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Problem of finding the longest simple path for a given graph
computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph. A path is called simple if it
Longest_path_problem
Algorithm for finding shortest paths
shortest path problem. A* search algorithm Bellman–Ford algorithm Euclidean shortest path Floyd–Warshall algorithm Johnson's algorithm Longest path problem Parallel
Dijkstra's_algorithm
Sequence of edges which join a sequence of vertices on a given graph
vertex-disjoint paths of length at most k. Glossary of graph theory Path graph Polygonal chain Shortest path problem Longest path problem Dijkstra's algorithm
Path_(graph_theory)
Computational problem of graph theory
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights
Shortest_path_problem
completion Hamiltonian path problem, directed and undirected. Induced subgraph isomorphism problem Graph intersection number Longest path problem Maximum bipartite
List_of_NP-complete_problems
Mathematical problem set on a chessboard
The longest uncrossed (or nonintersecting) knight's path is a mathematical problem involving a knight on the standard 8×8 chessboard or, more generally
Longest uncrossed knight's path
Longest_uncrossed_knight's_path
Graph path which is an induced subgraph
The problem of finding the longest induced path or cycle in a hypercube, first posed by Kautz (1958), is known as the snake-in-the-box problem, and it
Induced_path
Property of a computational problem
substructure. Longest common subsequence problem Longest increasing subsequence Longest palindromic substring All-Pairs Shortest Path Any problem that can
Optimal_substructure
Method of scheduling activities
identify its longest series of dependent activities (its longest path). These tools can display the critical path (and near-critical path activities if
Critical_path_method
Algorithmic problem on pairs of sequences
longest common substring: unlike substrings, subsequences are not required to occupy consecutive positions within the original sequences. The problem
Longest_common_subsequence
Path in a graph that visits each vertex exactly once
Hamiltonian path. The computational problems of determining whether such paths and cycles exist in graphs are NP-complete; see Hamiltonian path problem for details
Hamiltonian_path
minimum spanning tree of a set of points in the plane Longest path problem: find a simple path of maximum length in a given graph Minimum spanning tree
List_of_algorithms
NP-hard problem in combinatorial optimization
computational complexity of the problem; see Hamiltonian path problem. Another related problem is the bottleneck travelling salesman problem: Find a Hamiltonian cycle
Travelling_salesman_problem
Computational problem
Motion planning, also path planning (also known as the navigation problem or the piano mover's problem) is a computational problem to find a sequence of
Motion_planning
Mathematical problem set on a chessboard
boards. The knight's tour problem is an instance of the more general Hamiltonian path problem in graph theory. The problem of finding a closed knight's
Knight's_tour
Task of computing complete subgraphs
algorithms for the longest decreasing subsequence problem. Conversely, every instance of the longest decreasing subsequence problem can be described equivalently
Clique_problem
Computational problem in graph theory
finding the longest possible induced path in a hypercube; it can be viewed as a special case of the induced subgraph isomorphism problem. There is a similar
Snake-in-the-box
Algorithm for finding the shortest paths in graphs
shortest paths from a single source vertex to all of the other vertices in a weighted digraph. It is slower than Dijkstra's algorithm for the same problem, but
Bellman–Ford_algorithm
Complexity class
optimization problem Maximum clique Longest simple path Graph coloring; an application: register allocation in compilers Lists of problems Lists of unsolved
NP-hardness
its vertex-deleted subgraphs. The snake-in-the-box problem: what is the longest possible induced path in an n {\displaystyle n} -dimensional hypercube graph
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Directed graph with no directed cycles
take a team of workers to perform the task. The longest path in this DAG represents the critical path of the project, the one that controls the total
Directed_acyclic_graph
Node ordering for directed acyclic graphs
resulting matrix describes the longest path distances in the graph. Sorting the vertices by the lengths of their longest incoming paths produces a topological
Topological_sorting
Graph made from a subset of another graph's nodes and their edges
Induced paths are induced subgraphs that are paths. The shortest path between any two vertices in an unweighted graph is always an induced path, because
Induced_subgraph
Rapid transit system in the northeast US
through the Holland Tunnel. The 81-day strike was the longest in PATH's history. Substantial growth in PATH ridership during the 1980s required expansion and
PATH_(rail_system)
Chess composition whose solution is a mate or other clear objective
pieces of the chessboard. A famous such problem is the knight's tour, in which one is to determine the path of a knight that visits each square of the
Chess_problem
