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Smallest box which encloses some set of points
minimum box is usually called accordingly, e.g., "minimum-perimeter bounding box". The minimum bounding box of a point set is the same as the minimum
Minimum_bounding_box
Algorithms in computational geometry
smallest enclosing box problem is that of finding the oriented minimum bounding box enclosing a set of points. It is a type of bounding volume. "Smallest"
Minimum bounding box algorithms
Minimum_bounding_box_algorithms
algorithm Bentley–Ottmann algorithm Shamos–Hoey algorithm Minimum bounding box algorithms: find the oriented minimum bounding box enclosing a set of points
List_of_algorithms
Smallest rectangle which encloses some planar set of points
In computational geometry, the minimum bounding rectangle (MBR), also known as bounding box (BBOX) or envelope, is an expression of the maximum extents
Minimum_bounding_rectangle
Graphics structure
used bounding volumes is an axis-aligned minimum bounding box. The axis-aligned minimum bounding box for a given set of data objects is easy to compute
Bounding_volume_hierarchy
Closed volume that completely contains the union of a set of objects
bounding volume (or bounding region) for a set of objects is a closed region that completely contains the union of the objects in the set. Bounding volumes
Bounding_volume
Branch of computer science
algorithm Bentley–Ottmann algorithm Shamos–Hoey algorithm Minimum bounding box algorithms: find the oriented minimum bounding box enclosing a set of points
Computational_geometry
Kinetic data structure
Kinetic minimum box is a kinetic data structure to maintain the minimum bounding box of a set of points whose positions change continuously with time.
Kinetic_minimum_box
A bounding interval hierarchy (BIH) is a partitioning data structure similar to that of bounding volume hierarchies or kd-trees. Bounding interval hierarchies
Bounding_interval_hierarchy
Optimization problem in mathematics
program. Further, constraints and variables can be added to minimize the bounding-box-netlength. Given small rectangles R 1 , . . . R n {\displaystyle R_{1}
Rectangle_packing
Shortest network connecting points
realizations, with polynomially bounded edge lengths and bounding boxes. Rectilinear minimum spanning tree, a minimum spanning tree with distances measured
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
Method of executing orders
explains that "DC algorithms detect subtle trend transitions, improving trade timing and profitability in turbulent markets". DC algorithms detect subtle
Algorithmic_trading
Data structures used in spatial indexing
their minimum bounding rectangle in the next higher level of the tree; the "R" in R-tree is for rectangle. Since all objects lie within this bounding rectangle
R-tree
Measure method in computational geometry
in medical imaging and solid modeling) Minimum area oriented bounding box Minimum perimeter oriented bounding box Onion triangulations Spiral triangulations
Rotating_calipers
Class of algorithms that find approximate solutions to optimization problems
computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems
Approximation_algorithm
hyperrectangles), the ones with edges parallel to the coordinate axes. Minimum bounding boxes are often implicitly assumed to be axis-aligned. A more general
Axis-aligned_object
Computational geometry problem
systematic study of the computational complexity of geometric algorithms. Randomized algorithms that solve the problem in linear time are known, in Euclidean
Closest pair of points problem
Closest_pair_of_points_problem
Shape that blocks all lines of sight
} The general idea of the algorithm is to construct a "bow and arrow" like barrier from the minimum-perimeter bounding box of the input, consisting of
Opaque_set
common assumption in both document layout analysis algorithms and optical character recognition algorithms that the characters in the document image are oriented
Document_layout_analysis
American computer scientist
O'Rourke's early results was an algorithm for finding the minimum bounding box of a point set in three dimensions when the box is not required to be axis-aligned
Joseph_O'Rourke_(professor)
Statistical optimization technique
algorithms. KDD 2013: 847–855 Jasper Snoek, Hugo Larochelle and Ryan Prescott Adams. Practical Bayesian Optimization of Machine Learning Algorithms.
