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Transport, logistics and mobility
air-traffic-control
air traffic control
EUROCONTROL
System
Techniques · 25
Primitives · 60
air-traffic-control
Clock synchronization
distributed · medium: Estimate a clock's offset from four timestamps, filter out queueing noise, and steer the clock smoothly; NTP gets about a millisecond, PTP with hardware timestamps under a microsecond.
›
Model checking and formal proof
embedded · medium: Exhaustively explore a model's reachable states (or prove its invariants with a solver or proof assistant) to find rule violations with a shortest counterexample trace.
›
Hot-standby redundancy
embedded · medium: A second, always-current controller shadows the primary and takes over within a few cycles of silence; epochs stop the old primary from fighting back.
›
Safety-critical coding standards
embedded · medium: Which rule sets (MISRA C, CERT C, JPL Power of Ten, Rust lint subsets) apply when software must not fail, what they forbid, and how to enforce them in CI.
›
Assignment problem (Hungarian / Jon…
graphs · medium: Optimal one-to-one matching of rows to columns in O(n³) by growing a matching along shortest augmenting paths over dual potentials.
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Multi-object tracking
machine-learning · medium: Turn per-frame detections (camera boxes or radar plots) into persistent IDs by predicting each track, gating, assigning and managing track births and deaths.
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Arrival sequencing and scheduling
optimization · medium: Runway arrival sequencing with separation constraints (constrained position shifting, MIP/heuristics)
Kalman filter
robotics · low: Optimal recursive estimator for a linear system with Gaussian noise: fuses a motion model with noisy measurements into a state estimate plus its covariance.
›
Geodesic distance (haversine, Vince…
geometry · low: Shortest-path distance between two lat/lon points on the Earth: haversine on a sphere (about 0.5% error), Vincenty or Karney on the WGS84 ellipsoid (sub-millimetre).
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Point in polygon
geometry · low: Ray-casting/winding tests and indexed polygon lookup for reverse geocoding
PID controller
robotics · low: Drive a measured value to a setpoint with three terms on the error: proportional, integral, derivative. The default feedback loop for motors, heaters, drones and gimbals.
›
Phase-locked loop (digital)
signal-processing · low: Feedback loop that locks a local oscillator to the phase and frequency of an input tone; the core of carrier recovery, clock recovery and GNSS tracking.
›
Robust statistics
statistics · low: Location and scale estimates (median, MAD, trimmed mean, Huber M-estimator) that stay correct when a minority of the data is garbage.
›
Swiss table
data-structures · low: Open-addressing hash table that filters 8-16 slots at once with 1-byte hash tags and SIMD, giving fast lookups at 87.5 % load.
›
BFS and DFS
graphs · low: The two basic graph traversals; BFS gives hop distances and levels, DFS gives discovery/finish order for cycles, components and topological order.
›
Binary decision diagrams
optimization · low: A reduced ordered BDD stores a Boolean function as a shared DAG that is unique per variable order, so equivalence is one integer compare and counting is one pass.
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Watchdog timer
embedded · low: A hardware down-counter that resets the chip unless software proves, in time and in a plausible pattern, that it is still healthy.
›
Code coverage instrumentation
compilers · low: Insert counters into compiled code to record which blocks, edges or lines ran; a spanning tree of the control-flow graph cuts the counters needed.
›
d-ary heap
data-structures · low: Array heap with d children per node (d = 4 typical): half the binary heap's depth, siblings in one cache line, faster priority queues.
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Dijkstra's algorithm
graphs · low: Single-source shortest paths with non-negative edge weights by settling vertices in order of distance with a priority queue.
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Non-maximum suppression
machine-learning · low: Keep the best-scoring candidate in each neighbourhood and drop the rest; greedy NMS, Soft-NMS and 1-D peak picking share one loop.
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Time-window feasibility
optimization · low: Keep earliest/latest start and slack per segment so "does this insertion or move keep every window?" costs O(1) instead of a walk down the sequence.
›
Simplex method
optimization · low: Solves linear programs by walking along the edges of the feasible polytope from vertex to vertex, one basis swap (pivot) at a time; the workhorse behind MIP solvers.
›
+ 18 more techniques
+ 44 more primitives
System
Techniques · 25
Primitives · 60
air-traffic-control
Clock synchronization
distributed · medium: Estimate a clock's offset from four timestamps, filter out queueing noise, and steer the clock smoothly; NTP gets about a millisecond, PTP with hardware timestamps under a microsecond.
