|
| 1 | +public:: true |
| 2 | + |
| 3 | +# A Star Algorithm |
| 4 | + |
| 5 | +```json-ld |
| 6 | +{ |
| 7 | + "@context": "https://narrativegoldmine.com/ns/v1", |
| 8 | + "@id": "urn:visionflow:page:a-star-algorithm", |
| 9 | + "@type": "Page", |
| 10 | + "title": "A Star Algorithm", |
| 11 | + "vc:slug": "a-star-algorithm", |
| 12 | + "vc:public": true, |
| 13 | + "vc:schemaVersion": 2, |
| 14 | + "vc:outboundWikilinks": [] |
| 15 | +} |
| 16 | +``` |
| 17 | + |
| 18 | +```json-ld |
| 19 | +{ |
| 20 | + "@context": "https://narrativegoldmine.com/ns/v2.jsonld", |
| 21 | + "@id": "urn:ngm:class:a-star-algorithm", |
| 22 | + "@type": "Class", |
| 23 | + "label": "A Star Algorithm", |
| 24 | + "definition": "The A Star algorithm is an informed graph-search method that finds a least-cost path between nodes by combining the accumulated cost from the start with a heuristic estimate of the remaining cost to the goal. By expanding the node with the lowest combined estimate, it guarantees an optimal path when the heuristic is admissible. A Star generalises Dijkstra's algorithm by adding goal-directed guidance.", |
| 25 | + "domain": "artificial-intelligence", |
| 26 | + "maturity": "established", |
| 27 | + "subClassOf": [ |
| 28 | + { |
| 29 | + "@id": "urn:ngm:class:search-algorithm", |
| 30 | + "label": "Search Algorithm" |
| 31 | + } |
| 32 | + ], |
| 33 | + "relations": { |
| 34 | + "implements": [ |
| 35 | + { |
| 36 | + "@id": "urn:ngm:class:informed-search", |
| 37 | + "label": "Informed Search" |
| 38 | + }, |
| 39 | + { |
| 40 | + "@id": "urn:ngm:class:graph-search", |
| 41 | + "label": "Graph Search" |
| 42 | + } |
| 43 | + ], |
| 44 | + "hasPart": [ |
| 45 | + { |
| 46 | + "@id": "urn:ngm:class:cost-function", |
| 47 | + "label": "Cost Function" |
| 48 | + } |
| 49 | + ], |
| 50 | + "uses": [ |
| 51 | + { |
| 52 | + "@id": "urn:ngm:class:cost-function", |
| 53 | + "label": "Cost Function" |
| 54 | + }, |
| 55 | + { |
| 56 | + "@id": "urn:ngm:class:graph-search", |
| 57 | + "label": "Graph Search" |
| 58 | + } |
| 59 | + ], |
| 60 | + "partOf": [ |
| 61 | + { |
| 62 | + "@id": "urn:ngm:class:search-algorithm", |
| 63 | + "label": "Search Algorithm" |
| 64 | + } |
| 65 | + ], |
| 66 | + "contrastsWith": [ |
| 67 | + { |
| 68 | + "@id": "urn:ngm:class:dijkstra-algorithm", |
| 69 | + "label": "Dijkstra Algorithm" |
| 70 | + } |
| 71 | + ], |
| 72 | + "supports": [ |
| 73 | + { |
| 74 | + "@id": "urn:ngm:class:pathfinding", |
| 75 | + "label": "Pathfinding" |
| 76 | + }, |
| 77 | + { |
| 78 | + "@id": "urn:ngm:class:autonomous-navigation", |
| 79 | + "label": "Autonomous Navigation" |
| 80 | + } |
| 81 | + ], |
| 82 | + "enables": [ |
| 83 | + { |
| 84 | + "@id": "urn:ngm:class:pathfinding", |
| 85 | + "label": "Pathfinding" |
| 86 | + } |
| 87 | + ], |
| 88 | + "requires": [ |
| 89 | + { |
| 90 | + "@id": "urn:ngm:class:graph-search", |
| 91 | + "label": "Graph Search" |
| 92 | + } |
| 93 | + ], |
| 94 | + "relatedTo": [ |
| 95 | + { |
| 96 | + "@id": "urn:ngm:class:optimisation", |
| 97 | + "label": "Optimisation" |
| 98 | + }, |
| 99 | + { |
| 100 | + "@id": "urn:ngm:class:robotics", |
