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the zero-weight cycle problem is the problem of deciding whether a directed graph with weights on the edges (which may be positive or negative or zero) has
Zero-weight_cycle_problem
mean weight cycle is a cycle whose average weight (total weight divided by length) is smallest among all cycles in the graph. An analogous problem is the
Minimum_mean_weight_cycle
All even-degree subgraphs of a graph
include cycles that are not faces, and some faces may not be included as cycles in the minimum weight cycle basis. There exists a minimum weight cycle basis
Cycle_space
Graph with oriented edges
Directed graph with reversed edges Vertical constraint graph Zero-weight cycle problem Bang-Jensen & Gutin (2000). Bang-Jensen & Gutin (2018), Chapter
Directed_graph
Mathematical optimization problem
flow instance to zero, and introduce a new edge from source to sink with unit cost and capacity d {\displaystyle d} . Assignment problem. Suppose that each
Minimum-cost_flow_problem
Absence of the sensation of weight
of weight, i.e., zero apparent weight. It is also termed zero g-force, or zero-g (named after the g-force) or, misleadingly, zero gravity. Weight is a
Weightlessness
Path in a graph that visits each vertex exactly once
products of the arc weights of the digraph's Hamiltonian cycles. This polynomial is not identically zero as a function in the arc weights if and only if the
Hamiltonian_path
Problem of finding the longest simple path for a given graph
the weights of its edges. In contrast to the shortest path problem, which can be solved in polynomial time in graphs without negative-weight cycles, the
Longest_path_problem
Combinatorial optimization problem
size, in which the sum of weights of the edges is minimum. If the numbers of agents and tasks are equal, then the problem is called balanced assignment
Assignment_problem
Set of principles focused on waste management
Zero waste, or waste minimization, is a set of principles focused on waste prevention that encourages redesigning resource life cycles so that all products
Zero_waste
2015 Indian film by Prakash Kovelamudi
Simran. Sweety is devastated and joins a weight loss clinic called Size Zero as she thinks that her weight is the issue. One of her friends, Jyothi,
Size_Zero
Algorithm for finding the shortest paths in graphs
edge weights are found in various applications of graphs. This is why this algorithm is useful. If a graph contains a "negative cycle" (i.e. a cycle whose
Bellman–Ford_algorithm
Method to find shortest paths
directed graph. It allows some of the edge weights to be negative numbers, but no negative-weight cycles may exist. It works by using the Bellman–Ford
Johnson's_algorithm
Hamiltonian cycle problem is computable on such graphs in polynomial time. In characteristic 2, the Hamiltonian cycle polynomial of an n×n-matrix is zero if n
Hamiltonian_cycle_polynomial
Mathematical proof about the permanent of matrices
sum of the weights of all cycle-covers of the graph; this is a graph-theoretic interpretation of the permanent. #SAT, a function problem related to the
♯P-completeness of 01-permanent
♯P-completeness_of_01-permanent
Decision problem in computer science
that this is for the version of the problem where the target sum is not necessarily zero, as otherwise the problem would be trivial). In 2015, Koiliaris
Subset_sum_problem
Software resource tracking technique
cause problems). Weighted reference counts are a good solution for garbage collecting a distributed system. Tracing garbage collection cycles are triggered
Reference_counting
Algorithm for two disjoint paths in a graph
second path. The problem of finding two disjoint paths of minimum weight can be seen as a special case of a minimum cost flow problem, where in this case
Suurballe's_algorithm
Measure of temperature relative to absolute zero
is a physical quantity that measures temperature starting from absolute zero, the point at which particles have minimal thermal motion. Thermodynamic
Thermodynamic_temperature
Largest independent set of paired elements
element, it is also possible to find a minimum-weight solution to the matroid parity problem, or a maximum-weight paired independent set, in linear matroids
Matroid_parity_problem
Lowest possible energy of a quantum system or field
where zero-point cancellations occur in the low-energy universe we observe today. This discrepancy is known as the cosmological constant problem and it
Zero-point_energy
directed cycle with edges of zero weight, and inherit the outgoing edges from the original graph shifting by one vertex backwards along this cycle. The salesman
Set_TSP_problem
Graph with sign-labeled edges
edges in it (where zero is even). In the mathematical balance theory of Frank Harary, a signed graph is balanced when every cycle is positive. Harary
Signed_graph
Graph divided into two independent sets
realization problem is the problem of finding a simple bipartite graph with the degree sequence being two given lists of natural numbers. (Trailing zeros may
Bipartite_graph
Tree which includes all vertices of a graph
weights. However, it is not necessary to construct this graph in order to solve the optimization problem; the Euclidean minimum spanning tree problem
Spanning_tree
Approximation for the travelling salesman problem
travelling salesman problem. That is, G is a complete graph on the set V of vertices, and the function w assigns a nonnegative real weight to every edge of
Christofides_algorithm
Pedal-driven two-wheel vehicle
A bicycle, also called a pedal cycle, bike, push-bike or cycle, is a human-powered or motor-assisted, pedal-driven, single-track vehicle, with two wheels
