Faster shortest-path algorithms for planar graphs
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Finding the detour-critical edge of a shortest path between two nodes
Information Processing Letters
Undirected single-source shortest paths with positive integer weights in linear time
Journal of the ACM (JACM)
Applications of Path Compression on Balanced Trees
Journal of the ACM (JACM)
Floats, integers, and single source shortest paths
Journal of Algorithms
A faster computation of the most vital edge of a shortest path
Information Processing Letters
Erratum to "Vickrey Pricing and Shortest Paths: What is an Edge Worth?"
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Finding the most vital node of a shortest path
Theoretical Computer Science - Computing and combinatorics
Vickrey Prices and Shortest Paths: What is an Edge Worth?
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Graph Theory with Applications to Engineering and Computer Science (Prentice Hall Series in Automatic Computation)
Finding the k shortest simple paths: A new algorithm and its implementation
ACM Transactions on Algorithms (TALG)
The k most vital arcs in the shortest path problem
Operations Research Letters
| Hi-index | 0.00 |
In this paper, we study the following replacement paths problem for undirected graphs in case of edge or node failures.1.In the edge failure problem, for each edge e on a shortest s-t path in G, we are required to find a shortest s-t path in G-e. 2.In the node failure problem, for each node v on a shortest s-t path, we need to report a shortest s-t path in G-v. 3.In the detour critical problem, for each edge (u,v) on a shortest s-t path, we have to report a shortest u-t path in G-(u,v). If m is the number of edges and d is the distance between s and t, which in turn will be bounded by the diameter of the graph, the proposed algorithm for all these problems takes O(m+d^2) time, for graphs with integer weights (on the RAM model) and on planar graphs. For typically dense graphs, or graphs with small diameter (formally, when d=O(m)), the algorithms take linear time.