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Topic: Polynomial time

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	Polynomial time - Wikipedia, the free encyclopedia
		In computational complexity theory, polynomial time refers to the computation time of a problem where the time, m(n), is no greater than a polynomial function of the problem size, n.
		Mathematicians sometimes use the notion of "polynomial time on the length of the input" as a definition of a "fast" computation, as opposed to "super-polynomial time", which is anything slower than that.
		Polynomial time is the smallest time-complexity class on a deterministic machine which is robust in terms of machine model changes, and is the smallest class closed under composition of subproblems.
	en.wikipedia.org /wiki/Polynomial_time (259 words)

	PlanetMath: time complexity
		Time complexity refers to a function describing how much time it will take an algorithm to execute, based on the parameters of its input.
		Complexity classes are equivalence classes of time complexities which are “equal” in Big-O notation.
		This is version 5 of time complexity, born on 2001-10-18, modified 2005-04-18.
	planetmath.org /encyclopedia/TimeComplexity.html (185 words)

	Average Polynomial Time
		Expected polynomial time is an obvious choice as a natural notion of average-case efficiency of an algorithm.
		Moreover, if a problem is polynomial on average under one encoding method, then it should be polynomial on average under all polynomially equivalent encodings.
		Under the worst-case measurement, the running time of an algorithm is measured as a function of the length of the input.
	www.uncg.edu /mat/avg/avgcomp/node3.html (703 words)

	Primality Proving 4.3: A polynomial-time algorithm
		Adleman and Hang [AH1992] modified the Goldwasser-Killian algorithm [GK86] to produce a randomized polynomial time algorithm that always produced a certificate of primality...
		(This means the time it takes to run the algorithm is at most a constant times the number of digits to the twelfth power times a polynomial evaluated at the log of the number of digits.)
		AKS also showed that if Sophie Germain primes have the expected distribution [HL23] (and they certainly should!), then the exponent 12 in the time estimate can be reduced to 6, bringing it much closer to the the (probabilistic) ECPP method.
	primes.utm.edu /prove/prove4_3.html (720 words)

	polynomial approximation scheme
		A polynomial time algorithm is defined to be one whose time complexity function is O(p(n)) for some polynomial function p, where n is used to denote the input length.
		)-approximation algorithm and the execution time is bounded by a polynomial in the length of the input.
		A polynomial time algorithm is an alternative of the second kind, usually referred as a heuristic.
	www.bilkent.edu.tr /~egunes/polynomial2.htm (1785 words)

	Polynomial Time Query Processing in Temporal Deductive Databases - Chomicki (ResearchIndex) (Site not responding. Last check: 2007-10-13)
		We show that if for a given set of temporal rules, the period of its least models is bounded from the above by a polynomial in the database size, then also the time to process yes-no queries (as well as to compute finite representations of all query answers) can be polynomially bounded.
		We present a bottom-up query processing algorithm BT that is guaranteed to terminate in polynomial time...
		Polynomial time query processing in temporal deductive databases.
	citeseer.ist.psu.edu /chomicki90polynomial.html (609 words)

	nondeterministic polynomial time (Site not responding. Last check: 2007-10-13)
		This may take exponential time as long as a potential solution can be verified in polynomial time.
		NP is obviously a superset of P (polynomial time problems solvable by a deterministic Turing Machine in polynomial time) since a deterministic algorithm can be considered as a degenerate form of nondeterministic algorithm.
		If a problem A is in NP and a polynomial time algorithm for A could also be used to solve problem B in polynomial time, then B is also in NP.
	www.cacs.louisiana.edu /~mgr/404/burks/foldoc/82/80.htm (189 words)

	Complexity Zoo - Qwiki
		Given a grid graph of polynomial length and width k, decide whether there is a path between vertices s and t (which can be given as part of the input).
		The class of multivariate polynomials over the integers that can be evaluated using a polynomial (in the input size n) number of additions, subtractions, and multiplications, together with the constants -1 and 1.
		Similar to TreeBQP except that the quantum computer's state at each time step is restricted to being exponentially close to a state in AmpP (that is, a state for which the amplitudes are computable by a classical polynomial-size circuit).
	qwiki.caltech.edu /wiki/Complexity_Zoo (6771 words)

