A

along the same lines as in the proof of Theorem 1 one can check -

amount of work to be done by the algorithm as a whole would grow as n3 -

to abort a program execution - zerwać obliczenia programu

We shall furthermore use the abbreviation... - Ponadto dla uproszczenia zapisu wprowadzi  oznaczenie...

will lead to abortion - doprowadzi do zerwania

Because of the apparent absence from the literature -

All results on ... that we are aware of are ... -

analogues - analogowy

However, it is atrociously inefficient from the standpoint of computing time -

angle brackets -  <  >

an IBM370/158 -

This alerts as -

arbitrarily - dowolnie

assessment - oszacowanie

anticlockwise - w kierunku przeciwnym ruchowi wskazówek zegara

abscissa - oś x

These families are all very similar -

abort - zerwij

to attain - osiągać

to aim at bringing together - celem zgromadzenia

this inclusive amount cannot be broken up - ta łączna suma nie może być przekroczona

to attend - towarzyszyć

algorithms may be arrived at using - można dojść do algorytmów używając

to address the audience -

this article discusses the -

automated system -

in addition to the -

as to - co do

approached from new angles - podchodzony z nowej strony

on the average - średnio

aim at - mieć na celu

no single node can be added without requiring nonexisting edges to make it a declique (lub without destroying the planarity)

The argument G will be omitted in those cases in which only one graph is under consideration.

this is not allowed - jest to zabronione

argument - rozumowanie

as far as - o ile

to take advantage of - korzystać z

applied to - stosowana do

for according to - dla zgodności z

according to the algorithm - zgodnie z algorytmem

we use A(G) to denote ... when applied to G - piszemy A(G) dla ..., gdy stosuje się to do G.

can be attacked as a graph coloring -

only one adjacency to Vi - tylko jedno połączenie z Vi

After all - przecież, w końcu

for algorithms above = for above mentioned algorithms

G is a bipartite graph, all of whose edges are ... -

in all - w sumie, łącznie

it is asserted that ... - jest dowiedzione, że ...

it allows one to abstract away such issues as numerical stability and round-off error -

, abbreviated simply to IS.

, yet there  appears to be no information in the literature concerning nontrivial upper bound on the ... -

amount of storage required by -

so us to avoid - aby unikać

(plus assembly language subroutines) -

Actually, - Faktycznie,

# is assumed to be - przyjęto, że # jest

approximately equal to -

the core of the algorithm -

to be associated with -

The CPU - time was averaged over such a collection.

the assembly language

in accord (ance) with -

alternate - zmienny, kolejny, przeciwległy

Asymptotically in n, almost all pairs of matrices may be multiplied ... -

One is led to the study of approximate algorithms, (i.e. algorithms which, while not obtaining the optimal solution, do guarantee solutions reasonably close to the optimal, which are of low polynomial complexity (i.e. O(nk) for some "small" k) -

argue - dowodzić

axis - oś

added together - dodane do siebie

# makes the Sun appear - # sprawia, że słońce zdaje się ...

exact and approximate algorithms -

All the approximation schemes can guarantee worst case error ratios of  or less while running in time a polynomial in both problem size and 1/. They are like the more "practical" approximation schemes of

[1] as opposed to those of [2]

..., which achieves the minimum growth rate permissible by Shannon's information bound -

we are not aware of any work on - nic nam nie wiadomo o jakiejś pracy na temat -

Thus altogether,  #1 and #2 take O(-). -

compare its time against your favorite sorting method -

the argument goes along the lines of the proof of Theorem 1, with the difference that ...

Without loss of generality, assume that ... (otherwise a symmetric argument applies).

a polynomial - time algorithm that delivers a feasible solution of objective function value within a factor of r of optimal.

# is denoted by d(G) or by d when there is no danger of ambiguity

affinity between tasks and processors - podobieństwo pomiędzy ...

by adding in

We can prove analogs to the results of the previous section.

In this paper we address some scheduling problems.

(a.k.a. legal coloring ) – also known as

the most  atypical case at the far left. – nietypowy

We suggest some avenues of further research

Our definition is similar to the spine in SAT, although not exactly analogous.

# is the only edge-chromatic parameter, whose value at Km is unknown.

# settled Conjecture 2 in the affirmative.