Bicycle
Method to maintain data backups
media is used until the end of the cycle. Then the cycle is repeated using media numbered the same as the previous cycle, but incremented by one. The lowest
Backup_rotation_scheme
Numerical method for solving physical or engineering problems
integral of the inner product of the residual and the weight functions; then, set the integral to zero. In simple terms, it is a procedure that minimizes
Finite_element_method
Directed graph where edges have a capacity
if it has a bottleneck with a value equal to zero. If any augmenting path exists, its bottleneck weight will be greater than 0. In other words, if there
Flow_network
Digital circuit optimisation
series of registers or latches (the number of registers or latches can be zero). Each vertex has a value corresponding to the delay through the combinational
Retiming
Hybrid-electric military motorcycle
of the MMX, an all-electric bike developed by Zero Motorcycles for the military. However, the problem with the MMX was that its battery needed to be
SilentHawk
Technique to compress data
implemented, finding a code in time linear to the number of input weights if these weights are sorted. However, although optimal among methods encoding symbols
Huffman_coding
Aircraft propulsion system efficient at a range of speeds higher and lower than sound's
A variable cycle engine (VCE), also referred to as adaptive cycle engine (ACE), is an aircraft jet engine that is designed to operate efficiently under
Variable_cycle_engine
Settlement without third party involvement
objective of the MLC problem is to find a compensation having the minimum weight. The authors note that a simple greedy approach of cycle compensations does
Collaborative_finance
Method for finding minimum spanning trees
the inner loop, which determines the next edge of minimum weight that does not form a cycle, can be parallelized by dividing the vertices and edges between
Prim's_algorithm
Rockets that use supersonic exhaust to create additional acceleration
rocket/ramjet engines, similar to a ramjet, but able to give useful thrust from zero speed, and is also able in some cases to operate outside the atmosphere,
Air-augmented_rocket
Algorithm for finding shortest paths
negative edge weights, as long as the graph contains no negative cycle reachable from the source vertex s. The presence of such cycles means that no shortest
Dijkstra's_algorithm
sink is a one-vertex closure. The closure problem is the problem of finding a closure of minimum or maximum weight. co- This prefix has various meanings usually
Glossary_of_graph_theory
Process of producing small rectangular items of fixed dimensions
cuts have zero width. This does not lose much generality, since if each cut has a fixed width of d>0, then the problem can be reduced to the zero-width variant
Guillotine_cutting
Positive-displacement pump
MPa or 2900 psi) and the swash plate is driven towards zero angle (piston stroke nearly zero) and with the inherent leaks in the system allows the pump
Axial_piston_pump
Mathematical version of an order change
the lengths of these cycles form an integer partition of n, which is called the cycle type (or sometimes cycle structure or cycle shape) of σ {\displaystyle
Permutation
Computational problem in graph theory
minimum-cost flow problem of which the maximum flow problem is a particular case. For the single-source shortest path (SSSP) problem with negative weights – another
Maximum_flow_problem
System that converts heat or thermal energy to mechanical work
using different cycles can also attain maximum efficiency. Mathematically, after a full cycle, the overall change of entropy is zero: Δ S h + Δ
Heat_engine
Graph representing faces of another graph
these cycles). For edge-weighted planar graphs (with sufficiently general weights that no two cycles have the same weight) the minimum-weight cycle basis
Dual_graph
Algorithm in graph theory
positive or negative edge weights (but with no negative cycles). A single execution of the algorithm will find the lengths (summed weights) of shortest paths
Floyd–Warshall_algorithm
last three zeros with the letter "K" or "k": for instance, writing "$30k" for $30,000 or using "Y2K" to denote the Year 2000 computer problem. A thousand
1000_(number)
Type of wheel without a hub
LEGACY Light Cycle Replica". Collider. Retrieved 2022-08-09. Welsh, Jonathan (2011-02-16). "For 'Tron' Fans: Your Very Own Light Cycle". Wall Street
Centreless_wheel
Study of mathematical algorithms for optimization problems
is zero (that is, the stationary points). More generally, a zero subgradient certifies that a local minimum has been found for minimization problems with
Mathematical_optimization
Set of edges without common vertices
the optimization problem is to find a maximum-weight matching; a dual problem is to find a minimum-weight matching. This problem is often called maximum
Matching_(graph_theory)
Elastic object that stores mechanical energy
spring outer diameter Zero-length spring is a term for a specially designed coil spring that would exert zero force if it had zero length. That is, in a
Spring_(device)
Simplest known jet propulsion device
known jet propulsion device. Valveless pulsejets are low in cost, light weight, powerful and easy to operate. They have all the advantages (and most of
Valveless_pulsejet
Type of helmet
interference with peripheral vision. A cycle helmet should generally be light in weight and provide ample ventilation because cycling can be an intense aerobic activity
Bicycle_helmet
Node ordering for directed acyclic graphs
