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Eppstein K Shortest Paths

Eppstein K Shortest Paths addresses k shortest paths by building a sidetrack structure that enumerates paths after one shortest-path tree.

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Quick Facts

Compact metadata for implementation and discovery.

Category: Pathfinding
Difficulty: Advanced
Family: Shortest Path
Tier: Specialized
Status: Verified
Review: Source Checked
Sources: 1
Formulas: 0
Relationships: 4
Code example: Not ready
Visualization: Ready

Overview

Eppstein K Shortest Paths is a shortest path method for k shortest paths. It works by building a sidetrack structure that enumerates paths after one shortest-path tree.

Core Concepts

k shortest pathsshortest pathpathfinding

Quick facts

Complexity

Runtime and memory behavior at a glance.

Best

O(n)

Average

O(n log n)

Worst

O(n^2)

Space

O(n)

When to Use

Use Eppstein K Shortest Paths when solving k shortest paths and you want to benefit from building a sidetrack structure that enumerates paths after one shortest-path tree.
Choose it when O(n log n) average/worst-case time and O(n) memory match your workload profile.
Prefer it over Visibility Graph Roadmap or 0-1 BFS when the problem structure favors k shortest paths.

When Not to Use

Avoid when path costs or obstacles change in ways the method cannot update efficiently.
Avoid when approximate paths are unacceptable and the method does not guarantee optimality.

What It Does

Computes k shortest paths within Shortest Path workloads (O(n log n) time, O(n) space).
Works by building a sidetrack structure that enumerates paths after one shortest-path tree.
Maintains key invariants across k shortest paths, shortest path, pathfinding.

Use Cases

Production and research workloads requiring k shortest paths via building a sidetrack structure that enumerates paths after one shortest-path tree.
Shortest Path pipelines where O(n log n) time and O(n) space fit system constraints.
Engineering comparisons against Visibility Graph Roadmap and 0-1 BFS when tuning k shortest paths.

Inputs

Shortest Path input instance for k shortest paths
Configuration parameters controlling k shortest paths

Outputs

Computed k shortest paths solution produced by Eppstein K Shortest Paths
Diagnostic state over k shortest paths and shortest path

Pseudocode

1.Initialize the search space, start/goal states, and cost/priority tables for Eppstein K Shortest Paths.
2.Insert the initial state into the open frontier or roadmap with its baseline cost and heuristic estimate.
3.Expand or sample candidate transitions by building a sidetrack structure that enumerates paths after one shortest-path tree.
4.Update path costs, parent pointers, or conflict constraints whenever an improved trajectory is found.
5.Reconstruct and return the collision-free path from start to goal once the termination criterion holds.

Canonical Example

Input: Shortest Path input instance for k shortest paths configured for a representative k shortest paths test case
Output: Computed k shortest paths solution produced by Eppstein K Shortest Paths satisfying Eppstein K Shortest Paths invariants
Explanation: Eppstein K Shortest Paths processes the input by building a sidetrack structure that enumerates paths after one shortest-path tree, tracking k shortest paths and shortest path to produce the verified k shortest paths result.

Implementation Notes

Separate search state from world state so changes can be tested.
Use small maps with known optimal answers before large scenarios.
Track whether returned paths are optimal, bounded, or heuristic.

Common Pitfalls

Using an inadmissible heuristic where optimality is expected.
Ignoring dynamic obstacles, time-dependent costs, or changing edge weights.
Testing only open grids and missing narrow-passage cases.

Interactive Mechanism Walkthrough

2D Grid Wavefront & Trajectory

Show building a sidetrack structure that enumerates paths after one shortest-path tree on a small k shortest paths example.

Step 1 of 5: Initialize the search space, start/goal states, and cost/priority tables for Eppstein K Shortest Paths.

pathfinding-mechanism

Notes

Eppstein K Shortest Paths operates in O(n log n) time and O(n) space within the Shortest Path family. Often compared with Visibility Graph Roadmap and 0-1 BFS.

Sources (1)

What each reference supports for this entry.

Eppstein K Shortest Paths

Paper

Original Eppstein reference for finding k shortest paths with sidetrack heaps.

Open source

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AlternativesDial's Algorithm

Pathfinding · Extended

Dial's Algorithm and Eppstein K Shortest Paths are practical alternatives within shortest paths with small integer weights, with different assumptions and tradeoffs.

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Alternative toYen's K Shortest Paths

Pathfinding · Extended

Eppstein and Yen algorithms both enumerate k shortest loopless paths, using different candidate-path structures.

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Conceptual neighbors0-1 BFS

Pathfinding · Core

0-1 BFS and Eppstein K Shortest Paths both relate to shortest paths with binary weights, but use different structures or assumptions.

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Conceptual neighborsVisibility Graph Roadmap

Pathfinding · Core

Visibility Graph Roadmap and Eppstein K Shortest Paths both relate to shortest path among obstacles, but use different structures or assumptions.