›
Model checking and formal proof
embedded · medium: Exhaustively explore a model's reachable states (or prove its invariants with a solver or proof assistant) to find rule violations with a shortest counterexample trace.
›
Hot-standby redundancy
embedded · medium: A second, always-current controller shadows the primary and takes over within a few cycles of silence; epochs stop the old primary from fighting back.
›
Safety-critical coding standards
embedded · medium: Which rule sets (MISRA C, CERT C, JPL Power of Ten, Rust lint subsets) apply when software must not fail, what they forbid, and how to enforce them in CI.
›
Assignment problem (Hungarian / Jon…
graphs · medium: Optimal one-to-one matching of rows to columns in O(n³) by growing a matching along shortest augmenting paths over dual potentials.
›
Multi-object tracking
machine-learning · medium: Turn per-frame detections (camera boxes or radar plots) into persistent IDs by predicting each track, gating, assigning and managing track births and deaths.
›
Arrival sequencing and scheduling
optimization · medium: Runway arrival sequencing with separation constraints (constrained position shifting, MIP/heuristics)
Mixed-integer programming (branch a…
optimization · medium: Solves LPs with integer variables by solving the LP relaxation, branching on a fractional variable, and pruning subtrees whose LP bound cannot beat the incumbent.
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Conflict detection and resolution
robotics · medium: Predict trajectories, detect loss of separation and compute resolution maneuvers for aircraft/drones
Interacting multiple model filter
robotics · medium: IMM filter mixing several motion models for maneuvering targets
Sensor fusion
robotics · medium: Combining IMU, GNSS, camera, lidar and radar estimates with Kalman-type filters and time alignment
Multilateration tdoa
signal-processing · medium: Locate a transmitter from time differences of arrival at synchronized receivers
Dataflow analysis
compilers · medium: Compute a fact per program point (live variables, reaching definitions, available expressions) by iterating transfer functions over the CFG to a fixed point.
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Primary-backup replication
distributed · medium: One node orders all writes and ships them to standbys; the acknowledgement rule (none, one, all) sets what a crash loses, and an external arbiter decides who takes over.
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Object detection
machine-learning · medium: A network turns an image into scored, classified boxes in one pass; anchor-based, anchor-free and set-prediction heads differ in how they assign labels and remove duplicates.
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Levenberg marquardt
numerics · medium: Damped Gauss-Newton nonlinear least squares for model calibration
CDCL SAT solving
optimization · medium: Search for a satisfying assignment, learn a new constraint from every dead end, and jump back past irrelevant choices; handles industrial formulas with millions of clauses.
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Cutting planes
optimization · medium: Valid inequalities added to an LP relaxation to cut off its fractional optimum without removing any integer point; the engine of branch-and-cut MIP solvers.
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Dpll t
optimization · medium: SMT architecture: CDCL over boolean abstraction plus theory solvers, theory propagation, Nelson-Oppen
Local search 2opt or opt
optimization · medium: 2-opt, Or-opt, relocate and swap neighborhoods with fast delta evaluation for routes
Presolve reductions
optimization · medium: Cheap, provably safe reductions run before the solver (fix variables, drop rows, tighten bounds and coefficients) so LP and MIP solves start from a smaller, tighter model.
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Transform tree
robotics · medium: Time-indexed tree of coordinate frames with interpolated lookups between any two frames
Fft convolution
signal-processing · medium: Overlap-add and uniformly partitioned convolution for long FIR filters and reverb
Congruence closure
compilers · medium: Union-find over terms with congruence propagation; decides equality with uninterpreted functions
Bit blasting
optimization · medium: Reduce bit-vector constraints to CNF via adder, multiplier and comparator circuits
Kalman filter
robotics · low: Optimal recursive estimator for a linear system with Gaussian noise: fuses a motion model with noisy measurements into a state estimate plus its covariance.
›
Geodesic distance (haversine, Vince…
geometry · low: Shortest-path distance between two lat/lon points on the Earth: haversine on a sphere (about 0.5% error), Vincenty or Karney on the WGS84 ellipsoid (sub-millimetre).
›
Point in polygon
geometry · low: Ray-casting/winding tests and indexed polygon lookup for reverse geocoding
PID controller
robotics · low: Drive a measured value to a setpoint with three terms on the error: proportional, integral, derivative. The default feedback loop for motors, heaters, drones and gimbals.
