomplish tasks. Considering the sensors equipped on the USV, visible images provide the fastest and most efficient way of determining the hull number. The current studies divide the task of recognizing vessel plate number into two independent subtasks: text localization in the image and its recognition. Then, researchers are focusing on improving the accuracy of localization and recognition separately. However, these methods cannot be directly applied to USVs due to the difference between these two application scenarios. In addition, as the two independent models are serial, there will be inevitable propagation of error between them, as well as an increase in time costs, resulting in a less satisfactory performance. In view of the above, we proposed a method based on object detection model for recognizing vessel plate number in complicated sea environments applied to USVs. The accuracy and stability of model have been promoted by recursive gated convolution structure, decoupled head, reconstructing loss function, and redesigning the sizes of anchor boxes. To facilitate this research, a vessel plate number dataset is established in this paper. Furthermore, we conducted a experiment utilizing a USV platform in the South China Sea. Compared with the original YOLOv5, the mAP (mean Average Precision) value of proposed method is increased by 6.23%. The method is employed on the "Tian Xing" USV platform and the experiment results indicates both the ship and vessel plate number can be recognized in real-time. In both the civilian and military sectors, this has a great deal of significance.

On monophonic position sets in graphs

The general position problem in graph theory asks for the largest set S of vertices of a graph G such that no shortest path of G contains more than two vertices of S. In this paper we consider a variant of the general position problem called the monophonic position problem, obtained by replacing ‘shortest path’ by ‘induced path’. We prove some basic properties and bounds for the monophonic position number of a graph and determine the monophonic position number of some graph families, including unicyclic graphs, complements of bipartite graphs and split graphs. We show that the monophonic position number of triangle-free graphs is bounded above by the independence number. We present realisation results for the general position number, monophonic position number and monophonic hull number. Finally we discuss the complexity of the monophonic position problem.

