Constructing Eulerian Trails in a Graph: Difference between revisions
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[[File:Constructing Eulerian Trails in a Graph - Space.png|1000px]] | [[File:Constructing Eulerian Trails in a Graph - Space.png|1000px]] | ||
== Space | == Time-Space Tradeoff == | ||
[[File:Constructing Eulerian Trails in a Graph - Pareto Frontier.png|1000px]] | [[File:Constructing Eulerian Trails in a Graph - Pareto Frontier.png|1000px]] | ||
Revision as of 14:44, 15 February 2023
Description
In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices). Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail that starts and ends on the same vertex.
Parameters
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Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Fleury's algorithm + Tarjan | 1974 | $O(E^{2})$ | $O(E)$ | Exact | Deterministic | Time |
| Hierholzer's algorithm | 1873 | $O(E)$ | $O(E)$ | Exact | Deterministic | |
| Fleury's algorithm + Thorup | 2000 | $O(E log^{3}(E)$ loglogE) | $O(E)$ | Exact | Deterministic | Time |
Time Complexity Graph
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Space Complexity Graph
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Time-Space Tradeoff
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