Bayesian_optimization
all maximal isothetic empty cuboids. Largest empty sphere Minimum bounding box, Minimum bounding rectangle A. Naamad, D. T. Lee and W.-L. Hsu (1984). "On
Largest_empty_rectangle
Algorithm that employs a degree of randomness as part of its logic or procedure
(Las Vegas algorithms, for example Quicksort), and algorithms which have a chance of producing an incorrect result (Monte Carlo algorithms, for example
Randomized_algorithm
triangulation Voronoi diagram Minimum bounding box (Smallest enclosing box, Smallest bounding box) 2-D case: Smallest bounding rectangle (Smallest enclosing
List of combinatorial computational geometry topics
List_of_combinatorial_computational_geometry_topics
procedural constraints. Bounding box One of the simplest type of bounding volume, consisting of axis-aligned or object-aligned extents. Bounding volume A mathematically
Glossary_of_computer_graphics
Optimization method
simple box constraints. The BFGS matrix also admits a compact representation, which makes it better suited for large constrained problems. The algorithm is
Broyden–Fletcher–Goldfarb–Shanno algorithm
Broyden–Fletcher–Goldfarb–Shanno_algorithm
Visualization of node-link graphs
so graph drawing algorithms must generally allow for edge crossings. The area of a drawing is the size of its smallest bounding box, relative to the closest
Graph_drawing
Branch of numerical optimization
any case bounding is required, which is why deterministic global optimization methods cannot give a rigorous result when working with black-box code, unless
Deterministic global optimization
Deterministic_global_optimization
Algorithm in graph theory
Floyd–Warshall algorithm (also known as Floyd's algorithm, the Roy–Warshall algorithm, the Roy–Floyd algorithm, or the WFI algorithm) is an algorithm for finding
Floyd–Warshall_algorithm
Optimization problem in computer science
cluster-distance bounding for similarity search in image databases". ICIP. Ramaswamy, Sharadh; Rose, Kenneth (2010). "Adaptive cluster-distance bounding for high-dimensional
Nearest_neighbor_search
Equivalence of average-case and expected complexity
performance of randomized algorithms to deterministic (non-random) algorithms. It states that, for certain classes of algorithms, and certain measures of
Yao's_principle
Branch of mathematics
search capable of escaping from local minima Evolutionary algorithms (e.g., genetic algorithms and evolution strategies) Differential evolution, a method
Global_optimization
Bloom (shader effect) Bounding interval hierarchy Bounding sphere Bounding volume Bounding volume hierarchy Bresenham's line algorithm Bump mapping Calligraphic
List of computer graphics and descriptive geometry topics
List_of_computer_graphics_and_descriptive_geometry_topics
Techniques to improve network performance
algorithms are aware of the state of the network. This consist of three primary categories: black box, grey box, and green box. Black box algorithms offer
TCP_congestion_control
{R} ^{d}} , R ( X ) {\displaystyle R(X)} denote the axis-aligned minimum bounding box for the points in X {\displaystyle X} , and s > 0 {\displaystyle
Well-separated pair decomposition
Well-separated_pair_decomposition
Task of computing complete subgraphs
although the running time of known algorithms for the clique problem is polynomial for any fixed k, these algorithms do not suffice for fixed-parameter
Clique_problem
Optimization algorithm
Pytlak, Radoslaw (2009). "Limited Memory Quasi-Newton Algorithms". Conjugate Gradient Algorithms in Nonconvex Optimization. Springer. pp. 159–190. ISBN 978-3-540-85633-7
Limited-memory_BFGS
Intersection graph of trapezoids between parallel lines
{\displaystyle {O}(n\log ^{k-1}n)} time. Algorithms for trapezoid graphs should be compared with algorithms for general co-comparability graphs. For this
Trapezoid_graph
Subfield of mathematical topology
complexity theory. A primary concern of algorithmic topology, as its name suggests, is to develop efficient algorithms for solving problems that arise naturally
Computational_topology
zero matrix Algorithms for matrix multiplication: Strassen algorithm Coppersmith–Winograd algorithm Cannon's algorithm — a distributed algorithm, especially
List of numerical analysis topics
List_of_numerical_analysis_topics
Probabilistic optimization technique and metaheuristic
In such cases, SA may be preferable to exact algorithms such as gradient descent or branch and bound. The problems solved by SA are currently formulated
Simulated_annealing
Smallest dimension where a graph can be represented as an intersection graph of boxes