Computational problems no algorithm can solve
Determining if a particle path of an ideal fluid on a three dimensional domain eventually reaches a certain region in space. The problem of determining if a
List_of_undecidable_problems
Auxiliary data structure to the suffix array in computer science
science, the longest common prefix array (LCP array) is an auxiliary data structure to the suffix array. It stores the lengths of the longest common prefixes
LCP_array
Sufficiently long sequences of numbers have long monotonic subsequences
is of length at least s. Longest increasing subsequence problem Erdős, Paul; Szekeres, George (1935), "A combinatorial problem in geometry", Compositio
Erdős–Szekeres_theorem
Topics referred to by the same term
in a field of view Diameter (computational geometry), the problem of computing the longest distance between two of n {\displaystyle n} given points or
Diameter_(disambiguation)
This is a list of longest prison sentences served by a single person, worldwide, without a period of freedom followed by a second conviction. These cases
List of longest prison sentences served
List_of_longest_prison_sentences_served
Statistical tool used in project management
the critical path and if any activities have slack. The critical path is the path that takes the longest to complete. To determine the path times, add the
Program evaluation and review technique
Program_evaluation_and_review_technique
Overview of and topical guide to algorithms
algorithm Graph coloring Clique problem Independent set (graph theory) Hamiltonian path problem Travelling salesman problem String-searching algorithm Knuth–Morris–Pratt
Outline_of_algorithms
On Hamiltonian cycles in toroidal graphs
toroidal graph has a Hamiltonian path. Kawarabayashi, Ken-ichi; Niu, Jianbing; Zhang, Cun-Quan (2007), "Chords of longest circuits in locally planar graphs"
Grünbaum–Nash-Williams conjecture
Grünbaum–Nash-Williams_conjecture
the number of edges on the shortest path from the root of the tree to node v. It is possible to solve this problem in constant time per query, after a
Level_ancestor_problem
Minimizing problem in computer programming
computer science, such as the lowest common ancestor problem and the longest common prefix problem (LCP). Given an array A[1 … n] of n objects taken from
Range_minimum_query
Methodic assignment of colors to elements of a graph
k-coloring if and only if it has an acyclic orientation for which the longest path has length at most k; this is the Gallai–Hasse–Roy–Vitaver theorem (Nešetřil
Graph_coloring
Design technique for parallel algorithms
follow paths with a time complexity that is logarithmic with respect to the length of the longest path. It does this by "jumping" to the end of the path computed
Pointer_jumping
Head of the Catholic Church
Saint Peter and Saint Paul in the first century. The papacy is one of the longest enduring institutions in the world and has been a prominent force in human
Pope
Animated educational children's TV series
season, focusing more on environmental science. Cyberchase is the sixth longest-running animated series in the United States, behind The Simpsons, South
Cyberchase
Road bridge in Auckland, New Zealand
Transport Agency Waka Kotahi (NZTA). It is the second-longest road bridge in New Zealand, and the longest in the North Island. The original inner four lanes
Auckland_Harbour_Bridge
Undirected, connected, and acyclic graph
longest downward path to a leaf from that vertex. The height of the tree is the height of the root. The depth of a vertex is the length of the path to
Tree_(graph_theory)
Mathematical puzzle game
different shortest paths. From every arbitrary distribution of disks, there are one or two different longest non-self-crossing paths to move all disks
Tower_of_Hanoi
Common term for the state of not wearing any footwear
world record (pending confirmation by Guinness World Records) for the longest distance run barefoot on June 5, 2010, as part of the Relay for Life fundraiser
Barefoot
Node labeling problem in graph theory
In graph theory, the graph bandwidth problem may be visualized as placing the vertices of a given graph at distinct integer positions along the number
Graph_bandwidth
Simulation technique in computer hardware design
identifying the critical path involves analyzing the longest topological path through a logic network. However, not all topological paths are functionally feasible
Static_timing_analysis
American writer, engineer and musician
Barrett wrote and recorded the song "Find the Longest Path," a parody incorporating an NP-complete problem in computer science and the frustrations of graduate
Daniel_J._Barrett
Category of routing problem minimizing total distance and time
minimized the duration of the longest route with a fixed maximum number of vehicles. There are generalizations of arc routing problems that introduce multiple
Arc_routing
Tree connecting given points by short paths
points in a metric space is a spanning tree in which the diameter (the longest path length in the tree between two of its points) is as small as possible
Minimum-diameter spanning tree
Minimum-diameter_spanning_tree
"2010 Jacqueline Donnet Emerging Documentary Filmmaker Award—Cutting a Path of Understanding: Jeff Malmberg". International Documentary Association.
