Next Steps

Explore advanced and specialized topics to continue growing.

1. Parallel and distributed data structures

Data structures designed for concurrent and distributed computing environments:

  • Concurrent data structures: Thread-safe implementations
    • Lock-free queues and stacks using CAS (Compare-And-Swap)
    • Concurrent hash maps (Java’s ConcurrentHashMap, C++ concurrent containers)
    • Read-Write locks for reader-writer problems
    • Example: Producer-consumer queues with multiple threads
  • Distributed data structures: Across multiple machines
    • Distributed Hash Tables (DHT): Chord, Kademlia for P2P systems
    • Consistent hashing: Load balancing in distributed caches (Memcached, Redis Cluster)
    • CRDT (Conflict-free Replicated Data Types): Eventually consistent data structures
      • G-Counter, PN-Counter for distributed counters
      • OR-Set for distributed sets
      • Used in: Riak, Redis, collaborative editing (Google Docs)
  • Parallel algorithms:
    • Parallel sorting: Merge sort, quick sort with fork-join
    • Parallel prefix sum (scan operations)
    • Map-Reduce paradigm for distributed processing
  • Synchronization primitives:
    • Mutexes, semaphores, condition variables
    • Barriers for phase synchronization
    • Atomic operations and memory models

2. Data structures in ML: tensors, graphs

Specialized structures for machine learning and deep learning:

  • Tensors: Multi-dimensional arrays
    • Representation: N-dimensional generalizations of matrices
    • Operations: Broadcasting, reshaping, slicing
    • Frameworks: NumPy arrays, PyTorch tensors, TensorFlow tensors
    • Storage formats: Row-major (C-style) vs column-major (Fortran-style)
    • Sparse tensors: COO (Coordinate), CSR (Compressed Sparse Row) for memory efficiency
    • Example: 4D tensor for images (batch_size, channels, height, width)
  • Graph neural networks (GNN) structures:
    • Adjacency matrix: Dense O(V²) representation
    • Adjacency list: Sparse representation for large graphs
    • Edge list: Simple (source, target, weight) tuples
    • Graph libraries: NetworkX, PyTorch Geometric, DGL (Deep Graph Library)
    • Message passing: Aggregating neighbor information
    • Applications: Social networks, molecular structures, recommendation systems
  • Embedding structures:
    • Embedding tables: Lookup tables for categorical features
    • KD-trees and Ball trees: For nearest neighbor search in embeddings
    • HNSW (Hierarchical Navigable Small World): Fast approximate nearest neighbor
    • FAISS: Facebook’s library for similarity search
  • Batch processing structures:
    • Data loaders with prefetching
    • Mini-batch sampling strategies
    • Shuffling buffers for training data

3. Persistent and functional data structures

Immutable structures that preserve previous versions:

  • Persistence types:
    • Ephemeral: Standard mutable structures (destroyed on update)
    • Partially persistent: Access all versions, modify only latest
    • Fully persistent: Access and modify any version
    • Confluently persistent: Merge different versions
  • Persistent data structures:
    • Persistent lists: Linked lists with structural sharing 
      # Clojure-style persistent list
list1 = [1, 2, 3]
list2 = cons(0, list1)  # Shares structure with list1
# list1 unchanged: [1, 2, 3]
# list2: [0, 1, 2, 3]
    • Persistent trees:
      • Red-Black trees with path copying
      • AVL trees with structural sharing
      • Time: O(log n) per operation, Space: O(log n) per version
    • Persistent hash maps:
      • Hash Array Mapped Trie (HAMT) used in Clojure, Scala
      • 32-way branching for efficient updates
    • Persistent vectors:
      • Clojure’s vector with 32-way branching
      • O(log₃₂ n) ≈ O(1) for practical sizes
  • Path copying technique: Copy only nodes on path from root to modified node
  • Fat node method: Store all versions in each node
  • Applications:
    • Functional programming languages (Haskell, Clojure, Scala)
    • Version control systems
    • Undo/redo functionality
    • Concurrent programming without locks

4. External memory and cache-oblivious structures

Optimizing for disk I/O and memory hierarchy:

  • External memory model:
    • Assumptions: Data on disk, limited RAM, block transfers
    • Cost model: Count I/O operations (block reads/writes)
    • Goal: Minimize disk accesses
  • External memory structures:
    • B-trees and B+ trees:
      • High branching factor (100-1000) to minimize height
      • Used in: Databases (MySQL InnoDB, PostgreSQL), file systems
      • Operations: O(log_B N) I/Os where B = block size
    • External merge sort:
      • K-way merge with external memory
      • Used in: Large-scale data processing
    • Buffer trees: Batching updates for efficiency
    • LSM trees (Log-Structured Merge trees):
      • Write-optimized structure
      • Used in: LevelDB, RocksDB, Cassandra, HBase
      • Memtable → SSTable hierarchy
  • Cache-oblivious algorithms:
    • Definition: Optimal for all levels of memory hierarchy without knowing cache parameters
    • Techniques:
      • Divide-and-conquer with recursive decomposition
      • Van Emde Boas layout for trees
      • Funnel sort: Cache-oblivious sorting
    • Examples:
      • Cache-oblivious B-trees
      • Matrix multiplication with recursive blocking
      • Funnelsort: O(N/B log_{M/B} N/B) I/Os
  • Memory hierarchy awareness:
    • L1/L2/L3 cache optimization
    • NUMA (Non-Uniform Memory Access) considerations
    • Prefetching and cache line alignment
    • Blocking and tiling for matrix operations

5. Reading research papers and implementations

Developing skills to learn cutting-edge data structures:

  • Finding papers:
    • Venues: STOC, FOCS, SODA, ICALP (theory), SIGMOD, VLDB (databases)
    • Archives: arXiv.org, Google Scholar, ACM Digital Library, IEEE Xplore
    • Surveys: Start with survey papers for broad overviews
    • Citations: Follow citation chains (backward and forward)
  • Reading strategy:
    1. First pass (5-10 min): Read title, abstract, introduction, conclusion
      • Understand: What problem? Why important? Main contribution?
    2. Second pass (1 hour): Read carefully, skip proofs
      • Understand: Algorithm/structure design, key insights, complexity analysis
    3. Third pass (4-5 hours): Deep dive, verify proofs
      • Re-implement from scratch, challenge assumptions
  • Key sections to focus on:
    • Abstract: Problem, solution, results
    • Introduction: Motivation, related work, contributions
    • Preliminaries: Definitions, notation, model
    • Main algorithm: Pseudocode, invariants, correctness
    • Analysis: Time/space complexity, lower bounds
    • Experiments: Performance comparisons, real-world validation
  • Implementation resources:
    • GitHub repositories: Search for paper implementations
    • Competitive programming libraries: cp-algorithms.com, KACTL
    • Algorithm visualization: VisuAlgo, Algorithm Visualizer
    • Benchmark suites: CLRS implementations, Boost libraries
  • Practice projects:
    • Implement a classic paper (e.g., Skip Lists, Bloom Filters)
    • Reproduce experimental results
    • Compare with standard library implementations
    • Write blog posts explaining the structure
  • Staying current:
    • Follow researchers on Twitter/Mastodon
    • Subscribe to arXiv RSS feeds for cs.DS (Data Structures)
    • Attend virtual conferences (recordings available)
    • Join reading groups or study circles
  • Building intuition:
    • Ask: “Why does this work? What’s the key insight?”
    • Draw diagrams and examples
    • Identify the invariant or potential function
    • Connect to structures you already know