the mathematical field of graph theory, the boxicity of a graph is a graph invariant defined to be the minimum dimension of Euclidean space required to represent
Boxicity
Multidimensional search tree for spatial coordinates
into n+1 regions, each corresponding to a leaf in the K-d tree. The bounding box (or bounds array) of a node {x,j} is the region of the space delimited
Relaxed_k-d_tree
Optimization technique
vision, the minimum energy solution corresponds to the maximum a posteriori estimate of a solution. Although many computer vision algorithms involve cutting
Graph cuts in computer vision and artificial intelligence
Graph_cuts_in_computer_vision_and_artificial_intelligence
Methodic assignment of colors to elements of a graph
these algorithms are sometimes called sequential coloring algorithms. The maximum (worst) number of colors that can be obtained by the greedy algorithm, by
Graph_coloring
Financial software
broker algorithms, they had grown to enjoy the revenue that they could command from both their customers and from brokers keen to get their algorithms onto
FIXatdl
Representation of a graph as a path graph "thickened" by some amount
exponential-time algorithms for the maximum cut and minimum dominating set problems in cubic graphs, and for several other NP-hard optimization problems. Boxicity, a
Pathwidth
Solution process for some optimization problems
the best lower bound obtained for any of the approximate solutions. This solution is optimal, although possibly not unique. The algorithm may also be stopped
Nonlinear_programming
Computational problem
problems can be solved with grid-based algorithms that overlay a grid on top of configuration space, or geometric algorithms that compute the shape and connectivity
Motion_planning
Property of artificial neural networks
using control-theoretic arguments. In 2023, Cai obtained the optimal minimum width bound for the universal approximation. For the arbitrary depth case, Leonie
Universal approximation theorem
Universal_approximation_theorem
Set of basic shapes which assemble into a polygon
to guarantee that the divisions found by an algorithms have minimum size. There are linear-time algorithms for quadrangulations of hole-free polygons with
Polygon_partition
R-tree in that it defines a given object's N-dimensional bounding volume (called Minimum Bounding Rectangles – MBR) as a point in N-dimensions, represented
Priority_R-tree
Computer hardware technology that uses quantum mechanics
classical algorithms. Quantum algorithms that offer more than a polynomial speedup over the best-known classical algorithm include Shor's algorithm for factoring
Quantum_computing
Property in graph theory
must have integer coordinates. For drawings of this type, the minimum volume of a bounding box of the drawing must be at least proportional to the cutwidth
Cutwidth
optimization, Multilevel Coordinate Search (MCS) is an efficient algorithm for bound constrained global optimization using function values only. To do
MCS_algorithm
Problem of finding the longest simple path for a given graph
Fenghui (2007), "Improved algorithms for path, matching, and packing problems", Proc. 18th ACM-SIAM Symposium on Discrete algorithms (SODA '07) (PDF), pp. 298–307
Longest_path_problem
Type of cipher
block cipher consists of two paired algorithms, one for encryption, E, and the other for decryption, D. Both algorithms accept two inputs: an input block
Block_cipher
Classical problem in combinatorics
December 2025 (link) Young, Neal E. (2016), "Greedy Set‑Cover Algorithms", Encyclopedia of Algorithms, Springer, pp. 886–889, ISBN 978-1-4939-2868-7 {{citation}}:
Set_cover_problem
Open-source 3D modelling software
representation (B-rep) models. Modeling Algorithms – contains a vast range of geometrical and topological algorithms (intersection, Boolean operations, surface
Open_Cascade_Technology
Methodological basis for 3D CAD/CAM solid modeling and image rendering
number of primitive solids/surfaces in the composition. By using minimum bounding boxes around the solids in the composition tree, the exhaustive search
Ray_casting
Area of discrete mathematics
Harold S. (1997). "On finding a minimum spanning tree in a network with random weights" (PDF). Random Structures & Algorithms. 10 (1–2): 187–204. doi:10
Graph_theory
Process of partitioning a rectilinear polygon
NP-hard. These results can be extended to a d-dimensional box: a guillotine-partition with minimum edge-length can be found in time O ( d n 2 d + 1 ) {\displaystyle
Guillotine_partition
Polygon in which all angles are right
parallel to the x axis and 2 sides parallel to the y axis. See also: Minimum bounding rectangle. A golygon is a rectilinear polygon whose side lengths in