| 101 | + "label": "Robotics" |
| 102 | + }, |
| 103 | + { |
| 104 | + "@id": "urn:ngm:class:game-ai", |
| 105 | + "label": "Game AI" |
| 106 | + }, |
| 107 | + { |
| 108 | + "@id": "urn:ngm:class:dijkstra-algorithm", |
| 109 | + "label": "Dijkstra Algorithm" |
| 110 | + } |
| 111 | + ] |
| 112 | + }, |
| 113 | + "sameAs": [], |
| 114 | + "quality": 0.62, |
| 115 | + "provenance": { |
| 116 | + "attributedTo": "did:nostr:ontology-mesh", |
| 117 | + "generatedAt": "2026-06-15T00:00:00Z", |
| 118 | + "inferenceRule": "GapMaterialisation" |
| 119 | + } |
| 120 | +} |
| 121 | +``` |
| 122 | + |
| 123 | +- ### Definition |
| 124 | + - The A Star algorithm is an informed graph-search method that finds a least-cost path between nodes by combining the accumulated cost from the start with a heuristic estimate of the remaining cost to the goal. By expanding the node with the lowest combined estimate, it guarantees an optimal path when the heuristic is admissible. A Star generalises Dijkstra's algorithm by adding goal-directed guidance. |
| 125 | + - Related: [[Search Algorithm]] [[Pathfinding]] [[Dijkstra Algorithm]] [[Cost Function]] |
| 126 | +- ### Overview |
| 127 | + - A Star maintains a priority queue ordered by the evaluation function f(n) = g(n) + h(n), where g is the cost so far and h is the heuristic estimate to the goal. Admissibility of the heuristic ensures optimality, while consistency additionally guarantees that nodes are never re-expanded. |
| 128 | +- ### Mechanisms |
| 129 | + - Evaluation function combining path cost and heuristic estimate |
| 130 | + - Admissible heuristics guaranteeing optimal solutions |
| 131 | + - Priority queue expansion of the most promising node |
| 132 | + - Reduction to Dijkstra's algorithm when the heuristic is zero |
| 133 | + - Trade-off between heuristic accuracy and nodes expanded |
| 134 | +- ### Applications |
| 135 | + - Pathfinding in robotics and autonomous navigation |
| 136 | + - Route planning in maps and logistics |
| 137 | + - Movement and navigation in game artificial intelligence |
| 138 | + - General least-cost search over weighted graphs |
| 139 | +- ### Relationships |
| 140 | + - subClassOf:: [[Search Algorithm]] |
| 141 | + - implements:: [[Informed Search]] |
| 142 | + - implements:: [[Graph Search]] |
| 143 | + - hasPart:: [[Cost Function]] |
| 144 | + - uses:: [[Cost Function]] |
| 145 | + - uses:: [[Graph Search]] |
| 146 | + - partOf:: [[Search Algorithm]] |
| 147 | + - contrastsWith:: [[Dijkstra Algorithm]] |
| 148 | + - supports:: [[Pathfinding]] |
| 149 | + - supports:: [[Autonomous Navigation]] |
| 150 | + - enables:: [[Pathfinding]] |
| 151 | + - requires:: [[Graph Search]] |
| 152 | + - relatedTo:: [[Optimisation]] |
| 153 | + - relatedTo:: [[Robotics]] |
| 154 | + - relatedTo:: [[Game AI]] |
| 155 | + - relatedTo:: [[Dijkstra Algorithm]] |
| 156 | +- ### Provenance |
| 157 | + - attributedTo:: did:nostr:ontology-mesh |
| 158 | + - inferenceRule:: GapMaterialisation |
| 159 | + - quality:: 0.62 |
| 160 | + - updated:: 2026-06-15 |
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