List of films with the longest production time
List_of_films_with_the_longest_production_time
Shell command for comparing file content
other. The operation of diff is based on solving the longest common subsequence problem. In this problem, given two sequences of items: a b c d f g h j q
Diff
1981 book by Richard Buckminster Fuller
possible to draw numerous paths through the chart from beginning to end, but it is the longest path, called the critical path, that determines the time
Critical_Path_(book)
Kind of binary decision diagram
so the longest such paths are Hamiltonian, with a size of 2,707,075. ZDDs in this case, are efficient for simple paths and Hamiltonian paths. Define
Zero-suppressed decision diagram
Zero-suppressed_decision_diagram
Set of all vertices of minimum eccentricity
1-center problem and can be extended to the vertex k-center problem. Finding the center of a graph is useful in facility location problems where the
Graph_center
Experiments examining the average path length for social networks
small world problem. An alternative view of the problem is to imagine the population as a social network and attempt to find the average path length between
Small-world_experiment
Mathematical concept
been completed. In this case, the makespan can be computed from the longest path in the oriented graph, which can be found in polynomial time for directed
Disjunctive_graph
American Indian civil rights organization
relations with several tribes which were determined to be far along the path of assimilation. These policies were enacted by the United States Congress
American_Indian_Movement
String-searching algorithm
is the longest possible strict suffix of it in the graph. For example, for node (caa), its strict suffixes are (aa) and (a) and (). The longest of these
Aho–Corasick_algorithm
Maximum length of time a computed task could take to execute
measurements place a high burden on software testing to achieve the longest path; counting instructions is only applicable to simple software and hardware
Worst-case_execution_time
2000 (2000-11-04) 805 10.72 First episode of a four-part storyline, the longest in the series, which aired over four weeks during the November sweeps in
List of Walker, Texas Ranger episodes
List_of_Walker,_Texas_Ranger_episodes
it the world's oldest metro system. The Beijing Subway is the world's longest metro network at 879 kilometres (546 mi) and the busiest one with annual
List_of_metro_systems
Tree containing all suffixes of a given text
also provided one of the first linear-time solutions for the longest common substring problem. These speedups come at a cost: storing a string's suffix tree
Suffix_tree
Defunct railway tunnel in Somerset, England
the UK's longest without intermediate ventilation. The tunnel now forms part of the £1.8 million Two Tunnels Greenway walking and cycling path opened on
Combe_Down_Tunnel
Subfield of computer science
the length of the longest series of operations that have to be performed sequentially due to data dependencies (the critical path). The depth may also
Analysis of parallel algorithms
Analysis_of_parallel_algorithms
Shape that blocks all lines of sight
forests. Opaque sets were introduced by Stefan Mazurkiewicz in 1916, and the problem of minimizing their total length was posed by Frederick Bagemihl in 1959
Opaque_set
Tree node with two other nodes as descendants
this algorithm is O(h) where h is the height of the tree (length of longest path from a leaf to the root). However, there exist several algorithms for
Lowest_common_ancestor
Former population control policy in China
contraceptive choices". China Daily. Kallgren, Joice K. (2007). "Review of China's Longest Campaign: Birth Planning in the People's Republic, 1949-2005 by Tyrene
One-child_policy
2024 diss track by Kendrick Lamar
40 million radio airplay audience impressions, and 8,000 copies sold. It is the longest-running solo chart-topper of Lamar's career, surpassing "Humble". In October
Not_Like_Us
Spanish tennis player (born 2003)
in the second-set tiebreak. It was the longest ever best-of-three-sets ATP Masters 1000 final and the longest match in the tournament's history, at 3