Rectilinear_polygon
Formal information theory restatement of Occam's Razor
Minimum message length (MML) is a Bayesian information-theoretic method for statistical model comparison and selection. It provides a formal information
Minimum_message_length
Adaptive boosting based classification algorithm
enforcing some limit on the absolute value of z and the minimum value of w While previous boosting algorithms choose f t {\displaystyle f_{t}} greedily, minimizing
AdaBoost
Computational complexity of quantum algorithms
time. Asymptotic computational complexities of both quantum algorithms and classical algorithms are often expressed with asymptotic notation. Some common
Quantum_complexity_theory
Machine learning algorithm
Instead, one can use tracking algorithms like the KLT algorithm to detect salient features within the detection bounding boxes and track their movement between
Viola–Jones object detection framework
Viola–Jones_object_detection_framework
Distance estimation problems in computational geometry
of possible configurations, especially in 3D and higher dimensions. Bounding box, the minimal axis-aligned hyperrectangle that contains all geometric
Proximity_problems
Multidimensional search tree for points in k dimensional space
based nearest neighbor and approximate nearest neighbor algorithms CGAL the Computational Algorithms Library, has an implementations of k-d tree based nearest
K-d_tree
values for each land cover class within each image band and creates bounding boxes where pixels from each land cover class are selected for training the
Land_cover_maps
In the study of algorithms, an LP-type problem (also called a generalized linear program) is an optimization problem that shares certain properties with
LP-type_problem
Optimal data structure for priority queues
Discrete Algorithms, pp. 52–58 Goodrich, Michael T.; Tamassia, Roberto (2004). "7.3.6. Bottom-Up Heap Construction". Data Structures and Algorithms in Java
Strict_Fibonacci_heap
Family of iterative methods
algorithms of this kind are the Robbins–Monro and Kiefer–Wolfowitz algorithms introduced respectively in 1951 and 1952. The Robbins–Monro algorithm,
Stochastic_approximation
Partitioning a digital image into segments
from these algorithms are considered an object segment in the image; see Segmentation-based object categorization. Some popular algorithms of this category
Image_segmentation
Grouping a set of objects by similarity
overview of algorithms explained in Wikipedia can be found in the list of statistics algorithms. There is no objectively "correct" clustering algorithm, but
Cluster_analysis
Iterative method for minimizing convex functions
László; Schrijver, Alexander (1993), Geometric algorithms and combinatorial optimization, Algorithms and Combinatorics, vol. 2 (2nd ed.), Springer-Verlag
Ellipsoid_method
Notion for comparing dimensions of particles in different states of matter
standardized shape, like a sphere (the most usual) or a cuboid (when minimum bounding box is used), where the size parameter (ex. diameter of sphere) makes
Particle_size
Algorithmically defined graph
graph models, Black box group, an implicit model for group-theoretic algorithms Matroid oracle, an implicit model for matroid algorithms Korf, Richard E.
Implicit_graph
Dataset of images
Each set of annotations contains two pieces of information: the general bounding box in which the object is located and a detailed human-specified outline
Caltech_101
Method by which work is assigned
scheduling algorithm is used as an alternative to first-come first-served queuing of data packets. The simplest best-effort scheduling algorithms are round-robin
Scheduling_(computing)
set, that is, the ratio of maximum and minimum interior distances is in O(n1/d). Matousek proved an upper bound of C d n 1 / 2 − d / 2 {\displaystyle C_{d}n^{1/2-d/2}}
Geometric_discrepancy
Rational design of new protein molecules
heuristic algorithms, such as Monte Carlo, that are faster than exact algorithms but have no guarantees on the optimality of the results. Exact algorithms guarantee
Protein_design
Calculation of complex statistical distributions
techniques alone. Various algorithms exist for constructing such Markov chains, including the Metropolis–Hastings algorithm. Markov chain Monte Carlo
Markov_chain_Monte_Carlo
Subfield of information theory and computer science
(2005). Super-recursive algorithms. Monographs in computer science. Springer. ISBN 9780387955698. Calude, C.S. (1996). "Algorithmic information theory: Open
Algorithmic information theory
Algorithmic_information_theory
