Nonnegative Integer Weights (Shortest Path (Directed Graphs))
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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 | $O(E + V*((\log(L))^{0.5}) )$ | $O(E + \log C)$ | 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
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Space Complexity Graph
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Time-Space Tradeoff
_-_Nonnegative_Integer_Weights_-_Pareto_Frontier.png)