topological ordering is possible if and only if the graph has no directed cycles, that is, if it is a directed acyclic graph (DAG). Any DAG has at least
Topological_sorting
Pairing where no unchosen pair prefers each other over their choice
hospitals/residents problem renders the problem NP-complete. The assignment problem seeks to find a matching in a weighted bipartite graph that has maximum weight. Maximum
Stable_matching_problem
Process of calculating the causal factors that produced a set of observations
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating
Inverse_problem
Computational graph problem
visit every vertex of a cycle and return to the start. This differs from the shortest path problem (with strictly positive weights), where repetitions in
Canadian_traveller_problem
exchange Shortest path problem Bellman–Ford algorithm: computes shortest paths in a weighted graph (where some of the edge weights may be negative) Dijkstra's
List_of_algorithms
Engine in which fuel combusts with an oxidizer
simplicity and a higher power-to-weight ratio than their 4-stroke counterparts. Despite having twice as many power strokes per cycle, less than twice the power
Internal_combustion_engine
Matroid with graph forests as independent sets
In the mathematical theory of matroids, a graphic matroid (also called a cycle matroid or polygon matroid) is a matroid whose independent sets are the
Graphic_matroid
Process of producing a flight plan
weight empty is the basic weight of the aircraft when ready for operation, including crew but excluding any payload or usable fuel. Zero fuel weight is
Flight_planning
Binary representation for signed numbers
is the most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values. As
Two's_complement
Public bicycle hire scheme in London
Santander Cycles (formerly Barclays Cycle Hire) is a public bicycle hire scheme in London in the United Kingdom. The scheme's bicycles have been popularly
Santander_Cycles
Area of discrete mathematics
decomposition problems and similar problems that have been studied include: Arboricity, a decomposition into as few forests as possible Cycle double cover
Graph_theory
Types of quantities in financial fields
body weight over time). In Earth system science, many stock and flow problems arise, such as in the carbon cycle, the nitrogen cycle, the water cycle, and
Stock_and_flow
Sports motorcycle
increased to a 128 hp (95 kW). This year's model finally addressed the weight problems that had plagued the GSX-R through the first half of the 90s. Other
Suzuki_GSX-R750
Links are weighted as in the classical problem. At the beginning of the algorithm, nodes know only the weights of the links which are connected to them
Distributed minimum spanning tree
Distributed_minimum_spanning_tree
Type of spanning tree
this tie-breaking rule is needed to prevent loops when there exist zero-length cycles. Construct the shortest-path tree using the edges between each node
Shortest-path_tree
Power supply with switching regulator
zero magnetic flux every cycle. Chopper controller: The output voltage is coupled to the input thus very tightly controlled In a quasi-resonant zero
Switched-mode_power_supply
Type of energy-storing battery
the lithium acts as a charge carrier, rather than remaining at the anode (zero excess lithium). Manufacturing a lithium anode is also complex, as this involves
Anode-free_battery
Graph with at most one cycle per component
component has at most one cycle. That is, it is a system of vertices and edges connecting pairs of vertices, such that no two cycles of consecutive edges share
Pseudoforest
Clean air agency in California, United States
mitigation. The CARB Zero-Emission Vehicle (ZEV) program was enacted by the California government starting in 1990 to promote the use of zero emission vehicles
California Air Resources Board
California_Air_Resources_Board
Launch system that only uses one rocket stage
Only when the structural factor approaches zero [very little vehicle structure weight] does the payload/weight ratio of a single-stage rocket approach that
Single-stage-to-orbit
Motor vehicle
pivot helped maintain wheel alignment changes at a near zero value throughout the suspension cycle. Other notable features included an independent, 4-channel
Honda_NSX_(first_generation)
Two- or three-wheeled motor vehicle
first commercial design for a self-propelled cycle was a three-wheel design called the Butler Petrol Cycle, conceived of Edward Butler in England in 1884
Motorcycle
Algorithm for supervised learning of binary classifiers
its predictions based on a linear predictor function combining a set of weights with the feature vector. The artificial neuron and artificial neural network
Perceptron
Guidance and navigation computer used in Apollo spacecraft
setting up the DAP cycle termination sequence in the Digital Autopilot of the lunar module. It is believed to be responsible for problems emulating the LEM
Apollo_Guidance_Computer
Sequence of operations for a task
divide the problem into sub-problems and collect the results back together. Resource consumption in these algorithms is not only processor cycles on each
Algorithm
Method of partitioning data points into groups based on their similarity
correlation clustering problem in terms of non-negative edge weights and a partition of the edges into attractive and repulsive edges the problem is also formulated
Correlation_clustering
Class of pseudorandom number generators
{ uint32_t a; } XorShift32State; // The state must be initialized to non-zero uint32_t xorshift32(XorShift32State* state) { // Algorithm "xor" from p.