›
Phase-locked loop (digital)
signal-processing · low: Feedback loop that locks a local oscillator to the phase and frequency of an input tone; the core of carrier recovery, clock recovery and GNSS tracking.
›
Robust statistics
statistics · low: Location and scale estimates (median, MAD, trimmed mean, Huber M-estimator) that stay correct when a minority of the data is garbage.
›
Swiss table
data-structures · low: Open-addressing hash table that filters 8-16 slots at once with 1-byte hash tags and SIMD, giving fast lookups at 87.5 % load.
›
BFS and DFS
graphs · low: The two basic graph traversals; BFS gives hop distances and levels, DFS gives discovery/finish order for cycles, components and topological order.
›
Binary decision diagrams
optimization · low: A reduced ordered BDD stores a Boolean function as a shared DAG that is unique per variable order, so equivalence is one integer compare and counting is one pass.
›
Watchdog timer
embedded · low: A hardware down-counter that resets the chip unless software proves, in time and in a plausible pattern, that it is still healthy.
›
Code coverage instrumentation
compilers · low: Insert counters into compiled code to record which blocks, edges or lines ran; a spanning tree of the control-flow graph cuts the counters needed.
›
d-ary heap
data-structures · low: Array heap with d children per node (d = 4 typical): half the binary heap's depth, siblings in one cache line, faster priority queues.
›
Dijkstra's algorithm
graphs · low: Single-source shortest paths with non-negative edge weights by settling vertices in order of distance with a priority queue.
›
Non-maximum suppression
machine-learning · low: Keep the best-scoring candidate in each neighbourhood and drop the rest; greedy NMS, Soft-NMS and 1-D peak picking share one loop.
›
Time-window feasibility
optimization · low: Keep earliest/latest start and slack per segment so "does this insertion or move keep every window?" costs O(1) instead of a walk down the sequence.
›
Simplex method
optimization · low: Solves linear programs by walking along the edges of the feasible polytope from vertex to vertex, one basis swap (pivot) at a time; the workhorse behind MIP solvers.
›
R-tree
geometry · low: A balanced tree of nested bounding boxes that indexes rectangles and points, answering window and nearest-neighbour queries by pruning whole subtrees.
›
Extended Kalman filter
robotics · low: Kalman filter for nonlinear motion and measurement models: linearize f and h with Jacobians at the current estimate each step. The default estimator in robot navigation.
›
SPSC ring buffer
data-structures · low: Bounded wait-free queue for exactly one producer and one consumer thread, built from an array and two indices with acquire/release ordering.
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Complementary filter
robotics · low: Blend high-passed gyro integration with low-passed accelerometer/magnetometer attitude (Mahony/Madgwick)
Control-flow graph
compilers · low: Split a linear instruction list into basic blocks and connect them by jumps; the graph every optimizer, SSA builder and dataflow pass walks.
›
Topological sort
graphs · low: Order the vertices of a DAG so every edge points forward; the core of build systems, schedulers and dependency resolution, with cycle detection for free.
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Leases
distributed · low: A lock that expires on its own: bounded-time ownership that survives crashes and partitions, given bounded clock drift and fencing tokens on writes.
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Write-ahead log
storage · low: Append each change to a checksummed sequential log and fsync it before touching data pages; the basis of crash durability in nearly every database.
›
Health checking
systems · low: Decide per backend whether to route to it using probes and real-traffic errors, with consecutive-count hysteresis, capped ejection and a panic fallback.
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Data augmentation
machine-learning · low: Generate label-preserving variants of each training example on the fly to enlarge the effective dataset and bake in invariances.
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Loss functions
machine-learning · low: The scalar a model minimizes: cross-entropy for classes and tokens, MSE or Huber for values, each with a stable form and simple gradient.
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Convolutional networks
ml-training · low: Layers that slide a small shared kernel over a grid, giving translation equivariance and few parameters; still the most compute-efficient choice for many vision tasks.
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Finite differences
numerics · low: Replace derivatives with weighted differences of grid values; simple stencils plus a stability condition (CFL) turn PDEs like heat, advection and waves into array loops.
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LU and Cholesky factorization
numerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).
›
Drat proof certificates
optimization · low: DRAT and LRAT proofs emitted by SAT solvers and checked independently
Two watched literals
optimization · low: Unit propagation for SAT that watches just two literals per clause, so backtracking costs nothing and long clauses are rarely touched.