Ship hull number detection and recognition under sparse samples

目的 舰船舷号检测识别是海面态势感知的关键技术，精准的舷号检测识别对海洋权益保护具有重要意义。但目前没有公开数据提供支持。为此，本文先构建了一个真实场景下的稀疏舰船舷号数据集（sparse ship hullnumber dataset in real scene，SSHN-RS），包含3 004幅舰船图像，共计11 328个舷号字符，覆盖了多国、各类、水平、倾斜、背景简单、背景复杂、光线不佳和被遮挡的舰船舷号样本，是一个具有挑战性的数据集。基于SSHN-RS，开展舰船舷号检测识别研究，其主要难点在于：1）样本稀疏，模型容易过拟合；2）舷号字符分布密集，网络难以充分提取各字符特征；3）部分字符存在嵌套区域和相似区域，网络会识别出大量冗余结果。针对上述难点，提出了一种基于多视角渐进式上下文解耦的舰船舷号检测识别算法。方法 首先，引入一个固定中心和最大化面积的随机透视变换技术，在不增加样本数量的前提下扩充舷号姿态，实现了数据增广，提升了模型的泛化能力；其次，提出了一个渐进式上下文解耦技术，先通过依次擦除舷号各字符生成一系列新样本，再利用特征提取网络提取和融合各样本的多尺度特征，不仅减少字符上下文信息对特征学习的干扰，而且再次增广了数据；最后，在测试阶段，提出了一个掩码间扰动抑制技术，先根据预测结果采用与渐进式上下文解耦技术类似的方法生成新样本并重新进行预测，再引入一个1维非极大值抑制技术去除预测结果中错误的冗余字符，输出最佳检测识别结果，进一步优化网络性能。结果 在SSHN-RS上采用主流实例分割算法进行定性和定量评估。在定量评估上，本文算法舷号的检测精确率、召回率、F值和识别率分别可达0.985 4，0.957 6，0.971 3，0.901 8，均优于其他算法。相比指标排名第2的算法，分别提高了4.51%，3.45%，3.97%，8.83%；在定性评估上，本文算法更适合舰船舷号检测识别任务，检测识别性能更高。此外，本文算法可以泛化到其他实例分割算法中，以经典算法Mask RCNN（mask region based convolutional neural network）为例，加入本文算法各模块后，各指标分别提升了9.82%，6.04%，7.80%，6.73%。结论 本文算法可以解决舷号检测识别任务中因样本稀疏、舷号分布密集、部分字符存在嵌套和相似性带来的问题，在主观和客观上均取得了最先进的性能，并且具有通用性。SSHN-RS可通过https://github.com/Bingchuan897/SSHN-RS获取。;Objective Ship hull number detection and recognition can be as the key technologies for marine awareness. It is essential for the preservation of maritime rights and interests. However，it is required to data-driven researches in support of ship hull number detection and recognition. Therefore，we develop a sparse ship hull number dataset in real scene （SSHN-RS），which contains 3 004 images with a total of 11 328 hull numbers. The challenging SSHN-RS dataset is featured of ship hull numbers of various countries，hull numbers of various types，horizontal hull numbers，inclined hull numbers，hull numbers with complex background，hull numbers with simple background，poorly illuminated hull numbers and partially occluded hull numbers. We carry out SSHN-RS-related research on ship hull number detection and recognition. The main challenges are required to be resolved on three aspects as following：1）the hull number samples are sparse， which causes over-fitting of the network，2）the features of hull number are densely distributed，which is challenged to learn some of the hull number characteristics fully，and 3）some hull number have its nested areas and a high degree of similarity，which is costly for large number of redundant results. Method To resolve these problems mentioned above，we demonstrate a ship hull number detection and recognition algorithm in terms of multi-view progressive context decoupling. First，a random perspective transformation technology with fixed center and maximized area is illustrated. To realize data augmentation and improve the generalization ability of the model，the hull number spatial attitude is extended without increasing the number of samples. Second，a progressive context decoupling technology is proposed. A series of new samples are first generated by sequentially erasing each character of the hull number，and the feature extraction network is then used to extract and fuse the multi-scale features of each sample. It can reduce the influence of feature-contextual information on feature learning and rich the data expansion. It can improve the feature expression ability effectively as well. Finally，in the testing stage，to generate new samples，and inputs the new samples into the testing network for prediction， an inter mask disturbance suppression technology is first focused on a method similar to the progressive context decoupling technology. At the same time，a one-dimensional non-maximum suppression technology is introduced that it can mainly process the hull number recognition results of each sample twice. To suppress the redundant mask in the detection and recognition results effectively，it can make each character of the hull number of all samples correspond to a recognition result. For the testing network，the output has only a set of optimal results. However，there is hull number noisy recognition in some samples. Therefore，the hull number recognition results of all samples are added on the original images，and the second one-dimensional non-maximum suppression technology is performed and processed on it. It can suppress the noises in some samples and outputs a set of optimal results. The post-processing module can optimize the detection and recognition performance further. Result The comparative experiment is mainly carried out on SSHN-RS. First，we conduct evaluation analysis on the general instance segmentation algorithms. Multi-view progressive context decoupling-based detection precision，recall，f-score and recognition rate of the ship number detection and recognition algorithm can reach 0. 985 4，0. 957 6， 0. 971 3 and 0. 901 8，which are improved by 4. 51%，3. 45%，3. 97% and 8. 83% respectively compared to the secondranked method. Second，the ablation experiments on the ship hull number detection and recognition algorithm are carried out in terms of multi-view progressive context decoupling. The experimental results show that the performance of ship hull number detection and recognition is improved whether each technology is used solely or mixed. Finally，to validate its effectiveness，we apply some popular modules of the ship hull number detection and recognition algorithm based on multiview progressive context decoupling to other general instance segmentation algorithms. Taking the classic algorithm mask region based convolutional neural network（Mask RCNN）as an example，the indexes have been improved by 9. 82%， 6. 04%，7. 80% and 6. 73% of each after our algorithm module is added. Conclusion Our SSHN-RS contains rich and effective ship hull number information，which can provide data support for ship hull number detection and recognition. The experimental results show that the multi-view progressive context decoupling-based ship hull number detection and recognition algorithm can optimize the detection and recognition performance of hull numbers due to sparse samples，dense character distribution，nested areas，and characters-between high similarity. This algorithm can be generalized to other deep learning based segmentation algorithms. The benchmarks-relevant are provided as a basis for future research on ship hull number detection and recognition. The dataset is available at https://github.com/Bingchuan897/SSHN-RS.

