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NP-complete problem in computer science
science, the partition problem, or number partitioning, is the task of deciding whether a given multiset S of positive integers can be partitioned into two
Partition_problem
Strongly NP-complete problem in computer science
The 3-partition problem is a strongly NP-complete problem in computer science. The problem is to decide whether a given multiset of integers can be partitioned
3-partition_problem
Subdivision of vertices into disjoint sets
of graph partitioning are minimum cut and maximum cut problems. Typically, graph partition problems fall under the category of NP-hard problems. Solutions
Graph_partition
Decomposition of an integer as a sum of positive integers
In number theory and combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive
Integer_partition
Probability of shared birthdays
confident about their estimates. A related problem is the partition problem, a variant of the knapsack problem from operations research. Some weights are
Birthday_problem
Sequence of edges which join a sequence of vertices on a given graph
of vertices in weighted directed graphs. The k-path partition problem is the problem of partitioning a given graph to a smallest collection of vertex-disjoint
Path_(graph_theory)
Set of basic shapes which assemble into a polygon
polygon. A polygon partition problem is a problem of finding a partition which is minimal in some sense, for example a partition with a smallest number
Polygon_partition
Partition of a graph's nodes into cliques
G, so a partition of the vertices of G is a clique cover of G if and only if it is a coloring of the complement of G. The clique cover problem in computational
Clique_cover
partition function Partition of an interval Partition of a set Ordered partition Partition refinement Disjoint-set data structure Partition problem 3-partition
List_of_partition_topics
Topics referred to by the same term
Logical partition, a subset of a computer's resources, virtualized as a separate computer Binary space partitioning, in computer science Partition problem, in
Partition
each set. The input to the problem is a set of n items of different sizes, and two integers m, k. The output is a partition of the items into m subsets
Balanced_number_partitioning
Combinatorial optimization problem
theoretical computer science, like maximum cut, graph coloring and the partition problem, embeddings into QUBO have been formulated. Embeddings for machine
Quadratic unconstrained binary optimization
Quadratic_unconstrained_binary_optimization
1947 division of British India
The partition of India in 1947 was the division of British India into two independent dominion states, the Union of India and Dominion of Pakistan. The
Partition_of_India
In computer science, multiway number partitioning is the problem of partitioning a multiset of numbers into a fixed number of subsets, such that the sums
Multiway_number_partitioning
Mathematical and computational problem
{NP}}} . This can be proven by a reduction from the partition problem: given an instance of Partition where the sum of all input numbers is 2 T {\displaystyle
Bin_packing_problem
Territorial partition in British India
The Partition of Bengal in 1905, also known as the First Partition of Bengal, was a territorial reorganization of the Bengal Presidency in British India
Partition_of_Bengal_(1905)
Decision problem in computer science
This special case of SSP is known as the partition problem. SSP can also be regarded as an optimization problem: find a subset whose sum is at most T, and
Subset_sum_problem
maximum leaf spanning tree problem. Feedback vertex set Feedback arc set Graph coloring Graph homomorphism problem Graph partition into subgraphs of specific
List_of_NP-complete_problems
Process of partitioning a rectilinear polygon
partitioning problems, where the cuts are constrained to be guillotine cuts. A related but different problem is guillotine cutting. In that problem,
Guillotine_partition
Subdivision into few independent sets
Matroid partitioning is a problem arising in the mathematical study of matroids and in the design and analysis of algorithms. Its goal is to partition the
Matroid_partitioning
Problem in graph theory
the decision problem was one of Karp's 21 NP-complete problems; Karp showed the NP-completeness by a reduction from the partition problem. The canonical
Maximum_cut
Algorithm for solving the partition problem
differencing method is an algorithm for solving the partition problem and the multiway number partitioning. It is also called the Karmarkar–Karp algorithm
Largest_differencing_method
18th-century forced partitions of the Polish–Lithuanian Commonwealth
The Partitions of Poland were three partitions of the Polish–Lithuanian Commonwealth that took place between 1772 and 1795, toward the end of the 18th
Partitions_of_Poland
1947 plan to divide British Palestine
The United Nations Partition Plan for Palestine was a proposal by the United Nations to partition Mandatory Palestine at the end of the British Mandate
United Nations Partition Plan for Palestine
United_Nations_Partition_Plan_for_Palestine
First sector of partitioned PC computer disk
master boot record (MBR) is a type of boot sector in the first block of partitioned computer mass storage devices like fixed disks or removable drives intended
Master_boot_record
Concept in complexity theory
is the partition problem. Both weak NP-hardness and weak polynomial-time correspond to encoding the input integers in binary coding. If a problem is strongly
Pseudo-polynomial_time
Unsolved problem in computer science
Unsolved problem in computer science If the solution to a problem can be checked in polynomial time, must the problem be solvable in polynomial time? More
P_versus_NP_problem
Algorithm for job scheduling
prtpy package. Greedy number partitioning - generalizations and extensions of LPT for the problem of multiway number partitioning. Proof. Normalize the input
Longest-processing-time-first scheduling
Longest-processing-time-first_scheduling
Canadian computer scientist (born 1942)
heuristics for two NP-complete optimization problems: graph partitioning and the travelling salesman problem. In a display of authorial equity, the former
Brian_Kernighan
Mathematics optimization problem
optimal one. The algorithm starts by translating the problem to the polygon partitioning problem. To each vertex V of the polygon is associated a weight
Matrix_chain_multiplication
Can every bounded subset of Rn be partitioned into (n+1) smaller diameter sets?
