I

Before beginning any computation on a graph we will normally have to initialize an adjacency matrix so that it contains the graph we are going to operate on.

The computation is done in-place -

Line 9 is iterated n3  times -

the i+1st bin -

It is intriguing open question whether -

If we let # denote ..., then # is the ...-

In the introductory remarks -

More importantly -

isosceles triangle - trójkąt równoramienny

We all use words  #1 and  #2interchangeably -

the time is advanced in fixed increments -

immediately - bezpośrednio

at the initiative - z inicjatywy

involved  in - związany z ..., biorących udział w ..., zaangażowanych w ...

to get the impression

it is the school that should ... - to szkoła właśnie powinna

impose - narzucać (warunki)

in the input (on input) - na wejściu

these include results - dotyczy to również rezultatów

if not, - jeśli nie ( w przeciwnym razie )

quantitative idea of - ilościowe pojęcie o

it is not interest to note that -

it is important to observe that in using ...-

By induction, it is ..-

We will use induction on k -

subgraph induced on set V -

#  increases the overall program speed by a factor of 4 -

this definition may easily be extended to include -

to inherit - dziedziczyć

involve - pociągać za sobą, wciągać, wplątywać, angażować, implikować

to have the major influence on the... -

results are independent of  ... -

Brooks [1] has improved upon this - Brooks ulepszył to

Some instances of this will be - przykłady na to będą

the performance may not be indicative of - ...

to be hopefully indicative of - wskazuje optymistycznie na (ich ogólne zachowanie)

irrational number - l. urojona

invoking Theorem 5 - odwołując się do twierdzenia 5

impurity - zanieczyszczenie

individual - oddzielny, jednostka itd.

investigation - badanie, dociekanie

independent of - niezależny od

to improve on algorithm A -

issues - zagadnienia

If any upper bound were imposed on these numbers in advance ... -

, a considerable improvement over our previous algorithm, - , co jest poważnym ulepszeniem względem naszego poprzedniego algorytmu

recent improvements in the Ford-Fulkerson algorithm -

size of S approaches infinity -

identity matrix - macierz

improvement on A - ulepszenie A

improvement over A - postęp w stosunku do A

Our interest is in finding - jesteśmy zainteresowani w znalezieniu

is kept invariant - jest niezmiennikiem

Edge {v,w} is incident to v and  to w and vertices v and w are adjacent

Irrespective of the choice made in coloring ... -

assume that vertices are indexed so that  and are considered in index order

The number of operations is a  poor indicator of the actual running time of the algorithm.

with numbers 1 to 100 inclusive. -

in-day scheduling -

the algorithm iterates on the following two-step routine -

the insertion of vertices of degree two is irrelevant to any considerations of planarity.

Improvements in algorithms are important

in-degree of a vertex is the number of edges with i as its second component -

, which improves on the worst-case bound of O(-) for the standard algorithm. -

Our algorithm proceeds by iterating over the rows of A. -

infer - wywnioskować

impose - narzucać (warunki)

Based on this limited data sample and the usual inaccuracies of timing, the  algorithms  are judged to be indistinguishable in terms of  performance.

set S includes all ...

assumptions remain intact - założenia pozostają nienaruszone

insight into - wnikliwość, wgląd

insights concerning  Section 3