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LAR
Live Air Routing
48 topics
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1
Geodesy and Trajectory Math
Geodesy
Spherical Earth and Great-Circle Distance
The Haversine Formula
Trajectories
Cumulative Arc Length on a Polyline
Linear Interpolation Along a Trajectory
Time Discretization and 15-Minute Buckets
2
Spatial Indexing and Polygonization
Polygon Geometry
Planar Partitions and Polygon Geometry
Point-in-Polygon and Polygon Touches Predicates
Spatial Indexing
Bounding-Box Hierarchies and R-Trees
The STRtree: Sort-Tile-Recursive Spatial Indexing
Raster to Polygon
Connected-Components Labeling on a Raster
Marching-Squares Contour Extraction
Douglas-Peucker Polygon Simplification
3
Graphs and Shortest Paths
Graph Foundations
Weighted Graphs and Adjacency
Min-Heaps and Priority Queues
Shortest Paths
Dijkstra's Shortest-Path Algorithm
Heuristic Search and the A* Algorithm
Admissible Heuristics and Optimality of A*
Time-Dependent Shortest Paths and the FIFO Property
4
Network Flow and Capacitated Routing
Network Flow
Single-Commodity Network Flow
Multi-Commodity Flow
Time-Expanded Network Flow
Capacitated Routing on a Planar Partition
5
Integer Programming for Air Traffic Flow
Integer Programming
Linear Programming vs Integer Programming
LP Relaxation and Optimality Gaps
The Bertsimas-Patterson ATFM Integer Program
Decomposition Methods for Large-Scale Integer Programs
6
Congestion Games and Traffic Assignment
Equilibrium Theory
Congestion Games and Selfish Routing
Wardrop User Equilibrium
System Optimum vs User Equilibrium
The Price of Anarchy
Cost Functions
The BPR Latency Function
Convex Cost Functions and Equilibrium Existence
Assignment Algorithms
Frank-Wolfe Traffic Assignment
The Method of Successive Averages
7
Lagrangian Relaxation
Lagrangian Methods
Lagrange Multipliers and the Lagrangian
Lagrangian Relaxation of Capacity Constraints
Subgradient Ascent for Non-Smooth Duals
Diminishing-Step Subgradient Updates
8
Sequential Commitment and Incremental Replanning
Sequential Algorithms
List Scheduling on a Congestion Game
Sequential Commitment Against a Mutable Load Surface
Best-Response Dynamics and Iterated Routing
Incremental Replanning
D* Lite and Incremental Replanning
Cascade Detection via Fixed-Point Iteration
9
Applied Air Traffic Flow Management
Domain Modeling
ATC Sectors, Capacity, and Altitude Bands
Storm Polygonization from Weather Rasters
Virtual Wait Edges and Ground-Hold Modeling
Traffic Management Initiatives: GDP, AFP, MIT, CTOP
Coarsening Per-Flight Commitments to TMI Vocabulary
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