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Simulation and scientific computing
traffic-sim
traffic simulation
SUMO
System
Techniques · 8
Primitives · 13
traffic-sim
Contraction hierarchies (shortcut-b…
graphs · medium: Rank the nodes, remove them one by one while adding shortcut edges that keep distances intact, then answer queries with two tiny searches that only climb the ranking.
›
Car following models
numerics · medium: Microscopic traffic: IDM and Krauss models for acceleration from gap and speed difference
Discrete event simulation
numerics · medium: Simulation driven by a time-ordered event queue with deterministic, reproducible replay
Dynamic traffic assignment
numerics · medium: Route choice to user equilibrium (Frank-Wolfe, MSA) iterated with simulation
Lane change models
numerics · medium: Microscopic lane-change decisions (MOBIL, SUMO LC2013) based on gaps and incentives
K shortest paths
graphs · medium: Yen's / Eppstein's k shortest loopless paths for alternative itineraries
Time dependent shortest path
graphs · medium: Shortest paths where edge costs depend on departure time (FIFO property, timetable graphs)
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.
›
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.
›
PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
›
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.
›
Cellular automata
graphics · low: Grid cells updated by local rules (Life, cave generation, Nagel-Schreckenberg traffic)
A* search
graphs · low: Dijkstra ordered by cost-so-far plus an admissible estimate of the remaining cost; optimal paths while exploring far fewer nodes toward the goal.
›
Linear and logistic regression
machine-learning · low: Fit a weighted sum of features to a number (least squares) or a probability (logistic); the baseline every model must beat.
›
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.
›
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).
›
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.
›
L-BFGS
numerics · low: Quasi-Newton minimizer that approximates the inverse Hessian from the last m gradient differences via the two-loop recursion; O(m·n) memory and work per step.
›
Thomas tridiagonal solver
numerics · low: O(n) tridiagonal linear solve used in implicit finite-difference and spline schemes
+ 1 more techniques
System
Techniques · 8
Primitives · 13
traffic-sim
Contraction hierarchies (shortcut-b…
graphs · medium: Rank the nodes, remove them one by one while adding shortcut edges that keep distances intact, then answer queries with two tiny searches that only climb the ranking.
›
Car following models
numerics · medium: Microscopic traffic: IDM and Krauss models for acceleration from gap and speed difference
Discrete event simulation
numerics · medium: Simulation driven by a time-ordered event queue with deterministic, reproducible replay
Dynamic traffic assignment
numerics · medium: Route choice to user equilibrium (Frank-Wolfe, MSA) iterated with simulation
Lane change models
numerics · medium: Microscopic lane-change decisions (MOBIL, SUMO LC2013) based on gaps and incentives
K shortest paths
graphs · medium: Yen's / Eppstein's k shortest loopless paths for alternative itineraries
Time dependent shortest path
graphs · medium: Shortest paths where edge costs depend on departure time (FIFO property, timetable graphs)
Levenberg marquardt
numerics · medium: Damped Gauss-Newton nonlinear least squares for model calibration
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.
›
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.
›
PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
›
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.
›
Cellular automata
graphics · low: Grid cells updated by local rules (Life, cave generation, Nagel-Schreckenberg traffic)
A* search
graphs · low: Dijkstra ordered by cost-so-far plus an admissible estimate of the remaining cost; optimal paths while exploring far fewer nodes toward the goal.
›
Linear and logistic regression
machine-learning · low: Fit a weighted sum of features to a number (least squares) or a probability (logistic); the baseline every model must beat.
›
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.
›
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).
›
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.
›
L-BFGS
numerics · low: Quasi-Newton minimizer that approximates the inverse Hessian from the last m gradient differences via the two-loop recursion; O(m·n) memory and work per step.
›
Thomas tridiagonal solver
numerics · low: O(n) tridiagonal linear solve used in implicit finite-difference and spline schemes
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