Mastering Algorithms with C

Related Topics

Bellman-Ford algorithm

Another approach to solving the single-source shortest-paths problem. Unlike Dijkstra’s algorithm, the Bellman-Ford algorithm supports graphs whose edges have negative weights. Its runtime complexity is O (V E ), where V is the number of vertices in the graph and E is the number of edges.

Kruskal’s algorithm

Another approach to computing minimum spanning trees. The algorithm works as follows. To begin, we place every vertex in its own set. Next, we select edges in order of increasing weight. As we select each edge, we determine whether the vertices that define it are in different sets. If this is the case, we insert the edge into a set that is the minimum spanning tree and take the union of the sets containing each vertex; otherwise, we simply move on to the next edge. We repeat this process until all edges have been explored. Kruskal’s algorithm has a runtime complexity of O (E lg E ), assuming we use a priority queue to manage the edges, where E is the number of edges in the graph.

All-pairs shortest-paths problem

An additional type of shortest-path problem in which we find the shortest paths between every pair of vertices in a graph. One way to solve this problem is to solve the single-source shortest-paths problem once for each vertex in the graph. However, it can be solved faster using a dedicated approach.

Exchange heuristics

Heuristics designed to help improve approximate traveling-salesman tours that are reasonable to begin with, such ...