Abstract

Dijkstra’s algorithm solves the single-source shortest path problem on any directed graph in O(m + n log n) worst-case time when a Fibonacci heap is used as the frontier set data structure. Here n is the number of vertices and m is the number of edges in the graph. If the graph is nearly acyclic, then other algorithms can achieve a time complexity lower than that of Dijkstra’s algorithm. Abuaiadh and Kingston gave a single source shortest path algorithm for nearly acyclic graphs with O(m + n log t) worst-case time complexity, where the new parameter t is the number of delete-min operations performed in priority queue manipulation. For nearly acyclic graphs, the value of t is expected to be small, allowing the algorithm to outperform Dijkstra’s algorithm. Takaoka, using a different definition for acyclicity, gave an algorithm with O(m + n log k) worstcase time complexity. In this algorithm, the new parameter k is the maximum cardinality of the strongly connected components in the graph. This thesis presents several new shortest path algorithms that define trigger

Citations