The all-nodes shortest paths problem is undoubtedly one of
the most basic problems in algorithmic graph theory. In this paper,
we introduce simple and efficient algorithm for all nodes shortest
paths problem for directed (undirected) graphs. In th
is problem, we
find the shortest path from a given source node to all other nodes in
the graph, in which the shortest path is a path with minimum cost,
i.e., sum of the edge weights.
We proved that the complexity of the proposed algorithm in
this paper depends only on the edges graph, and we show that the
time of implementation of this algorithm is linear time O(m) and
This is considered the best times of the algorithms at all. And
a Comparison between complexity of proposed algorithm and the
famous shortest path algorithms have been made, and the obtained
results have shown that the complexity of the proposed algorithm
is best.
The shortest path problem can be categorized in to two
different problems; single source shortest path problem (SSSP) and
all pair shortest algorithm (APSP). In this paper, analysis and
comparison between complexity of the famous shortest path
al
gorithms have been made, and the obtained results have shown
that researchers have got remarkable success in designing better
algorithms in the terms of time complexity to solve shortest path
algorithms.