P3-convexity on graphs with diameter two: Computing hull and interval numbers

Given a finite, simple, and undirected graph G = ( V , E ) , a P 3 -convex set of G is a set S ⊆ V ( G ) such that every vertex of V ( G ) ∖ S has at most one neighbor in S , and the P 3 -convex hull of a vertex subset S ′ of G is the smallest P 3 -convex set containing S ′ . The P 3 -hull number h ( G ) is the cardinality of the smallest set of vertices whose P 3 -convex hull is V ( G ) . In this paper, we establish some bounds on the P 3 -hull number of graphs with diameter two. Particularly, for a biconnected diameter-two graph G it holds that h ( G ) ≤ ⌈ log ( Δ ( G ) + 1 ) ⌉ + 1 , while a non-biconnected diameter-two graph G has h ( G ) = c c ( G − v ) , where v is a cut vertex of G and c c ( G − v ) is the number of connected components of G [ V ∖ { v } ] . In addition, we show that the P 3 -hull number of biconnected C 6 -free diameter-two graphs is at most 4, while for strongly regular graphs G = G ( n , k , b , c ) it holds that h ( G ) ≤ min { ⌈ k 1 + b ⌉ + 1 , ⌈ log c + 1 ( k . c + 1 ) ⌉ + 1 } . Finally, we consider the P 3 -interval number, which is the cardinality of the smallest set S of vertices such that every vertex not in S has two neighbors in this set. We show that computing the P 3 -interval number on diameter-two split graphs is NP - complete .

Computational and structural aspects of the geodetic and the hull numbers of shadow graphs

Given a set X ⊆ V ( G ) , let [ X ] G denote the set of all vertices of G lying on some shortest path between two vertices of X . If [ X ] G = X , then X is a convex set of G . The convex hull of X , denoted by 〈 X 〉 G , is the smallest convex set containing X . We say that X is a hull set of G if 〈 X 〉 G = V ( G ) and that X is a geodetic set of G if [ X ] G = V ( G ) . The hull number h ( G ) of G is the minimum cardinality of a hull set of G ; and the geodetic number g ( G ) of G is the minimum cardinality of a geodetic set of G . The shadow graph of G , denoted by S ( G ) , is the graph obtained from G by adding a new vertex v ′ for each vertex v of G and joining v ′ to the neighbors of v in G . In this paper, we present sharp bounds for the geodetic and the hull numbers of shadow graphs. We characterize the classes of graphs for which some of these bounds are attained. We also prove for a fixed integer k , that the problem of deciding whether g ( S ( G ) ) ≤ n − k is NP -complete even if the diameter of G is 2; and that the problem of deciding whether h ( S ( G ) ) ≤ n − 1 belongs to P .

Computing the hull number in toll convexity

A tolled walk W between vertices u and v in a graph G is a walk in which u is adjacent only to the second vertex of W and v is adjacent only to the second-to-last vertex of W. A set \(S \subseteq V(G)\) is toll convex if the vertices contained in any tolled walk between two vertices of S are contained in S. The toll convex hull of S is the minimum toll convex set containing S. The toll hull number of G is the minimum cardinality of a set whose toll convex hull is V(G). The main contribution of this work is a polynomial-time algorithm for computing the toll hull number of a general graph.

The hull number in the convexity of induced paths of order 3

A set S of vertices of a graph G is P3⁎-convex if there is no vertex outside S having two non-adjacent neighbors in S. The P3⁎-convex hull of S is the minimum P3⁎-convex set containing S. If the P3⁎-convex hull of S is V(G), then S is a P3⁎-hull set. The minimum size of a P3⁎-hull set is the P3⁎-hull number of G. In this paper, we show that the problem of deciding whether the P3⁎-hull number of a chordal graph is at most k is NP-complete and present a linear-time algorithm to determine this parameter and provide a minimum P3⁎-hull set for unit interval graphs.