problem in mathematics What is the lowest n such that not every bounded subset E of the space R n {\displaystyle \mathbb {R} ^{n}} can be partitioned
Borsuk's_conjecture
Partition of a graph by removing fewest possible edges
cut (a partition of the vertices of a graph into two disjoint subsets) that is minimal in some metric. In the simplest unweighted min-cut problem, the goal
Minimum_cut
Computer data storage partitioning standard
The GUID Partition Table (GPT) is a standard for the layout of partition tables of a physical computer storage device, such as a hard disk drive or solid-state
GUID_Partition_Table
In graph theory, a skew partition of a graph is a partition of its vertices into two subsets, such that the induced subgraph formed by one of the two
Skew_partition
Operations in arithmetic
yielding piles of 13 cards each. If there is a remainder in solving a partition problem, the parts will end up with unequal sizes. For example, if 52 cards
Quotition_and_partition
Matroid theory
Matroid-constrained number partitioning is a variant of the multiway number partitioning problem, in which the subsets in the partition should be independent
Matroid-constrained number partitioning
Matroid-constrained_number_partitioning
Divide and conquer sorting algorithm
solve the Lomuto partition scheme problem (sometimes called the Dutch national flag problem), an alternative linear-time partition routine can be used
Quicksort
in the exponent. The biclique partition problem takes as input an arbitrary undirected graph, and asks for a partition of its edges into a minimum number
Graham–Pollak_theorem
is the partition problem. Both weak NP-hardness and weak polynomial-time correspond to encoding the input integers in binary coding. If a problem is strongly
Weak_NP-completeness
Optimization algorithm
assignment problem (GAP) Frequency assignment problem (FAP) Redundancy allocation problem (RAP) Set cover problem (SCP) Partition problem (SPP) Weight
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
pseudopolynomial time number partitioning is a pseudopolynomial time algorithm for solving the partition problem. The problem can be solved using dynamic
Pseudopolynomial time number partitioning
Pseudopolynomial_time_number_partitioning
Geometric problems involving the partition of a figure
In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged
Dissection_problem
Probability puzzle
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal
Monty_Hall_problem
Unsolved problem in mathematics Does every countable graph have an unfriendly partition into two parts? More unsolved problems in mathematics In the mathematics
Unfriendly_partition
Mathematical optimization problem
When m is variable (a part of the input), both problems are strongly NP-hard, by reduction from 3-partition. This means that they have no fully polynomial-time
Multiple_subset_sum
is the partition problem. Both weak NP-hardness and weak polynomial-time correspond to encoding the input integers in binary coding. If a problem is strongly
Strong_NP-completeness
Maximum number of disjoint dominating sets
In graph theory, a domatic partition of a graph G = ( V , E ) {\displaystyle G=(V,E)} is a partition of V {\displaystyle V} into disjoint sets V 1 {\displaystyle
Domatic_number
Table inside a master boot record
The partition type (or partition ID) in a partition's entry in the partition table inside a master boot record (MBR) is a byte value intended to specify
Partition_type
Quantum search algorithm
; Yan B. (2023). "Topologically protected Grover's oracle for the partition problem". Physical Review A. 108 (2) 022412. arXiv:2304.10488. Bibcode:2023PhRvA
Grover's_algorithm
Numerical 3-dimensional matching problem is an instance of both the 3-partition problem, and the 3-dimensional matching problem. Given an instance of numeric
Numerical 3-dimensional matching
Numerical_3-dimensional_matching
Topic in computer science
Ron. In their seminal paper published in 1998, an abstract graph partition problem is analyzed and some testers provided. These include as special cases
Property_testing
from the knapsack problem. It is NP-hard even if the number of machines is fixed and at least 2, by reduction from the partition problem. Sahni presents
Identical-machines_scheduling
Partition of Bengal into East Bengal and West Bengal in 1947
The Partition of Bengal in 1947, also known as the Second Partition of Bengal, part of the Partition of India, divided the British Indian Bengal Province
Partition_of_Bengal_(1947)
American computer scientist
analyses of the folk theorem (game theory), the planted clique, and the partition problem. For prior work on phase transitions, he was awarded the Karl Scheel
Christian_Borgs
{\displaystyle G} form a partition of G {\displaystyle G} , then the finite indices of said subgroups cannot be distinct. The inverse Galois problem: is every finite
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Method of partitioning data points into groups based on their similarity