›
Arena allocator
systems · low: Allocate by bumping a pointer through big chunks and free everything at once: a few instructions per allocation for objects sharing a lifetime.
›
Floating-point error
numerics · low: How IEEE 754 rounding error accumulates and how to contain it: compensated (Kahan/Neumaier) and pairwise summation, error-free transformations with FMA, ULP comparisons.
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k-d tree
geometry · low: A binary tree that splits k-dimensional points by one coordinate per level, giving fast nearest-neighbour and box queries on static low-dimensional data.
›
PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
›
Fast hash functions
data-structures · low: Non-cryptographic hashes built from 64×64→128-bit multiplies and xor-shifts; pick by key size, trust level and whether the hash is persisted.
›
Interval arithmetic
numerics · low: Rigorous bounds with outward rounding; root isolation and robust geometric tests
Sparse matrices (CSR)
numerics · low: Compressed sparse row stores only nonzeros as row pointers, column indices and values; SpMV streams them once, so it is memory-bandwidth bound.
›
Quaternion rotations
geometry · low: Unit quaternions as 3D rotations: 4 floats, cheap composition, no gimbal lock, plus the conversions, interpolation choices and numerical care needed in practice.
›
Lowest common ancestor
graphs · low: LCA/merge-base computation in trees and DAGs
Spline interpolation
numerics · low: Linear, bilinear/trilinear and cubic spline interpolation on grids and tables
Rigid-body transforms (SE(3) poses)
robotics · low: Represent, compose, invert, integrate and interpolate 3D poses as unit quaternion plus translation, with exp/log maps for small motions and uncertainty.
›
SIMD programming
hardware-os · low: Process 4-16 lanes per instruction with AVX2, AVX-512 or NEON via Rust std::arch, with runtime dispatch and a portable fallback.
›
Fast Fourier transform
numerics · low: Computes the DFT in O(n log n) by recursively splitting into even and odd halves; the basis of fast convolution and spectral methods.
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Hash consing
data-structures · low: Intern structurally equal immutable terms so equality is pointer comparison and sharing is maximal
Union-find
graphs · low: Disjoint-set forest with union by size and path compression; merges sets and answers same-set queries in effectively constant time.
›
Arithmetic circuits
hardware-os · low: Adder and multiplier circuits: carry-lookahead, prefix adders, Booth encoding, Wallace and Dadda trees
Tseitin transformation
optimization · low: Linear-size CNF encoding of formulas with auxiliary variables
False sharing
concurrency · low: Independent variables written by different cores on one cache line force the line to bounce between cores; pad or regroup hot data to fix it.
›
Memory ordering
concurrency · low: What Relaxed, Acquire, Release and SeqCst atomics actually guarantee, what they cost on x86 and ARM, and which one each pattern needs.
›
Fencing tokens
distributed · low: A number that grows with every lock grant and is checked by the protected resource, so a paused ex-holder's late write is rejected.
›
Homogeneous transforms
geometry · low: 4x4 affine and projective matrices, homogeneous coordinates, view and projection, normal matrices
Minimum spanning tree
graphs · low: Cheapest set of edges connecting all vertices; Kruskal sorts edges and joins components with union-find, Prim grows one tree, Boruvka merges in parallel rounds.
›
CPU caches and the memory hierarchy
hardware-os · low: Sizes, line widths and latencies of L1/L2/L3/DRAM on modern x86 and Apple M-series, and the data-layout rules that follow from them.
›
CRC32C checksums
hardware-os · low: The Castagnoli CRC-32 with dedicated instructions on x86 (SSE4.2) and ARMv8. It is the standard fast integrity check for storage blocks, logs and network frames.
›
fsync, O_DSYNC and O_DIRECT
hardware-os · low: What fsync, fdatasync, O_DSYNC, O_DIRECT and F_FULLFSYNC really guarantee on Linux and macOS, and the exact call sequences for crash-safe files.
›
Explicit Euler
numerics · low: Step an ODE forward by its current slope, y += h·f(t, y); first-order, one evaluation per step, the baseline every other integrator is measured against.
›
Newton root finding
numerics · low: Linearize at the guess and jump to the tangent root; quadratic convergence near a simple root, made robust by brackets (1D) or line search.
›
Thomas tridiagonal solver
numerics · low: O(n) tridiagonal linear solve used in implicit finite-difference and spline schemes
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