	Fields Institute - Manindra Agrawal (via CobWeb/3.1 planetlab2.cs.umd.edu) (Site not responding. Last check: 2007-10-13)
		He has been active over the past ten years in the field of decision theory, complexity, and the relation between the geometry of sets and their information content.
		For some years he has been interested in finding a polynomial time algorithm to test whether a given number is prime.
		Although random algorithms can solve this problem with high certainty in polynomial time, it remained a long-standing challenge to find a method that works in every case.
	www.fields.utoronto.ca.cob-web.org:8888 /programs/scientific/02-03/lectures/agrawal (149 words)

	Deciding Confluence of Certain Term Rewriting Systems in Polynomial Time (via CobWeb/3.1 planetlab2.cs.umd.edu) (Site not responding. Last check: 2007-10-13)
		We present a polynomial time algorithm for deciding confluence of ground term rewrite systems.
		We generalize the decision procedure to get a polynomial time algorithm, assuming that the maximum arity of a symbol in the signature is a constant, for deciding confluence of rewrite systems where each rule contains a shallow linear term on one side and a ground term on the other.
		The existence of a polynomial time algorithm for deciding confluence of ground rewrite systems was open for a long time and was independently solved only recently by Comon, Godoy, and Nieuwenhuis [FoCS 2001].
	www.csl.sri.com.cob-web.org:8888 /~tiwari/lics02.html (247 words)

	polynomial time (via CobWeb/3.1 planetlab2.cs.umd.edu) (Site not responding. Last check: 2007-10-13)
		Definition: When the execution time of a computation, m(n), is no more than a polynomial function of the problem size, n.
		Note: Broadly speaking, polynomial time algorithms are reasonable to compute.
		The time to run exponential algorithms grows too fast to expect to be able to compute exact solutions in all cases.
	www.nist.gov.cob-web.org:8888 /dads/HTML/polynomialtm.html (110 words)

	Polynomial-time reduction - Wikipedia, the free encyclopedia
		In computational complexity theory a polynomial-time reduction is a reduction which is computable by a deterministic Turing machine in polynomial time.
		If it is a many-one reduction, it is called a polynomial-time many-one reduction, polynomial transformation, or Karp reduction.
		If it is a Turing reduction, it is called a polynomial-time Turing reduction or Cook reduction.
	en.wikipedia.org /wiki/Polynomial-time_many-one_reduction (366 words)

	Computational Complexity: Favorite Theorems: The Polynomial-Time Hierarchy (Site not responding. Last check: 2007-10-13)
		, where NP represents the class of problems solvable in nondeterministic polynomial time with access to an oracle for solving problems in A. The union of all of the Σ
		I seem to recall that the SIGACT News complexity theory column was going to run a column on problems complete for "high" levels of the polynomial hierarchy.
		Marcus Schaefer and Chris Umans wrote a two-part survey on completeness in the polynomial-time hierarchy for SIGACT News.
	weblog.fortnow.com /2005/06/favorite-theorems-polynomial-time.html (424 words)

	A polynomial time list colouring algorithm for series-parallel graphs (via CobWeb/3.1 planetlab2.cs.umd.edu) (Site not responding. Last check: 2007-10-13)
		A polynomial time list colouring algorithm for series-parallel graphs (via CobWeb/3.1 planetlab2.cs.umd.edu)
		Computer Science » Research » Tech Reports » 2002 » A polynomial time list colouring algorithm for series-parallel graphs
		A polynomial time list colouring algorithm for series-parallel graphs
	www.cs.dal.ca.cob-web.org:8888 /research/techreports/2002/CS-2002-02.shtml (180 words)

	"ESP: Path-Sensitive Program Verification in Polynomial Time" (via CobWeb/3.1 planetlab2.cs.umd.edu) (Site not responding. Last check: 2007-10-13)
		In this paper, we present a new algorithm for partial program verification that runs in polynomial time and space.
		We are interested in checking that a program satisfies a given temporal safety property.
		Our results show that property simulation scales to large programs and is accurate enough to verify meaningful properties.
	www.cse.ucsd.edu.cob-web.org:8888 /groups/progsys/pubs/esp_pldi_02.html (204 words)

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