Clustering is the problem of partitioning data points into groups based on similarity or dissimilarity. Correlation clustering is a clustering framework
Correlation_clustering
Optimization problem
processing time over the machines. This is an optimization version of the partition problem 1|prec| L max {\displaystyle L_{\max }} – assigning to a single machine
Optimal_job_scheduling
valuations, for any n ≥ 2 {\displaystyle n\geq 2} , the problem is equivalent to the partition problem, and therefore it is NP-complete. With k ≥ n − 1 {\displaystyle
List of unsolved problems in fair division
List_of_unsolved_problems_in_fair_division
Number of partitions of an integer
In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because
Partition function (number theory)
Partition_function_(number_theory)
Problem in computer science and operations research
deciding whether an envy-free allocation exists is equivalent to the partition problem. However, there are optimization algorithms that can yield good results
Envy_minimization
Political viewpoint in South Asian politics
Opposition to the partition of India was widespread in British India in the 20th century and it continues to remain a talking point in South Asian politics
Opposition to the partition of India
Opposition_to_the_partition_of_India
Relation between transition systems in computer science
algorithms are quasilinear time using partition refinement through a reduction to the coarsest partition problem. Simulation preorder Congruence relation
Bisimulation
Procedure for fair item assignment
envy-free allocation, then this allocation represents an equal partition. Since the partition problem is NP-complete, it probably cannot be solved by a polynomial-time
Undercut_procedure
Family of problems in computational geometry
the problem is, given a partition of the space into disjoint regions, to determine the region where a query point lies. For example, the problem of determining
Point_location
15th c. Franciscan Friar, mathematician and publisher of accounting treatise
Cavazzoni (1996) along with a partial translation of the chapter on partitioning problems. Summa de arithmetica, geometria. Proportioni et proportionalita
Luca_Pacioli
1947 massacres of Sikhs and Hindus in Rawalpindi, British India
Punjab Province of British India in March 1947. The violence preceded the partition of India and was instigated and perpetrated by the Muslim League National
Rawalpindi_Massacres
Problem in computer science
In computability theory, the halting problem is the decision problem of determining, from a description of an arbitrary computer program and an input
Halting_problem
Graph made from disjoint union of complete graphs
complete graph with edge costs (positive and negative) the clique partitioning problem asks for a subgraph that is a cluster graph such that the sum of
Cluster_graph
distributions described previously has a matching kind of partition into subsets. So, a partition problem can be solved by transforming it into a distribution
Combinatorial_modelling
Choosing the fewest coins to make a given amount of money
problem, and has applications wider than just currency. It is also the most common variation of the coin change problem, a general case of partition in
Change-making_problem
2D geometric minimization problem
which can be proven by a reduction from the strongly NP-complete 3-partition problem. Note that both lower bounds 3 / 2 {\displaystyle 3/2} and 5 / 4 {\displaystyle
Strip_packing_problem
Software testing technique
partitioning or equivalence class partitioning (ECP) is a software testing technique that divides the input data of a software unit into partitions of
Equivalence_partitioning
Political border splitting a territory
relations, a partition is a division of a previously unified territory into two or more parts. Brendan O'Leary distinguishes partition, a change of political
Partition_(politics)
Problem in combinatorial optimization
subset-sum problem". Manag. Sci. 30 (6): 765–771. doi:10.1287/mnsc.30.6.765. Horowitz, Ellis; Sahni, Sartaj (1974), "Computing partitions with applications
Knapsack_problem
of algorithms, partition refinement is a technique for representing a partition of a set as a data structure that allows the partition to be refined by
Partition_refinement
Dispute between Greek and Turkish Cypriots
stable government. The desire of some of the ethnic Turkish people for the partition of the island of Cyprus through Taksim, the desire of some of the ethnic
Cyprus_problem
Partition of a graph's nodes into 2 disjoint subsets
In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets. Any cut determines a cut-set, the set of edges that have one
Cut_(graph_theory)
Clustering and community detection algorithm
C_{n}\}\end{aligned}}} How communities are partitioned is an integral part on the Leiden algorithm. How partitions are decided can depend on how their quality
Leiden_algorithm
