  In this paper I present general outlook on questions relevant to the basic
graph algorithms; Finding the Shortest Path with Positive Weights and Minimum
Spanning Tree. I will show so far known solution set of basic graph problems
and present my own. My solutions to graph problems are characterized by their
linear worst-case time complexity. It should be noticed that the algorithms
which compute the Shortest Path and Minimum Spanning Tree problems not only
analyze the weight of arcs (which is the main and often the only criterion of
solution hitherto known algorithms) but also in case of identical path weights
they select this path which walks through as few vertices as possible. I have
presented algorithms which use priority queue based on multilevel prefix tree
-- PTrie. PTrie is a clever combination of the idea of prefix tree -- Trie, the
structure of logarithmic time complexity for insert and remove operations,
doubly linked list and queues. In C++ I will implement linear worst-case time
algorithm computing the Single-Destination Shortest-Paths problem and I will
explain its usage.
