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...nomial in both models, whereas a '''weakly-polynomial time algorithm''' is polynomial only in the Turing machine model. ...nce between strongly- and weakly-polynomial time is when the inputs to the algorithms consist of integer or rational numbers. It is particularly common in [[Opti ...

...time number partitioning''' is a [[Pseudo-polynomial time|pseudopolynomial time]] algorithm for solving the [[partition problem]]. == The pseudo-polynomial algorithm == ...

In [[mathematics]] and [[optimization]], a '''pseudo-Boolean function''' is a [[function (mathematics)|function]] of the form ...=Rudeanu |first3=S.|date=1963 |title=On the determination of the minima of pseudo-Boolean functions |language=ro |journal=Studii și cercetări matematice |iss ...

{{short description|Combinatorial optimization method for pseudo-Boolean functions}} ...''') is a [[combinatorial optimization]] method for minimizing quadratic [[pseudo-Boolean function]]s in the form ...

...decomposition''' of a [[polynomial system]] {{mvar|S}} is a set of simpler polynomial systems {{math|''S''₁, ..., ''S_e''}} such that a poin ..., those simpler systems are [[regular chain]]s. If the coefficients of the polynomial systems {{math|''S''₁, ..., ''S_e''}} are real numbers ...

{{distinguish|Pseudo-polynomial time}} ...tant <math>c</math> such that the [[worst-case analysis|worst-case running time]] of the algorithm, on inputs of {{nowrap|size <math>n</math>,}} has an [[u ...

...onential. In some geometric intersection graphs, there are sub-exponential algorithms for finding a MDS.<ref>{{Cite journal | last1 = Ravi | first1 = S. S. | las ...proximation. In some geometric intersection graphs, there are [[polynomial-time approximation scheme]]s (PTAS) for finding a MDS. ...

...s equivalent to computing the [[maximum flow]] over the network. Given a [[pseudo-Boolean function]] <math>f</math>, if it is possible to construct a flow ne ...possible to find the [[global optimum]] of <math>f</math> in [[polynomial time]] by computing a minimum cut of the graph. The mapping between cuts and var ...

...give a more realistic analysis of the practical performance (e.g., running time, success rate, approximation quality) of the algorithm compared to analysis ...algorithm is low, then it is unlikely that the algorithm will take a long time to solve practical instances whose data are subject to slight noises and im ...

...parameter ''q''_j, and it must run for exactly ''p_j'' time-steps on exactly ''q''_j machines in ''parallel''. ...''_max means that the goal is to minimize the maximum completion time. Some authors use <math> P|m_j|C_{\max} </math> instead.'''<ref name="Joha ...

...ons required by the more efficient algorithms is at most ''n'', so the run-time is O(''n'' 2^''n''). ...input size is 2^''n'' , and so the above algorithms run in time polynomial in the input size. But when ''n'' is large, even representing such a game i ...

...Broadbent A. |author2-link= Anne Broadbent |author3=Tapp A. |title=Quantum pseudo-telepathy|journal=Foundations of Physics|year=2005|pages=1877–1907|doi=10.1 ...is considered to have a refereed game with error ε if it has a polynomial time verifier satisfying these conditions: for each string x∈L Alice (the yes pr ...

* In [[computational geometry]], algorithms for problems on general polygons are often more complex than those for rest ...polygon with <math>n</math> vertices, a triangulation can be calculated in time <math>\Theta(n)</math>. For a [[polygon with holes]], there is a lower boun ...

...i |first1=Simina |last2=Sandomirskiy |first2=Fedor |date=2019-07-03 |title=Algorithms for Competitive Division of Chores |class=cs.GT |eprint=1907.01766 }}</ref> == Algorithms == ...

...t models jobs that require a contiguous portion of the memory over a given time period. Another example is the area of industrial manufacturing, where rect ...h>. However, the best approximation ratio achieved so far (by a polynomial time algorithm by Harren et al.<ref name="Harren" />) is <math>(5/3 + \varepsilo ...

...an and Co.}}</ref> Thus, a given solution can be verified to in polynomial time while no algorithm can identify a solution efficiently. ...] and there is no known algorithm that can solve the problem in polynomial time. ...

...mands too much. A real-life adversary cannot spend an indefinite amount of time examining a message in order to find the one error pattern which an algorit ...e algorithm runs significantly slower. But since this would take O(''n''!) time, it is clearly infeasible for an adversary to do this. Similarly, it is unr ...

{{short description|Set of related approximation algorithms for the bin packing problem}} ...other algorithms with slightly different approximation guarantees and run-time bounds. ...

...lasses of polygons, a smallest polygon covering can be found in polynomial time. ...necessary (i.e., unneeded to support future squares). Here is a simplified pseudo-code of the algorithm: ...

...ite thesis |last1=Abam |first1=Mohammad Ali |title=New Data Structures and Algorithms for Mobile Data |publisher=Eindhoven University of Technology |url=http://r ...systems where there is a set of values that are changing as a function of time, in a known fashion. So the system has some values, and for each value <mat ...