Xorshift
Problem in mathematics
rational weights, and a set of directed arcs A with positive rational weights that covers each edge or arc at least once at minimal cost. The problem has been
Mixed_Chinese_postman_problem
Vehicle propelled fully or mostly by electricity
current output versus lead-acid batteries—has revived public interest as zero-emission vehicle options. Manufacturers mostly switched to hybrids that use
Electric_vehicle
Mathematical game played on a graph
Doing so is called finding the zero-mean partition (and is also related to solving energy games) It is a major open problem in computer science whether there
Mean_payoff_game
Plug-in electric vehicles with two or three wheels
February 2020. "Zero Motorcycles". Zero Motorcycles. Retrieved 3 October 2020. Chris Neiger (15 October 2013). "Solving electric cars' quiet problem". BBC Autos
Electric motorcycles and scooters
Electric_motorcycles_and_scooters
Rocket engine that uses liquid fuels and oxidizers
the rocket suffers from uncommanded cycles of acceleration. Liquid propellants often need ullage motors in zero-gravity or during staging to avoid sucking
Liquid-propellant_rocket
Concept in combinatorics
this problem we use a bivariate generating function g(z, u) as described in the introduction. The value of b for a cycle not of size m is zero, and one
Random_permutation_statistics
Family of related bitwise operations on machine words
ctz(2⌈log2(x)⌉) (which depends on ctz returning w for the zero input) On platforms with an efficient Hamming weight (population count) operation such as SPARC's POPC
Find_first_set
Medical condition caused by receiving too little or too many nutrients
when an organism gets too few or too many nutrients, resulting in health problems. Specifically, it is a deficiency, excess, or imbalance of energy, protein
Malnutrition
Central region of the Sun
which is responsible for most of the Sun's released energy – and the CNO cycle. The composition of the Sun varies with depth. In the photosphere, it is
Solar_core
do not decrease cost is that it may cycle over assignments of the same cost. Tabu search overcomes this problem by maintaining a list of "forbidden"
Local search (constraint satisfaction)
Local_search_(constraint_satisfaction)
Electric current that periodically reverses direction
course of one cycle (two cycle as the power) the voltage rises from zero to 325 V, the power from zero to 460 RW, and both falls through zero. Next, the
Alternating_current
Directed graph with no directed cycles
closure. The closure problem takes as input a vertex-weighted directed acyclic graph and seeks the minimum (or maximum) weight of a closure – a set of
Directed_acyclic_graph
Theoretical engine
out of flooded salt mines. Carnot defined work as "weight lifted through a height". The Carnot cycle when acting as a heat engine consists of the following
Carnot_heat_engine
Graph-theoretic description of polyhedra
one more vertex v {\displaystyle v} , finding a linear function that is zero on the resulting set of k {\displaystyle k} vertices, and following the paths
Steinitz's_theorem
Highly refined form of kerosene used as rocket fuel
new operating cycles, in attempts to better manage leftover fuel, achieve a more-gradual cooldown, or both. This still leaves the problem of non-dissociated
RP-1
Type of combined-cycle jet engine
not a problem because the burner and its hot exhaust gases are located behind the turbine blades. The air turboramjet engine is a combined cycle engine
Air_turborocket
Pump driven by a gas turbine
combustion chamber temperatures. Rocket engine cycles are all various workarounds to this fundamental problem. The first ever turbopump designs (by Goddard
Turbopump
Dependence of the state of a system on its history
force of the weights) because the length has not yet reached the value it had for the same weight during the loading part of the cycle. In terms of energy
Hysteresis
Method for representing or encoding numbers
to solve the balance problem, which requires finding a minimal set of known counter-weights to determine an unknown weight. Weights of 1, 3, 9, ..., 3n
Positional_notation
Concept in economics and game theory
\leq e^{-{\sqrt {d+1}}}+{\frac {1}{\sqrt {d+1}}}.} This quantity tends to zero when d {\displaystyle d} tends to infinity. PoA upper bounds can be obtained
Price_of_anarchy
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