Carlos_Alcaraz
Path for mostly non-motorized travel through a natural area
Path, the Pembrokeshire Coast Path, the Pennine Bridleway (bridleway), the South West Coast Path (South West Way) (the longest), and the Thames Path,
Trail
Total eclipse over North America
occurring about a day after perigee. With a magnitude of 1.0566, the eclipse's longest duration of totality was 4 minutes and 28 seconds near the Mexican town
Solar eclipse of April 8, 2024
Solar_eclipse_of_April_8,_2024
English football club season
club-record run of 87 consecutive Premier League appearances that was also the longest active run in the competition. In the 4th minute, Rice made a goal-line
2023–24_Arsenal_F.C._season
democratic" system with a socialist perspective, leads what will be the world's longest-running Maoist insurgency. 1969: Sison writes "The Philippine Crisis" (later
Timeline of the New People's Army rebellion
Timeline_of_the_New_People's_Army_rebellion
English football club season
in each of their last 34 meetings with Wolves in all competitions, the longest scoring streak against an opponent in the club's history. Raya Saliba Gabriel
2024–25_Arsenal_F.C._season
Archipelagic country in Southeast Asia
Philippines' coastline measures 36,289 kilometers (22,549 mi), the world's fifth-longest, and the country's exclusive economic zone covers 2,263,816 km2 (874,064 sq mi)
Philippines
Pattern of movement across water
offset from the path of the wake source by around arcsin(1/3) = 19.47° and is made up of feathery wavelets angled at roughly 53° to the path. The inside of
Kelvin_wake_pattern
Buddhist term for aspirant to enlightenment
skillful means (upāya). Mahāyāna Buddhism generally understands the bodhisattva path as being open to everyone, and Mahāyāna Buddhists encourage all individuals
Bodhisattva
independent candidate in the riding was endorsed by the NDP afterward. The Longest Ballot Committee targeted Poilievre's Carleton riding, which had 83 independents
2025 Canadian federal election
2025_Canadian_federal_election
project, but she soon discovers that the woman has an unpleasant hygiene problem. 9 9 "Thanksgiving" Mark Cendrowski Kirker Butler November 22, 2002 (2002-11-22)
List of What I Like About You episodes
List_of_What_I_Like_About_You_episodes
Experiences with software design
see and what they do, in comparison to the related web design term click path which is just a plain list of the text URLs that are hit when a user follows
User_journey
Country primarily in North America
political, cultural, economic, and military affairs. The 1990s saw the longest recorded economic expansion in American history, a dramatic decline in
United_States
Deliberate death by means of a railway vehicle
methods like jumping from a moving train and jumping from a bridge into the path of an approaching train. A railway suicide can also be committed by a vehicle
Rail_suicide
Country in West Asia
in the West Bank and considers Israel's control of the area to be the longest military occupation in modern history. The West Bank was occupied and annexed
Israel
Algorithm for virtual memory implementation
processor time) of the algorithm itself. The page replacing problem is a typical online problem from the competitive analysis perspective in the sense that
Page_replacement_algorithm
President of the United States from 2001 to 2009
numbers increased significantly. In 2007, the United States entered the longest post-World War II recession. Bush took office during a period of economic
George_W._Bush
Suspension bridge in New York City
span was the longest of any suspension bridge in the world until the Humber Bridge was completed in 1981. The bridge has the 18th-longest main span in
Verrazzano–Narrows_Bridge
Academic field
shortest path problem, transport problem, transshipment problem, location problem, matching problem, assignment problem, packing problem, routing problem, critical
Network_science
Decade of the Gregorian calendar (2000–2009)
supportive of Maoist political sentiment and ideology. It is presently the longest continuously active conflict worldwide. In 2006 Prime Minister Manmohan
