F

formula - wzór

in the field - na polu

This paper focuses on  - Artykuł koncentruje się

follow in detail - śledzić szczegółowo

and so forth - i tak dalej

first of all - przede wszystkim

following [1] - za [1]

following Bowers - za Bowersem

procedure is founded on the algorithm... -

from the fact that ... it follows that -

near future -  bliska przyszłość

to be far from tight - być daleko od dokładnego

, with the adjacency matrix of Fig.2 -

it follows from the way we construct the subgraph that ... -

from a computational viewpoint, -

The definitional set-up is as follows. -

The foregoing conclusions... - powyższe wnioski

.., for if not, ...  -  .., bo w przeciwnym razie, ...

The following is a brief summary of the contents of the paper -

friction - tarcie

fusion - stopienie, fuzja

We shall focus our attention on -

# is an example of a computation greatly faciliated by the FFT - # jest przykładem obliczania znacznie ułatwionego przez FFT

from which it follows that.. - 

First N must be factored  into its K prime factors -

Such time bounds are far better then the exponential time bounds associated with... -

foreclose - wykluczyć

Since ..., from here on we consider - Ponieważ wierzchołki stopnia 2 nie powodują kłopotów w 5-kolorowaniu, od tego miejsca będziemy rozważali

If the graph is sparse, that is, the number of edges are far fewer than n(n-1) ...

This follows because ... - wynika to stąd, że

flaw - wada, słabe miejsce rozumowania

farther - dalej (w czasie)

further - dalej (w przestrzeni)

the fewest possible number of colors -

in analogous fashion - w analogiczny sposób

Het reason for favoring the for loop in this context is not so much because we save two statements but because the number of iterations was fixed by n.

...then the while  loop is favored.

for  n=30 to 300 in increments of 30.

far fewer - znacznie mniej -

the fewest number of vertices

the algorithm may fail miserably on 3-colorable graphs -

The following instances each indicate the need for knowing...

The various enhancements utilized in the algorithm provide a further substantial improvement

a small number of edges , say fewer then... -

One can freely use O(n/log n) without worrying about the cases n=0 and n=1

freshman - student pierwszego roku

flunk the test - oblać egzamin

in such a fashion - w taki sposób

function's domain - dziedzina

function's target - przeciwdziedzina

function's image - przeciwdziedzina

frontispice - druga strona książki

Our main result is an O(-) algorithm that produces a solution with at least a fraction1/2+W (1/D) of the number of arcs in an optimal solution.

fulfills (po amerykańsku)

by arbitrarily identifying in a 1-1 fashion

to face a problem

The two programs were withn a factor of  8 or less in run time