A polynomial time algorithm for geodetic hull number for complementary prisms

Let G be a finite, simple, and undirected graph and let S ⊆ V (G). In the geodetic convexity, S is convex if all vertices belonging to any shortest path between two vertices of S lie in S. The convex hull H(S) of S is the smallest convex set containing S. The hull number h(G) is the minimum cardinality of a set S ⊆ V (G) such that H(S) = V (G). The complementary prism GG̅ of a graph G arises from the disjoint union of the graph G and G̅ by adding the edges of a perfect matching between the corresponding vertices of G and G̅. Previous works have determined h(GG̅) when both G and G̅ are connected and partially when G is disconnected. In this paper, we characterize convex sets in GG̅ and we present equalities and tight lower and upper bounds for h(GG̅). This fills a gap in the literature and allows us to show that h(GG̅) can be determined in polynomial time, for any graph G.

Hull Number Effect in Ship Using Conveyor on Ocean Waste Collection

The increase in ocean waste continues to grow from year to year, especially plastic and solid waste. Various ocean waste collection ships using conveyors exist, both in the form of designs and already in operation, but there has been no research on how many hulls are suitable for ocean waste collectors. This study aims to choose between the three-ship models, namely monohull type U, catamaran type inner flat hull, and trimaran type symmetrical. Assessment is based on ship resistance which relates to fuel consumption and flow distribution relates to ocean waste collection. This research uses Computational Fluid Dynamics (CFD) method which produces resistance, fluid flow velocity contours, and fluid flow patterns. Numerical simulation is based on Reynolds Averaged Navier Stokes (RANS). The turbulent model uses the standard k-epsilon equation. Then the volume of fluid sub-models used is open channel flow. The number of eulerian phases is two. Moreover, formulation of the volume fraction parameters used is an implicit body force. The results show that monohull type U is better than others in easiest to bring ocean waste closer to the conveyor and smallest resistance force. Then symmetric trimaran is faster than others in making ocean waste flow to the conveyor.

Computational and structural aspects of the geodetic and the hull numbers of shadow graphs

Given a set X⊆V(G), let [X]G denote the set of all vertices of G lying on some shortest path between two vertices of X. If [X]G=X, then X is a convex set of G. The convex hull of X, denoted by 〈X〉G, is the smallest convex set containing X. We say that X is a hull set of G if 〈X〉G=V(G) and that X is a geodetic set of G if [X]G=V(G). The hull number h(G) of G is the minimum cardinality of a hull set of G; and the geodetic number g(G) of G is the minimum cardinality of a geodetic set of G. The shadow graph of G, denoted by S(G), is the graph obtained from G by adding a new vertex v′ for each vertex v of G and joining v′ to the neighbors of v in G. In this paper, we present sharp bounds for the geodetic and the hull numbers of shadow graphs. We characterize the classes of graphs for which some of these bounds are attained. We also prove for a fixed integer k, that the problem of deciding whether g(S(G))≤n−k is NP-complete even if the diameter of G is 2; and that the problem of deciding whether h(S(G))≤n−1 belongs to P.

On the $P_3$-Hull Number of Kneser Graphs

This paper considers an infection spreading in a graph; a vertex gets infected if at least two of its neighbors are infected. The $P_3$-hull number is the minimum size of a vertex set that eventually infects the whole graph.
 In the specific case of the Kneser graph $K(n,k)$, with $n\ge 2k+1$, an infection spreading on the family of $k$-sets of an $n$-set is considered. A set is infected whenever two sets disjoint from it are infected. We compute the exact value of the $P_3$-hull number of $K(n,k)$ for $n>2k+1$. For $n = 2k+1$, using graph homomorphisms from the Knesser graph to the Hypercube, we give lower and upper bounds.

