complexity theory, especially the study of approximation algorithms, an approximation-preserving reduction is an algorithm for transforming one optimization...

approximation scheme, an approximation algorithm in computer science Pesetas, Spanish currency PTAS reduction, an approximation-preserving reduction in...

preserves approximability features; it is one type of approximation-preserving reduction. L-reductions in studies of approximability of optimization problems...

solutions to instances of problem A. Approximation-preserving reductions are often used to prove hardness of approximation results: if some optimization problem...

constant-factor approximation algorithm Approximation-preserving reduction Exact algorithm Bernard., Shmoys, David (2011). The design of approximation algorithms...

reduction is an approximation-preserving reduction that is often used to perform reductions between solutions to optimization problems. It preserves the...

exponential with a low base. Approximation-preserving reduction APX is the class of problems with some constant-factor approximation algorithm Heuristic algorithm...

have a PTAS unless P=NP. This can be proved by showing an approximation-preserving reduction from MAX 3-SAT-3 to GISMP2. The following greedy algorithm...

the Wayback Machine Orponen, P.; Mannila, H. (1987). On approximation preserving reductions: Complete problems and robust measures' (Report). Department...

solvable in polynomial time. Approximation-preserving reduction Optimization problem Approximation algorithm PTAS reduction Demaine, Erik (Fall 2014). 6...

approximation and projection for dimension reduction". arXiv:1802.03426. "UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction...

their value, hence the exponential factor. Approximation-preserving reduction Complexity class Approximation algorithm Max/min CSP/Ones classification...

APX-hardness is commonly shown via PTAS reduction or AP-reduction. Parameterized approximation scheme, an approximation scheme that runs in FPT time Sanjeev...

necessarily preserve densities or distances well. Uniform manifold approximation and projection (UMAP) is a nonlinear dimensionality reduction technique...

to within a factor O(log n). This factor is tight, via an approximation-preserving reduction from the set cover problem. If we assume distances between...

NP-hardness reduction for the k-minimum spanning tree problem preserves the weight of all solutions, it also preserves the hardness of approximation of the...

derived from the reduction will depend on how well the gap is preserved. Trevisan et al. (2000) formalize the problem of finding gap-preserving gadgets, for...

approximation-preserving way: The Independent Set problem has no constant-factor approximation unless P = NP. Approximation algorithm: APPROXIMATION-VERTEX-COVER(G)...

an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective...

polynomial time. In some cases parsimonious reductions, a more specific type of reduction that preserves the exact number of solutions, are used. #P-complete...

(LSH); or data-dependent methods, such as locality-preserving hashing (LPH). Locality-preserving hashing was initially devised as a way to facilitate...

combine a polynomial or rational approximation (such as Chebyshev approximation, best uniform approximation, Padé approximation, and typically for higher or...

A parameterized approximation algorithm is a type of algorithm that aims to find approximate solutions to NP-hard optimization problems in polynomial...

Dimensionality reduction is often used to reduce the problem of managing and manipulating large data sets. Dimensionality reduction techniques generally...

The existence of an approximation preserving L-reduction from the vertex cover problem to it; Existing constant-factor approximation algorithms. The best...

However, although this transformation preserves the optimal solution, it does not preserve the quality of approximations to that solution. If the graph is...

some reduction. Due to the connection between approximation algorithms and computational optimization problems, reductions which preserve approximation in...

and vice versa. Moreover, the reductions preserve the approximation ratio: for any α, a polynomial-time α-approximation algorithm for minimum dominating...

orders of approximation ordered array ordered binary decision diagram (OBDD) ordered linked list ordered tree order preserving hash order preserving minimal...

these methods typically construct a series of increasingly accurate approximations. Most square root computation methods are iterative: after choosing...