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Observability and operations
capacity-planning
capacity forecasting
Facebook capacity planning
System
Techniques · 6
Primitives · 27
capacity-planning
Change point detection
statistics · medium: CUSUM/E-divisive/PELT to find shifts in a time series mean or distribution
Queueing theory
statistics · medium: Little's law, M/M/c and the universal scalability law for capacity models
Time-series forecasting (baselines,…
statistics · medium: The end-to-end recipe: fix horizon and uncertainty, beat naive baselines, choose a model family, and validate with rolling-origin backtests and scale-free metrics.
›
Rollup aggregation
storage · medium: Fold raw events into one mergeable partial aggregate per time bucket and dimension key, then merge fine buckets into coarser ones, so long ranges read few rows and stay exact.
›
Discrete event simulation
numerics · medium: Simulation driven by a time-ordered event queue with deterministic, reproducible replay
Arima
statistics · medium: ARIMA/SARIMA forecasting: differencing, AR and MA terms, order selection, maximum-likelihood fit
Monte Carlo integration
numerics · low: Estimate an expectation by averaging random samples; error falls as σ/√N in any dimension, and variance reduction (antithetic, control variates, importance sampling) shrinks σ.
›
Quantile sketches
data-structures · low: Mergeable quantile sketches: t-digest, DDSketch, HDR histograms
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.
›
Bin packing
optimization · low: Pack items of given sizes into the fewest fixed-capacity bins; sort descending, then first-fit, gives at most 11/9 of optimal and runs in O(n log n).
›
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.
›
Bayesian rate estimation
statistics · low: Estimate a conversion or event rate from few observations with a Beta-Binomial or Gamma-Poisson update: two counters, an honest interval, and P(B beats A) directly.
›
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.
›
Croston method
statistics · low: Forecasting intermittent demand by separately smoothing demand sizes and intervals (Croston, SBA, TSB)
Exponential smoothing (ETS, Holt-Wi…
statistics · low: Forecast by keeping a few running states (level, trend, seasonal) updated by a fraction of each forecast error; O(1) memory per series and a strong baseline.
›
STL decomposition (seasonal-trend w…
statistics · low: Split a series into trend, seasonal and remainder with iterated loess smoothing; the seasonal shape may drift and robust weights keep outliers out of it.
›
Time-series cross-validation (rolli…
statistics · low: Estimate forecast error by repeatedly training on the past and testing on the next h steps, moving the origin forward; never trains on the future.
›
Hash aggregation
storage · low: GROUP BY via hash tables with partitioning and spill to disk
Time partitioning
storage · low: Cut a table into fixed-interval time blocks so queries read only overlapping blocks and retention drops a whole block as one metadata change.
›
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.
›
PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
›
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.
›
+ 11 more primitives
System
Techniques · 6
Primitives · 27
capacity-planning
Change point detection
statistics · medium: CUSUM/E-divisive/PELT to find shifts in a time series mean or distribution
Queueing theory
statistics · medium: Little's law, M/M/c and the universal scalability law for capacity models
Time-series forecasting (baselines,…
statistics · medium: The end-to-end recipe: fix horizon and uncertainty, beat naive baselines, choose a model family, and validate with rolling-origin backtests and scale-free metrics.
›
Rollup aggregation
storage · medium: Fold raw events into one mergeable partial aggregate per time bucket and dimension key, then merge fine buckets into coarser ones, so long ranges read few rows and stay exact.
›
Discrete event simulation
numerics · medium: Simulation driven by a time-ordered event queue with deterministic, reproducible replay
Arima
statistics · medium: ARIMA/SARIMA forecasting: differencing, AR and MA terms, order selection, maximum-likelihood fit
Monte Carlo integration
numerics · low: Estimate an expectation by averaging random samples; error falls as σ/√N in any dimension, and variance reduction (antithetic, control variates, importance sampling) shrinks σ.
›
Quantile sketches
data-structures · low: Mergeable quantile sketches: t-digest, DDSketch, HDR histograms
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.
›
Bin packing
optimization · low: Pack items of given sizes into the fewest fixed-capacity bins; sort descending, then first-fit, gives at most 11/9 of optimal and runs in O(n log n).
›
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.
›
Bayesian rate estimation
statistics · low: Estimate a conversion or event rate from few observations with a Beta-Binomial or Gamma-Poisson update: two counters, an honest interval, and P(B beats A) directly.
›
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.
›
Croston method
statistics · low: Forecasting intermittent demand by separately smoothing demand sizes and intervals (Croston, SBA, TSB)
Exponential smoothing (ETS, Holt-Wi…
statistics · low: Forecast by keeping a few running states (level, trend, seasonal) updated by a fraction of each forecast error; O(1) memory per series and a strong baseline.
›
STL decomposition (seasonal-trend w…
statistics · low: Split a series into trend, seasonal and remainder with iterated loess smoothing; the seasonal shape may drift and robust weights keep outliers out of it.
›
Time-series cross-validation (rolli…
statistics · low: Estimate forecast error by repeatedly training on the past and testing on the next h steps, moving the origin forward; never trains on the future.
›
Hash aggregation
storage · low: GROUP BY via hash tables with partitioning and spill to disk
Time partitioning
storage · low: Cut a table into fixed-interval time blocks so queries read only overlapping blocks and retention drops a whole block as one metadata change.
›
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.
›
PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
›
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.
›
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.
›
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.
›
Evaluation metrics
machine-learning · low: Precision, recall, ROC AUC, average precision, log loss, NDCG and pass@k computed correctly, plus paired confidence intervals for comparing models.
›
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.
›
Rejection sampling
ml-training · low: Best-of-n and filtered sampling: generate many candidates, keep those passing a verifier or reward threshold
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.
›
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.
›
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).
›
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.
›
Thomas tridiagonal solver
numerics · low: O(n) tridiagonal linear solve used in implicit finite-difference and spline schemes
Bootstrap confidence intervals
statistics · low: Resampling-based confidence intervals for arbitrary statistics
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