2000s
Season of television series
a floating platform in the water. Whoever stays on their platform the longest without falling off or touching the platform with any part of their body
Survivor:_Marquesas
Single-stage mountain ultramarathon held in Chamonix, France
approximately 170 km long, with about 10,000 m of elevation gain. It is the longest and flagship race of UTMB Mont-Blanc, the annual event week held around
Ultra-Trail_du_Mont-Blanc
Filipino television evangelist (1947–2021)
Dating Daan (English: The Old Path, Portuguese: O Caminho Antigo, Spanish: El Camino Antiguo), which is considered as the longest-running religious program
Eli_Soriano
Prime Minister of Italy since 2022
She is the first woman to hold the office and the head of the second-longest government in the history of the Italian Republic. A member of the Chamber
Giorgia_Meloni
Model of computation
circuit. The depth of a gate g {\displaystyle g} is the length of the longest path in G {\displaystyle G} beginning at g {\displaystyle g} up to an output
Circuit_(computer_science)
Major League Baseball franchise in Cleveland, Ohio
1948). The team's World Series championship drought since 1948 is the longest active among all 30 current Major League teams. The team's name references
Cleveland_Guardians
2024 aircraft shootdown over Russia
manufactured on 26 June 2013, was an Embraer E190AR (Advanced Range), the longest range variant of the aircraft. It was registered as 4K-AZ65, and named
Azerbaijan Airlines Flight 8243
Azerbaijan_Airlines_Flight_8243
Attitudes and behaviors towards sex in ancient Rome
religion of Cybele and the Attis myth are explored by Catullus in one of his longest poems, Carmen 63. Roman men were free to have sex with males of lower status
Sexuality_in_ancient_Rome
Diagram that represents a workflow or process
This diagrammatic representation illustrates a solution model to a given problem. Flowcharts are used in analyzing, designing, documenting or managing a
Flowchart
Misaligned timing signals from different paths
source register's clock to Q delay, path max {\displaystyle {\text{path}}_{\text{max}}} is the path with the longest delay from source to destination, J
Clock_skew
Type of graph in graph theory
Janeiro, 1981), North-Holland. Grünbaum, B. (1974), "Vertices missed by longest paths or circuits", Journal of Combinatorial Theory, Series A, 17: 31–38,
Hypohamiltonian_graph
American basketball player (born 1984)
efficiency records. The Heat began a 27-game winning streak, which is the third longest in NBA history, and James' performance was described as a "month for the
LeBron_James
President of the United States from 2021 to 2025
to William Roth until Roth was defeated in 2000. He remains one of the longest-serving senators in U.S. history. For 36 years, he commuted from Washington
Joe_Biden
LONGEST PATH-PROBLEM
LONGEST PATH-PROBLEM
Female
English
Short form of English Katherine, KATH means "pure."
Surname or Lastname
English
English : habitational name from the city of Bath in western England, which is the site of sumptuous, but in the Middle Ages ruined, Roman baths. The place is named with the dative plural of Old English bæð ‘bath’. In some cases the surname may have originated as a metonymic occupational name for an attendant at a public bath house.Scottish : reduced and altered form of McBeth.German : variant of Bathe.Indian (Panjab) : Sikh name based on the name of a Jat clan.
Girl/Female
Australian, British, English
Way
Male
Irish
Short form of Irish Gaelic Parthalán, possibly PARTH means "son of Talmai."
Surname or Lastname
English
English : possibly a reduced form of Longhurst.
Female
Hebrew
(×Ö¸×¡Ö°× Ö·×ª) Hebrew name of Egyptian origin, ACÄ”NATH means "belonging to the goddess Neith." In the bible, this is the name of Joseph's Egyptian wife.
Female
Hebrew
(בַּתש×וּעַ) Variant spelling of Hebrew Bath-Shuwa, BATH-SHUA means "daughter of wealth."Â
Boy/Male
Hindu
Name of a God
Surname or Lastname
English (Bath)
English (Bath) : unexplained.
Boy/Male
Arabic, Modern
Road; The Way
Surname or Lastname
English (mainly Devon)
English (mainly Devon) : variant of Pate 1.
