Modern Algorithms and Data Structures

Overview

Use OTP built-ins first. Escalate to specialized structures only when profiling shows a bottleneck. For most Elixir applications, Map, MapSet, List, and the OTP modules cover 95% of needs.

Quick Decision

What are you solving?
  Data storage/lookup       → See ets-and-persistent-term.md, otp-builtins.md
  Concurrent shared state   → See concurrent-data-structures.md, ets-and-persistent-term.md
  Graph/dependency problem  → See graph-algorithms.md
  Text search/matching      → See string-and-text.md
  Location/spatial          → See spatial.md
  Time ranges/scheduling    → See interval-and-range.md
  Streaming metrics         → See streaming-algorithms.md
  Large-scale counting/sets → See probabilistic.md
  Hashing                   → See hash-functions.md
  Compression               → See compression.md
  Sorting large datasets    → See sorting-and-search.md
  Optimization/constraints  → See optimization.md
  Statistics/analytics      → See statistics.md

Common Mistakes

• GenServer as concurrent cache: Serializes reads; use ETS with read_concurrency: true
• Application.getenv in hot paths: Use :persistentterm for config read on every request
• Lists as queues: queue ++ [item] is O(n); use :queue for O(1)
• GenServer as counter: Use :atomics or :counters instead
• MD5/SHA1 for non-crypto: 60× slower than xxHash3
• Exact counting at scale: HyperLogLog uses 16 KB where MapSet uses 800 MB (100M items)

Reference Files

Read the file that matches your current problem:

• ets-and-persistent-term.md — When: Need concurrent shared state or config cache. ETS table types, concurrency options, cache/rate-limiter patterns, :persistent_term for config
• otp-builtins.md — When: Looking for queue, tree, set, or counter primitives. :queue, :gbtrees, :gbsets, :atomics, :counters, :array, Okasaki structures
• graph-algorithms.md — When: Working with dependencies, networks, or paths. :digraph/:digraph_utils patterns: topological sort, shortest path, cycle detection, dependency resolution
• string-and-text.md — When: Building search, fuzzy matching, or autocomplete. Fuzzy matching (Levenshtein, Jaro-Winkler), full-text search (tsvector, pg_trgm), autocomplete
• concurrent-data-structures.md — When: Need lock-free or high-concurrency patterns. CAS with :atomics, lock-free patterns, ETS concurrency, :counters write_concurrency
• spatial.md — When: Working with geographic data or proximity queries. PostGIS (STDWithin, STContains), geohashing, Haversine distance
• interval-and-range.md — When: Handling time ranges, scheduling, or overlap detection. Postgres range types, overlap detection, exclusion constraints, scheduling
• streaming-algorithms.md — When: Computing metrics over unbounded data streams. Sliding windows, EMA, reservoir sampling, streaming percentiles
• optimization.md — When: Solving constraint, scheduling, or resource allocation problems. Dynamic programming, greedy, constraint satisfaction, gradient descent (Nx), simulated annealing, linear programming, when to push to Postgres
• statistics.md — When: Need analytics, anomaly detection, or A/B testing. Descriptive stats (Postgres and Elixir), anomaly detection (Z-score, IQR), A/B testing, Explorer DataFrames, histograms, correlation
• compression.md — When: Need to compress data for storage or transfer. :zlib, Zstd, LZ4, :erlang.termtobinary compressed option
• probabilistic.md — When: Counting or membership testing at massive scale. HyperLogLog, Cuckoo filters, Count-Min Sketch, Bloom filters
• hash-functions.md — When: Choosing hash function for non-crypto use. xxHash3, BLAKE3, HighwayHash selection guide
• sorting-and-search.md — When: Sorting large datasets or building indexes. Cache-efficient sorting, BlockQuicksort, pdqsort, B+ trees

Commands

• /algorithm-research — Deep research with academic paper citations
• /benchmark — Create Benchee benchmarks to compare data structure alternatives

Related Skills

• performance-analyzer: Profiling, benchmarking, latency analysis
• distributed-systems: Consensus and replication algorithms
• elixir-patterns: OTP process patterns, ETS usage

Use the algorithms-researcher agent for deep research with paper citations.