"Formulations and valid inequalities for the node capacitated graph partitioning problem". Mathematical Programming. 74 (3): 247–266. doi:10.1007/bf02592198
Quadratic_knapsack_problem
Generalization of the concept from statistical mechanics
probability theory, for the Boltzmann distribution. The partition function occurs in many problems of probability theory because, in situations where there
Partition function (mathematics)
Partition_function_(mathematics)
Systematic classification of 12 related enumerative problems concerning two finite sets
enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either
Twelvefold_way
1007/978-94-017-0470-0_7. ISBN 0-7923-6970-X. MR 1900271. Todorcevic, Stevo (1989). Partition problems in topology. Providence, R.I.: American Mathematical Society. ISBN 978-0-8218-5091-6
List of statements independent of ZFC
List_of_statements_independent_of_ZFC
Basic integral in elementary calculus
+ 1 for all i. Alone this restriction does not impose a problem: we can refine any partition in a way that makes it a left-hand or right-hand sum by subdividing
Riemann_integral
Fit of a species living under specific environmental conditions
that species can partition their niche. This list is not exhaustive, but illustrates several classic examples. Resource partitioning is the phenomenon
Ecological_niche
Mathematical game of resource allocation
or AI models. For a study of KPR-like approaches related to graph partitioning problem, see. Recently the KPR game has been extended (to Musical Chair type
Kolkata Paise Restaurant Problem
Kolkata_Paise_Restaurant_Problem
splitting problem is the following decision problem: given a family F of subsets of a finite set S, decide whether there exists a partition of S into
Set_splitting_problem
Method for recursively subdividing a space into two subsets using hyperplanes
In computer science, binary space partitioning (BSP) is a method for space partitioning which recursively subdivides a Euclidean space into two convex
Binary_space_partitioning
Yes/no problem in computer science
decision problem is a computational problem that can be posed as a yes–no question on a set of input values. An example of a decision problem is deciding
Decision_problem
Computational problem of graph theory
A central problem in algorithmic graph theory is the shortest path problem. Hereby, the problem of finding the shortest path between every pair of nodes
Parallel all-pairs shortest path algorithm
Parallel_all-pairs_shortest_path_algorithm
Mathematical propositions in network flow theory
graph partition and related problems, where finding the absolute best solution is computationally prohibitive. A "commodity" in a network flow problem is
Approximate max-flow min-cut theorem
Approximate_max-flow_min-cut_theorem
equitable partition. A partition of a graph is a collection of pairwise disjoint sets of vertices whose union is the vertex set of the graph. A partition is
Fractional_graph_isomorphism
Problem of fair division
amount of total switches is NP-hard (by reduction from Partition problem or from Hamming salesman problem), but can be solved in time O*(2k) by dynamic programming
Rental_harmony
Grazia; Tuza, Zsolt (1997-01-12). "Semi on-line algorithms for the partition problem". Operations Research Letters. 21 (5): 235–242. doi:10.1016/S0167-6377(98)00005-4
Online_job_scheduling
Number of forests a graph's edges may be partitioned into
graph can be expressed as a special case of a more general matroid partitioning problem, in which one wishes to express a set of elements of a matroid as
Arboricity
Unsolved problem in mathematics
Unsolved problem in mathematics Given arbitrary m, r, are there infinitely many values of n such that the partition function at n is congruent to r mod
Newman's_conjecture
Competitive algorithm for searching a problem space
Emanuel Falkenauer is that solving some complex problems, a.k.a. clustering or partitioning problems where a set of items must be split into disjoint
Genetic_algorithm
Portable partitions are a form of temporary walls which serve to divide rooms in place of permanent walls. They can be joined together section by section
Portable_partition
Computer bugs related to the year 2000
The term Year 2000 problem, or simply Y2K, refers to potential computer errors related to the formatting and storage of calendar data for dates in and
Year_2000_problem
Pakistani computer scientist
balancing and partitioning of distributed processes", while his IEEE Fellow award recognises his "contributions to the mapping problem in parallel and
Shahid_Hussain_Bokhari
science, the monochromatic triangle problem is an algorithmic problem on graphs, in which the goal is to partition the edges of a given graph into two
Monochromatic_triangle
PARTITION PROBLEM
PARTITION PROBLEM
Boy/Male
Arabic
Partition; Curtain
Girl/Female
Arabic, Gujarati, Hindu, Indian, Kannada, Muslim, Punjabi, Sikh
Wish; Petition to God; Special Prayer
Girl/Female
Indian, Telugu
Destroyer of Problems
Biblical
perdition, destruction
Boy/Male
Biblical
That hears, or obeys, perdition.
