Shortest Path Algorithms for Nearly Acyclic Directed Graphs
نویسنده
چکیده
Abuaiadh and Kingston gave an e cient algorithm for the single source shortest path problem for a nearly acyclic graph with O(m+n log t) computing time, where m and n are the numbers of edges and vertices of the given directed graph and t is the number of delete-min operations in the priority queue manipulation. They use the Fibonacci heap for the priority queue. If the graph is acyclic, we have t = 0 and the time complexity becomes O(m + n) which is linear and optimal. They claim that if the graph is nearly acyclic, t is expected to be small and the algorithm runs fast. In the present paper, we take another de nition of acyclicity. The degree of cyclicity cyc(G) of graph G is de ned by the maximum cardinality of the strongly connected components of G. When cyc(G) = k, we give an algorithm for the single source problem with O(m + n log k) time complexity. Finally we give a hybrid algorithm that incorporates the merits of the above two algorithms.
منابع مشابه
Efficient Algorithms for Solving Shortest Paths on Nearly Acyclic Directed Graphs
This paper presents new algorithms for computing shortest paths in a nearly acyclic directed graph G = (V, E). The new algorithms improve on the worst-case running time of previous algorithms. Such algorithms use the concept of a 1-dominator set. A 1-dominator set divides the graph into a unique collection of acyclic subgraphs, where each acyclic subgraph is dominated by a single associated tri...
متن کاملImproved Shortest Path Algorithms for Nearly Acyclic Graphs
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. Abuaia...
متن کاملImproved algorithms for replacement paths problems in restricted graphs
We present near-optimal algorithms for two problems related to finding the replacement paths for edges with respect to shortest paths in sparse graphs. The problems essentially study how the shortest paths change as edges on the path fail, one at a time. Our technique improves the existing bounds for these problems on directed acyclic graphs, planar graphs, and non-planar integer-edge-weighted ...
متن کاملImproved Shortest Path Algorithms For Nearly Acyclic Directed Graphs
This paper presents new algorithms for computing single source shortest paths (SSSPs) in a nearly acyclic directed graph G. The first part introduces higher-order decomposition. This decomposition is an extension of the technique of strongly connected component (sc-component) decomposition. The second part presents a new method for measuring acyclicity based on modifications to two existing met...
متن کاملSharing Information in All Pairs Shortest Path Algorithms
We show two improvements on time complexities of the all pairs shortest path (APSP) problem for directed graphs that satisfy certain properties. The idea for speed-up is information sharing by n single source shortest path (SSSP) problems that are solved for APSP. We consider two parameters, in addition to the numbers of vertices, n, and edges, m. First we improve the time complexity of O(mn+n ...
متن کامل