Surname or Lastname
English and Scottish
English and Scottish : from the personal name Pat(t), Pate, a short form of Patrick.English and Scottish : nickname for a man with a bald head, from Middle English pate ‘head’, ‘skull’.French (Paté) : from Old French pat(t)é ‘with paws’, ‘pawed’ (from pat(t)e ‘paw’), a nickname, applied presumably to a man with large and clumsy hands and feet.German : nickname for a trustworthy man, from Middle High German pate, Middle Low German pade ‘godfather’, ‘male relative’ (see Paeth), or alternatively from a personal name Bado, probably meaning ‘battle’, ‘fight’.
Female
English
English short form of French Catherine, CATH means "pure."
Boy/Male
Hindu, Indian, Tamil
Lord Shiva
Male
English
English unisex short form of English Patrick and Latin Patricia, PAT means "patrician; of noble birth."
Female
Hebrew
(בַּת-ש×ֶבַע) Hebrew name BATH-SHEBA means "daughter of the oath." In the bible, this is the name of a wife of Uriah then later King David, and mother of Solomon. Also spelled Bat-Sheva, Bathsheba, and Bathsheva.
Boy/Male
Hindu, Indian, Tamil, Unique
Leadership for World; Lord Shiva
Female
Hebrew
(בַּתש×וּעַ) Hebrew name BATH-SHUWA means "daughter of wealth." In the bible, this is another name Bath-Sheba is known by.
Boy/Male
Hindu
Surname or Lastname
English (Bristol and Bath)
English (Bristol and Bath) : unexplained.
LONGEST PATH-PROBLEM
LONGEST PATH-PROBLEM
Boy/Male
Hindu, Indian
Lord Vishnu
Boy/Male
Hindu, Indian
Sarawasti
Girl/Female
Arabic, Muslim
Spring
Girl/Female
English American Greek
From the Greek barbaros meaning foreign or strange, traveler from a foreign land. Popular in...
Girl/Female
Hindu
Novel
Girl/Female
Arabic, Muslim
Clouds
Boy/Male
Tamil
Thinakaran | தீநாகரண
Brilliant like the Sun, Intelligent
Girl/Female
Indian, Latin
Popularity; Golden
Girl/Female
Hindu, Indian
Rational
Biblical
Jehovah arises; brightness of Jehovah,produced by Jehovah,a leader of the choir
LONGEST PATH-PROBLEM
LONGEST PATH-PROBLEM
LONGEST PATH-PROBLEM
LONGEST PATH-PROBLEM
LONGEST PATH-PROBLEM
n.
Fig.: Anything regarded as a patch; a small piece of ground; a tract; a plot; as, scattered patches of trees or growing corn.
v. t.
To adorn, as the face, with a patch or patches.
n.
One who longs for anything.
v. t.
To mend by sewing on a piece or pieces of cloth, leather, or the like; as, to patch a coat.
pl.
of Path
v. t.
To make a path in, or on (something), or for (some one).
n.
Hence: The which contains the strength of life; the vital or essential part; concentrated force; vigor; strength; importance; as, the speech lacked pith.
a.
Open; frank; as, an honest countenance.
a.
Characterized by integrity or fairness and straight/forwardness in conduct, thought, speech, etc.; upright; just; equitable; trustworthy; truthful; sincere; free from fraud, guile, or duplicity; not false; -- said of persons and acts, and of things to which a moral quality is imputed; as, an honest judge or merchant; an honest statement; an honest bargain; an honest business; an honest book; an honest confession.
v. t.
To mend with pieces; to repair with pieces festened on; to repair clumsily; as, to patch the roof of a house.
a.
Longer; longest; -- obsolete compar. and superl. of long.
n.
A way, course, or track, in which anything moves or has moved; route; passage; an established way; as, the path of a meteor, of a caravan, of a storm, of a pestilence. Also used figuratively, of a course of life or action.
imp. & p. p.
of Path
n.
The act of exposing the body, or part of the body, for purposes of cleanliness, comfort, health, etc., to water, vapor, hot air, or the like; as, a cold or a hot bath; a medicated bath; a steam bath; a hip bath.
adv.
In a pat manner.
n.
A small piece of anything used to repair a breach; as, a patch on a kettle, a roof, etc.
pr.p. & vb. n.
of Path
n.
A small mass, as of butter, shaped by pats.