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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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
1947 plan to divide British Palestine
The United Nations Partition Plan for Palestine was a proposal developed by the United Nations for the future government of Mandatory Palestine following
United Nations Partition Plan for Palestine
United_Nations_Partition_Plan_for_Palestine
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
Computational property
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
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
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
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
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
{\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
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
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 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
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)
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
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
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
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
Hypothetical split of the country into Wallonia and Flanders
The partition of Belgium is a hypothetical situation, which has been discussed by both Belgian and international media, envisioning a split of Belgium
Hypothetical partition of Belgium
Hypothetical_partition_of_Belgium
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
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
Direct sum of uniform matroids
In mathematics, a partition matroid or partitional matroid is a matroid that is a direct sum of uniform matroids. It is defined over a base set in which
Partition_matroid
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
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
Way to write a number as a product of other numbers
MacMahon (1923) with the problem of counting the number of multiplicative partitions of n {\displaystyle n} ; this problem has since been studied by
Multiplicative_partition
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
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)
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
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
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
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
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
Historical proposals to divide Switzerland
The partition of Switzerland has been discussed in the modern era, envisioning a split of Switzerland along linguistic divisions, regarding German-speaking
Hypothetical partition of Switzerland
Hypothetical_partition_of_Switzerland
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)
Problem in computer science
In computability theory, the halting problem is the decision problem of, given an arbitrary computer program and an input, determining whether said program
Halting_problem
Fair item allocation problem
least-happy child is as happy as possible. Some related problems are: Multiway number partitioning with the max-min objective corresponds to a special case
Egalitarian_item_allocation
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
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
Optimization problem in computer science and operations research
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. Schulz and Skutella
Unrelated-machines_scheduling
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
Computational problem about sorting
The Dutch national flag problem is a computational problem proposed by Edsger Dijkstra. The flag of the Netherlands consists of three colors: red, white
Dutch_national_flag_problem
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
Class of computational problems
minimum cut, a partition of the vertices of the flow network that minimizes the total capacity of edges crossing from one side of the partition to the other
Network_flow_problem
Graph-theoretic connectivity parameter
spanning trees that can be contained in G. Contrary to the graph partition problem, the partitions output by computing the strength are not necessarily balanced
Strength_of_a_graph
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
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
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
Historical U.S. state partition proposals
Numerous state partition proposals have been put forward since the 1776 establishment of the United States that would partition an existing U.S. state
List of state partition proposals in the United States
List_of_state_partition_proposals_in_the_United_States
Computer software
Ranish Partition Manager is a freeware hard disk partition editor, disk cloning utility, and boot manager, that gives a high level of control for creating
Ranish_Partition_Manager
skeptics, includes the following topics: almost free abelian groups, partition problems, failure of preservation of chain conditions in Boolean algebras under
Pcf_theory
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)
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
Optimization problem in computer science
P 2 | | C max {\displaystyle P2||C_{\max }} , is a variant of the partition problem, which is known to be NP-hard. When the number of machines m is at
Parallel_task_scheduling
PARTITION PROBLEM
PARTITION PROBLEM
Girl/Female
Muslim/Islamic
Away from all Problems
Boy/Male
Hindu, Indian
Problem
Biblical
Shimeath, that hears, or obeys; perdition
Boy/Male
Indian, Tamil
People with this Name are Preferably Intelligent and Very Generous; Highly Knowledgeable in Problem Solving Skills
Boy/Male
Indian, Sikh
A Partition in the World
Girl/Female
Indian, Telugu
Destroyer of Problems
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.
Boy/Male
Biblical
That hears, or obeys, perdition.
Boy/Male
Hindu, Indian, Traditional
Noble Partition
Boy/Male
Arabic, Indian, Muslim
Problem Solver
Boy/Male
Muslim
Problem solver
Girl/Female
Biblical Greek Latin
Perdition, destruction.
Boy/Male
Arabic
Partition; Curtain
Girl/Female
Bengali, Indian
Eternity; Problem Solver
Girl/Female
Arabic, Gujarati, Hindu, Indian, Kannada, Muslim, Punjabi, Sikh
Wish; Petition to God; Special Prayer
Boy/Male
Biblical
That hears, or obeys, perdition.
Biblical
perdition, destruction
PARTITION PROBLEM
PARTITION PROBLEM
Biblical
rising early; crown
Male
Scottish
Pet form of Scottish Gaelic Uilleam, WILKIE means "will-helmet."Â
Boy/Male
Tamil
God of Sathi, Lord Shiva, Kind
Girl/Female
English American
and Charlene.
Boy/Male
Tamil
The Moon, Thought
Boy/Male
Australian, Irish
Surname
Girl/Female
Hindu, Indian
Daughter of Fire
Female
Japanese
(1-美ä¿, 2-美帆) Japanese name MIHO means 1) "beautiful guarantee" or "beautiful sail." Compare with masculine Miho.Â
Girl/Female
Indian, Telugu
God Durga
Girl/Female
Hindu, Indian
World; Earth
PARTITION PROBLEM
PARTITION PROBLEM
PARTITION PROBLEM
PARTITION PROBLEM
PARTITION PROBLEM
p. pr. & vb. n.
of Partition
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.
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 screen or partition wall behind an altar.
n.
A separating tissue; a partition; a septum.
imp. & p. p.
of Partition
v. t.
To divide into parts or shares; to divide and distribute; as, to partition an estate among various heirs.
v.
A score.
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.
The act of parting or dividing; the state of being parted; separation; division; distribution; as, the partition of a kingdom.
n.
Destruction; perdition.
a.
Denoting a part; as, a partitive genitive.
n.
A partition between flues in a chimney.
v. i.
To make a petition or solicitation.
v. t.
To divide into distinct parts by lines, walls, etc.; as, to partition a house.
a.
Divided by partition or partitions; having septa; as, a septate pod or shell.
a.
With two partitions or septa.
v.
A part divided off by walls; an apartment; a compartment.
n.
A word expressing partition, or denoting a part.
n.
Parturition.