Hull and geodetic numbers for some classes of oriented graphs

Let D be an orientation of a simple graph. Given u , v ∈ V ( D ) , a directed shortest ( u , v ) -path is a ( u , v ) -geodesic. S ⊆ V ( D ) is convex if, for every u , v ∈ S , the vertices in each ( u , v ) -geodesic and in each ( v , u ) -geodesic are in S . For each S ⊆ V ( D ) the (convex) hull of S , denoted by [ S ] , is the smallest convex set containing S . S ⊆ V ( D ) is a hull set if [ S ] = V ( D ) . S ⊆ V ( D ) is a geodetic set of D if each vertex of D lies in a ( u , v ) -geodesic, for some u , v ∈ S . The cardinality of a minimum hull set (resp. geodetic set) of G is the hull number (resp. geodetic number) of D , denoted by hn ⃗ ( D ) (resp. gn ⃗ ( D ) ). We first show a tight upper bound on hn ⃗ ( D ) . Given k ∈ Z + ∗ , we prove that deciding if hn ⃗ ( D ) ≤ k is NP -complete when D is an oriented partial cube; and if gn ⃗ ( D ) ≤ k is W [2]-hard parameterized by k and has no ( c ⋅ ln n ) -approximation algorithm, unless P = NP , even if D has an underlying graph that is bipartite or split or cobipartite. We also show polynomial-time algorithms to compute hn ⃗ ( D ) and gn ⃗ ( D ) when D is an oriented cactus.

On the geodetic hull number for complementary prisms II

In the geodetic convexity, a set of vertices S of a graph G is convex if all vertices belonging to any shortest path between two vertices of S lie in S. The convex hull H(S) of S is the smallest convex set containing S. If H(S) = V (G), then S is a hull set. The cardinality h(G) of a minimum hull set of G is the hull number of G. The complementary prism GḠ of a graph G arises from the disjoint union of the graph G and Ḡ by adding the edges of a perfect matching between the corresponding vertices of G and Ḡ. A graph G is autoconnected if both G and Ḡ are connected. Motivated by previous work, we study the hull number for complementary prisms of autoconnected graphs. When G is a split graph, we present lower and upper bounds showing that the hull number is unlimited. In the other case, when G is a non-split graph, it is limited by 3.

Computing the hull number in Δ-convexity

Given a graph G, a set S⊆V(G) is Δ-convex if there is no vertex u∈V(G)∖S forming a triangle with two vertices of S. The Δ-convex hull of S is the minimum Δ-convex set containing S. The Δ-hull number of a graph G is the cardinality of a minimum set such that its Δ-convex hull is V(G). We show that the problem of deciding whether the Δ-hull number of a general graph is at most k is an NP-complete problem and present polynomial-time algorithms for computing the Δ-hull number of some graph classes including chordal graphs, dually chordal graphs, and cographs.

The hull number of powers of cycle graphs under restricted conditions

Let [Formula: see text] be the cycle graph of order [Formula: see text] on the vertices [Formula: see text] and [Formula: see text] be the [Formula: see text]th power of [Formula: see text]. In this paper, we find the hull number of [Formula: see text] under restricted conditions on the vertices of the graph [Formula: see text] namely the independent and connected hull numbers of [Formula: see text].

Hull and Geodetic Numbers for Some Classes of Oriented Graphs

An oriented graph D is an orientation of a simple graph, i.e. a directed graph whose underlying graph is simple. A directed path from u to v with minimum number of arcs in D is an (u, v)-geodesic, for every u, v ∈ V(D). A set S ⊆ V(D) is (geodesically) convex if, for every u, v ∈ S, all the vertices in each (u, v)-geodesic and in each (v, u)-geodesic are in S. For every S ⊆ V(D) the (convex) hull of S is the smallest convex set containing S and it is denoted by [S]. A hull set of D is a set S ⊆ V(D) whose hull is V(D). The cardinality of a minimum hull set is the hull number of D and it is denoted by hn→(D). A geodetic set of D is a set S ⊆ V(D) such that each vertex of D lies in an (u, v)-geodesic, for some u, v ∈ S. The cardinality of a minimum geodetic set is the geodetic number of D and it is denoted by gn→(D).In this work, we first present an upper bound for the hull number of oriented split graphs. Then, we turn our attention to the computational complexity of determining such parameters. We first show that computing hn→(D) is NP-hard for partial cubes, a subclass of bipartite graphs, and that computing gn→(D) is also NP-hard for directed acyclic graphs (DAG). Finally, we present a positive result by showing how to compute such parameters in polynomial time when the input graph is an oriented cactus.