Programming : Solving Linear Programs in Õ(√rank) Iterations and Faster Algorithms for Maximum Flow" 2013 Jonah Sherman (University of California, Berkeley)
Machtey_Award
If there are more items than boxes holding them, one box must contain at least two items
early as 1622 in a book by Jean Leurechon, it is commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 treatment of the
Pigeonhole_principle
2D geometric minimization problem
This definition is used for all polynomial time algorithms. For pseudo-polynomial time and FPT-algorithms, the definition is slightly changed for the simplification
Strip_packing_problem
Matrix decomposition method
computational complexity of commonly used algorithms is O(n3) in general.[citation needed] The algorithms described below all involve about (1/3)n3 FLOPs
Cholesky_decomposition
Probabilistic problem-solving algorithm
experiments or Monte Carlo simulations, are a broad class of computational algorithms based on repeated random sampling for obtaining numerical results. The
Monte_Carlo_method
Intersection graph for intervals on the real number line
graph has boxicity at most one if and only if it is an interval graph; the boxicity of an arbitrary graph G {\displaystyle G} is the minimum number of
Interval_graph
Database of data representing objects in geometric space
spatial data. Objects (shapes, lines and points) are grouped using the minimum bounding rectangle (MBR). Objects are added to an MBR within the index that
Spatial_database
Index tree structure in computer science
nodes and supernodes. The data nodes of the X-tree contain rectilinear minimum bounding rectangles (MBRs) together with pointers to the actual data objects
X-tree
Type of Monte Carlo algorithms for signal processing and statistical inference
also known as sequential Monte Carlo methods, are a set of Monte Carlo algorithms used to find approximate solutions for filtering problems for nonlinear
Particle_filter
Measure of the joint variability
programs when the data has not been centered before. Numerically stable algorithms should be preferred in this case. The covariance is sometimes called a
Covariance
Type of plane partition
triangulation and then obtaining its dual. Direct algorithms include Fortune's algorithm, an O(n log(n)) algorithm for generating a Voronoi diagram from a set
Voronoi_diagram
Planar graph used as counterexample
remains an open problem. Unsolved problem in mathematics What is the minimum bounding box area of a grid drawing of the nested triangles graph, or of its maximal
Nested_triangles_graph
Approximation Algorithms", in Mayr, Ernst W.; Prömel, Hans Jürgen; Steger, Angelika (eds.), Lectures on Proof Verification and Approximation Algorithms, Lecture
Fully polynomial-time approximation scheme
Fully_polynomial-time_approximation_scheme
Subroutine for testing independence
for any matroid, it is possible to find the minimum weight basis of the matroid by applying a greedy algorithm that adds elements to the basis in sorted
Matroid_oracle
the algorithm above. Blended BBO is based on blended crossover in genetic algorithms, and has been shown to outperform standard BBO. The BBO algorithm presented
Biogeography-based optimization
Biogeography-based_optimization
Branch of statistics to estimate models based on measured data
Cramér–Rao bound Least squares Minimum mean squared error (MMSE), also known as Bayes least squared error (BLSE) Maximum a posteriori (MAP) Minimum variance
Estimation_theory
MINIMUM BOUNDING-BOX-ALGORITHMS
MINIMUM BOUNDING-BOX-ALGORITHMS
Girl/Female
English, Hindu, Indian, Marathi
Small Daughter
Female
Polish
Feminine form of Polish Bożydar, BOŻENA means "divine gift."
Surname or Lastname
English
English : variant of Blanton.
Surname or Lastname
English and German
English and German : patronymic from Bold as a personal name.Danish : habitational name from a place so named in Jutland.
Boy/Male
Tamil
Madhughosh | மதà¯à®•à¯‹à®·
Sweet sounding
Madhughosh | மதà¯à®•à¯‹à®·
Male
Hungarian
Hungarian form of Greek GabriÄ“l, GÃBOR means "man of God" or "warrior of God."
Surname or Lastname
English
English : from Middle English, Old English box ‘box tree’ (Latin buxus), in any of a number of possible applications. It may have been a topographic name for someone who lived by a box thicket, a habitational name from one of the places called Box, in Gloucestershire, Hertfordshire, and Wiltshire, or a metonymic occupational name for someone who worked box wood, which is very hard and for this reason was used to make a variety of tools. In some cases it may even have been a nickname for a person with pale or yellow skin, for example as the result of jaundice, a reference to the color of box wood.
