computational complexity theory of counting problems, a polynomial-time counting reduction is a type of reduction (a transformation from one problem to...

problem in #P has a Turing reduction or polynomial-time counting reduction to it. A counting reduction is a pair of polynomial-time transformations from inputs...

reductions are also polynomial-time reductions. However, log-space reductions are probably weaker than polynomial-time reductions; while any non-empty, non-full...

In computer science (particularly algorithmics), a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems...

Polynomial-time parsimonious reductions are a special case of a more general class of reductions for counting problems, the polynomial-time counting reductions...

showed that it is possible to use a weaker notion of reduction, a polynomial-time counting reduction, that translates the other problem into a single instance...

The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a...

machine in polynomial time, with an error probability of less than 1/2 for all instances. The abbreviation PP refers to probabilistic polynomial time. The complexity...

which states that every problem in the polynomial hierarchy has a polynomial-time Turing reduction to a counting problem. S. Toda Archived 2007-08-18 at...

computational number theory. As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity...

Satisfiability Problem (sometimes called Sharp-SAT, #SAT or model counting) is the problem of counting the number of interpretations that satisfy a given Boolean...

sum(S)/2. This can also be proved by reduction from the general variant; see partition problem. The analogous counting problem #SSP, which asks to enumerate...

a polynomial f is in I, if and only if some/every complete lead-reduction/reduction of f by G produces the zero polynomial; for every S-polynomial s of...

task and runs in polynomial time (as opposed to, say, exponential time), meaning the task completion time is bounded above by a polynomial function on the...

principle to reduce the problem of counting the number of Hamiltonian cycles to a simpler counting problem, of counting cycle covers, which can be solved...

The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. It is a polynomial in two variables which plays...

in the polynomial hierarchy there is a deterministic polynomial-time Turing reduction to a counting problem. An analogous result in the complexity theory...

Turing machine in polynomial time. There are, however, many complexity classes defined in terms of other types of problems (e.g. counting problems and function...

to counting the number of independent sets in G. As with any type of reduction, a holographic reduction does not, by itself, yield a polynomial time algorithm...

just the database. For instance, we say that query evaluation has polynomial-time data complexity for a class of queries if, for every fixed query Q...

complexity theory, arithmetic circuits are the standard model for computing polynomials. Informally, an arithmetic circuit takes as inputs either variables or...

this reduction is more liberal than the standard reduction used in computational complexity (sometimes called polynomial-time many-one reduction); for...

under which a finite set S of relations over the Boolean domain yields polynomial-time or NP-complete problems when the relations of S are used to constrain...

construct, while transitive reductions can be constructed in polynomial time. Transitive reduction can be defined for an abstract binary relation on a set...

simply counting the number of satisfied clauses, the problem can be solved in polynomial time since the number of possible costs is polynomial. However...

every problem in NEXPTIME has a polynomial-time many-one reduction to it. In other words, there is a polynomial-time algorithm that transforms instances...

NP-complete, this polynomial-time many-one reduction shows that subgraph isomorphism is also NP-complete. An alternative reduction from the Hamiltonian...

in computer science Can the graph isomorphism problem be solved in polynomial time? More unsolved problems in computer science The graph isomorphism problem...

polylogarithmic polynomial polynomial-time approximation scheme (PTAS) polynomial hierarchy polynomial time polynomial-time Church–Turing thesis polynomial-time reduction...

complexity of reductions, such as polynomial-time reductions or log-space reductions. The most commonly used reduction is a polynomial-time reduction. This means...