Boy/Male
Muslim
Problem solver
Boy/Male
Indian, Tamil
People with this Name are Preferably Intelligent and Very Generous; Highly Knowledgeable in Problem Solving Skills
Boy/Male
Arabic, Indian, Muslim
Problem Solver
Boy/Male
Biblical
That hears, or obeys, perdition.
Girl/Female
Muslim/Islamic
Away from all Problems
Girl/Female
Biblical Greek Latin
Perdition, destruction.
Biblical
Shimeath, that hears, or obeys; perdition
Male
English
Hebrew name SHELAH means "a petition, prayer." In the bible, this is the name of a son of Judah. Compare with another form of Shelah.
Girl/Female
Bengali, Indian
Eternity; Problem Solver
Boy/Male
Hindu, Indian
Problem
Boy/Male
Hindu, Indian, Traditional
Noble Partition
Boy/Male
Indian, Sikh
A Partition in the World
PARTITION PROBLEM
PARTITION PROBLEM
Male
Italian
Italian form of Latin Sebastianus, SEBASTIANO means "from Sebaste."
Girl/Female
Muslim/Islamic
Generous blessing of Allah
Girl/Female
Hindu
Wave
Male
Hebrew
(עַמִּיהוּד) Hebrew name AMMIYHUWD means "one of the people of Judah." In the bible, this is the name of several characters, including the father of Shemuel.
Girl/Female
Arabic, Muslim
Noble; Wise
Boy/Male
Indian
Forever absorbed in God, Ever absorbed in God
Female
English
Variant spelling of English Kayley, CALEIGH means "slender."
Boy/Male
Hindu, Indian
God of Creation
Boy/Male
Australian, Hindu, Indian
Devotional Place
Boy/Male
Indian, Tamil
God; Rakesh
PARTITION PROBLEM
PARTITION PROBLEM
PARTITION PROBLEM
PARTITION PROBLEM
PARTITION PROBLEM
n.
Destruction; perdition.
p. pr. & vb. n.
of Partition
v. t.
To divide into distinct parts by lines, walls, etc.; as, to partition a house.
v. i.
To make a petition or solicitation.
v.
A score.
n.
Parturition.
v.
The act of parting or dividing; the state of being parted; separation; division; distribution; as, the partition of a kingdom.
imp. & p. p.
of Partition
v.
That which divides or separates; that by which different things, or distinct parts of the same thing, are separated; separating boundary; dividing line or space; specifically, an interior wall dividing one part or apartment of a house, an inclosure, or the like, from another; as, a brick partition; lath and plaster partitions.
v. t.
To divide into parts or shares; to divide and distribute; as, to partition an estate among various heirs.
v.
The servance of common or undivided interests, particularly in real estate. It may be effected by consent of parties, or by compulsion of law.
a.
With two partitions or septa.
a.
Denoting a part; as, a partitive genitive.
n.
A word expressing partition, or denoting a part.
n.
A screen or partition wall behind an altar.
v. t.
To make a prayer or request to; to ask from; to solicit; to entreat; especially, to make a formal written supplication, or application to, as to any branch of the government; as, to petition the court; to petition the governor.
n.
A separating tissue; a partition; a septum.
v.
A part divided off by walls; an apartment; a compartment.
n.
A partition between flues in a chimney.
a.
Divided by partition or partitions; having septa; as, a septate pod or shell.