Surname or Lastname
English
English : metonymic occupational name for a maker or seller of bows, from Middle English bow (Old English boga, from būgan ‘to bend’). Before the invention of gunpowder, the bow was an important long-range weapon for shooting game as well as in warfare. Boga is also found as a personal name in Old English, and it is possible that this survived into Middle English and so may lie behind the surname in some instances. In other cases (for example, Richard atte Bowe, 1306), the name is topographic, from the same word in the transferred sense ‘arched bridge’, ‘river bend’, an allusion to their similarity in shape to a drawn bow.Irish : Anglicized form of Gaelic Ó Buadhaigh (see Bogue).
Boy/Male
English
Boy.
Surname or Lastname
English
English : from the late Old English personal name Golding.
Surname or Lastname
English
English : nickname from some fancied resemblance to the songbird (Emberiza spp.).German : patronymic from an unexplained Frisian-Lower Saxon personal name, or a derivative of Bunt- (see Bunten).Sarah Bunting (1686–1762), born in Matlock, Derbyshire, became a noted Quaker minister in Cross Wicks, NJ. It is believed but not certain that other members of her family, including her father, John Bunting, came with her to NJ sometime before 1704, when her marriage to William Murfin is recorded.
Boy/Male
Muslim/Islamic
Box-tree
Male
Slovene
Short form of Slovene Sebastjan, BOÅ TJAN means "from Sebaste."
Boy/Male
British, English
Free
Male
Polish
Polish form of Slavic Bozidar, BOŻYDAR means "divine gift."
Boy/Male
Hindu
Sweet sounding
Surname or Lastname
English (Suffolk)
English (Suffolk) : variant of Browning.
Surname or Lastname
English
English : variant of Boulding, a patronymic from the Germanic personal name Baldo, a short form of any of the various compound names with the first element bald ‘bold’.
Male
English
From an Old English byname, FOX means "fox."
Male
English
Short form of English Robert, BOB means "bright fame."Â
MINIMUM BOUNDING-BOX-ALGORITHMS
MINIMUM BOUNDING-BOX-ALGORITHMS
Female
Spanish
Spanish name ASUNCIÓN means "assumption," in reference to the Virgin Mary's assumption into heaven.
Girl/Female
Muslim/Islamic
It's shining
Boy/Male
Tamil
Blessing
Boy/Male
Tamil
Pradumna | பà¯à®°à®¤à¯à®®à®¨à®¾Â
Extremely mighty (Son of Lord Krishna)
Girl/Female
Arabic, Muslim
A Woman who Saves Someone
Boy/Male
Hindu
Eldest Pandavas brother, Firm in battle
Girl/Female
Arabic, Muslim
Bright
Boy/Male
Hindu
Girl/Female
Arabic, Australian, Muslim
Read; Garden in Heaven
Girl/Female
Gujarati, Hindu, Indian, Kannada
Bravery
MINIMUM BOUNDING-BOX-ALGORITHMS
MINIMUM BOUNDING-BOX-ALGORITHMS
MINIMUM BOUNDING-BOX-ALGORITHMS
MINIMUM BOUNDING-BOX-ALGORITHMS
MINIMUM BOUNDING-BOX-ALGORITHMS
a.
Making or emitting sound; hence, sonorous; as, sounding words.
n.
The least quantity assignable, admissible, or possible, in a given case; hence, a thing of small consequence; -- opposed to maximum.
v. t.
To inclose with boarding, lathing, etc., so as to bring to a required form.
n.
Minimum.
n.
measurement by sounding; also, the depth so ascertained.
v. t.
To inclose in a box.
n.
A present in a box; a present; esp. a Christmas box or gift.
n.
A minim.
n.
A self-registering thermometer, especially one that registers the maximum and minimum during long periods.
n.
An axle box, journal box, journal bearing, or bushing.
n.
A chest or any receptacle for the deposit of money; as, a poor box; a contribution box.
pl.
of Minimus
n.
The quantity that a box contain.
a.
Making blind or as if blind; depriving of sight or of understanding; obscuring; as, blinding tears; blinding snow.
n.
A boxlike shed for shelter; as, a sentry box.
a.
Greatest in quantity or highest in degree attainable or attained; as, a maximum consumption of fuel; maximum pressure; maximum heat.
n.
The sand, shells, or the like, that are brought up by the sounding lead when it has touched bottom.
pl.
of Minimum