T 

The results are shown in tabular form and by means of curves. -

This is of course to be expected -

the complete graph Kn

a common tangent - punkt styczności

and the like - i temu podobne

The a's are found by trial & error.

the other way round - na odwrót

tackle - atakować problem

tree of n vertices

to get in touch with -

touch upon  - poruszyć (temat)

thorough analysis - dokładna analiza

these include results ... - dotyczy to również rezultatów ...

in terms of - w terminach

this takes care of - dotyczy to

tighter bound  - dokładniejsza granica

# is partitioned  into what we term as compact sections -

# is termed - # jest nazywane

a total of twenty - łącznie 20

recorded in Table 2 - zapisany w tab. 2

, that is, ... - to jest (to znaczy)

this version tends to produce - wersja ta zmierza do produkcji

The aim of the book is twofold -

n-tuple  - n-tka uporządkowane np.<a1,a2,a3,...an>

The reason is that ... - przyczyna (tego) jest taka , że ...

thickness - grubość, gęstość

thrust - pchnięcie, parcie, ciśnienie

tide - fala, pływ

tube - rura, tuba, lampa, sonda

It turns out that, - okazuje się, że

this is to protect - ma to ma celu zabezpieczenie

we tacitly assumed that - milcząco przyjęliśmy

threshold function - funkcja progowa

#1takes on the value #2

the activity will fail to terminate properly - działanie nie dojdzie do pomyślnego końca

Activation will fail to lead to a properly terminating activity

Is sufficient to guarantee termination - gwarantuje zakończenie

All of them are NP-hard, and even the task of solving any of them approximately cannot be done in polynomial time under the common assumptions in Complexity Theory.

To analyze the timing, ...

If this case, the trading of some storage space against some computation time is indicated  - W takim właśnie przypadku jest wskazane, by wymienić nieco miejsca w pamięci na pewną dozę czasu obliczeń.

Ties in the choice of a machine are resolved in favor of the machine with  smallest index.

an asymptotic time bound of O(n2) -

We have three main reasons for doing this. Firstly ...; secondly ...; and thirdly...

Time-space tradeoff for -

, this amonts to saying  that  -

The li's are... -

The four iteration statements are the (i) loop-repeat, (ii) while repeat, (iii) loop - until repeat, and (iv) for - repeat.

trace out the algorithm as it ... - prześledź algorytm jak on

The set {A,B,C} is the set of leaf nodes.

The notion of a forest is -

} 65.536 two's.

the TD is the same

numbered 1 through 8 - od 1 do 8

Now we are ready to tackle the problem -

In lines 11-13 we trace back -

Tabulate the computing times - stabelaryzuj czasy

this behavior is typical of ... -

a terminaton conditon -

This completes the proof of Theorem #. q

numbers totalling  more than 1 - liczby, których suma przekracza 1

# may be thought of as  - może być pomyślany jako

Tables are tabulated in Section II

More detailed tabulations of the results on which average colorings are reported in this paper are given in [1].

The key trick is to notice -

# keeps track of the number  -

We shall show how to beat the 2,5*OPT bound of DLS by tailoring our algorithmms specifically to trees.

One school of thought would say  "  " -

Since a total of O(r2) such paths may be needed, the overall computing time for the process becames O(r2).

Two dots (..) are used to mean "through and including".

heuristics tailored for the problem  -

Typically some of the color classes ... - Naogół

There, it was also shown that ... - Pokazano tam też, że

This paper has threefold purpose.

, claim of  the theorem follows. q

is typical of all

Throughout the paper

The details get a little hairier, and the technicalities are quite lengthy.