Nonnegative Integer Weights: Difference between revisions
Jump to navigation
Jump to search
(Created page with "{{DISPLAYTITLE:Nonnegative Integer Weights (Shortest Path (Directed Graphs))}} == Description == The shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. Here, the weights are restricted to be nonnegative integers. == Related Problems == Generalizations: nonnegative weights Related: General Weights, Nonnegative Weights, Second Shortest...") |
No edit summary |
||
| Line 12: | Line 12: | ||
== Parameters == | == Parameters == | ||
V: number of vertices | |||
E: number of edges | E: number of edges | ||
L: maximum absolute value of edge cost | |||
L: maximum absolute value of edge cost | |||
== Table of Algorithms == | == Table of Algorithms == | ||
Revision as of 12:02, 15 February 2023
Description
The shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. Here, the weights are restricted to be nonnegative integers.
Related Problems
Generalizations: nonnegative weights
Related: General Weights, Nonnegative Weights, Second Shortest Simple Path, st-Shortest Path, 1-sensitive (3/2)-approximate ss-shortest paths, 2-sensitive (7/5)-approximate st-shortest paths, 1-sensitive decremental st-shortest paths, 2-sensitive decremental st-shortest paths, Replacement Paths Problem
Parameters
V: number of vertices
E: number of edges
L: maximum absolute value of edge cost
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Dijkstra's algorithm with Fibonacci heap (Johnson ; Karlsson & Poblete 1983) | 1981 | $O(E log log L)$ | $O(V+L)$ | Exact | Deterministic | Time & Space |
| Gabow Ahuja Algorithm | 1990 | $O(E + V*((log(L))^{0.5}) )$ | $O(m + log C)$ | Exact | Deterministic | Time & Space |
| Thorup's algorithm | 2004 | $O(E + V min(log log V, log log L))$ | $O(V)$? ("linear-space queue") | Exact | Deterministic | Time & Space |
Time Complexity graph
_-_Nonnegative_Integer_Weights_-_Time.png)
Space Complexity graph
_-_Nonnegative_Integer_Weights_-_Space.png)
Pareto Decades graph
_-_Nonnegative_Integer_Weights_-_Pareto_Frontier.png)