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Welcome to the DataStructures Zoo. This project was inspired by the success of the Complexity Zoo and the need to systematize data-structure knowledge.

Mission Statement

  • spelling of lower-bounds and data-structures
  • we study problems, not implementations (eg predecessor vs van Emde Boas)


  • models (cell-probe, RAM, pointer machine, comparison, algebraic)
  • what is a problem? (static vs dynamic, language membership)
  • lowerbounds (inc. communication complexity)

The Zoo Starts Here

Exact Search

Aka dictionaries, membership, hashing.

  • derandomization
  • small space
  • smaller space: approximate membership (Bloom filters), perfect hashing (no membership at all)
  • implementing hashing
  • load balancing problems (offline, online, with moves, small-space deciders)

Problems in One Dimension

  • priority queues
  • search problems:
    • predecessor search (longest prefix match on integers)
    • segment stabbing (IP lookup, routing)
    • range reporting
  • problems in rank space (array problems):
    • partial sums (rank and select, list indexing)
    • range-minimum query, RMQ (priority range search, 1 \frac{1}{2}-dimensional searching)
  • maintaining rank space: ordered file maintenance

Geometry in Low Dimensions

Problem types:

  • static
  • dynamic
  • incremental
  • decremental
  • fully decremental

Query types:

  • unique answer
  • optimization answer:
    • list best
    • iterate in order
  • aggregation queries:
    • (semi)group laws
    • existential
    • report
    • count, weighted sum
    • max
    • priority reporting
    • color reporting

Point location (unique answer)

Searching among points:

  • nearest neighbor (optimization)
  • approximate nearest neighbor (unique answer)
  • extreme point in a direction (optimization); aka LP / convex hull query
  • extreme point to a rotation (optimization)
    • special case: angle enclosing point, aka convex hull tangent

Point-shape problems:

  • range problems: aggregate over points in query shape
  • stabbing problems: aggregate over shapes stabbed by a point
    • special case: hierarchical shapes
    • optimization answer: report minimal in hierarchical shapes
    • unique answer: disjoint shapes

Approximation version where shapes are scaled by approximation.

Shapes can be:

  • orthogonal rectangles. Special cases:
    • dominance rectangles
    • ranges on each coordinate are bit prefixes
  • angles
  • polygons, in particular triangles. Triangulation gives reduction to triangles, but it's multiplicative (additive may be possible)
  • circles: near neighbor problems. Range/stabbing are equivalent. Approximate version is particularly meaningful.

Intersection problems: (ray shooting)

  • shooting rays into segments:
    • aggregate
    • in order of intersection (optimization)
  • segments intersected by segments (aggregate)

Special case of ray/segments being axis-parallel.

Geometry in High Dimensions

  • near neighbors in \ell_1, \ell_2 and Hamming norms

Derandomization leads to challenging problems.

  • partial match
  • near neighbors in \ell_\infty and geometric alignment problems.

String Searching

  • pattern matching and low space
  • searching with wildcards
  • approximate searching and edit distance

(Almost) Static Trees

  • lowest common ancestor
  • marked ancestor and path aggregation (sum, min)
  • something about small labelings

Static Graphs

Construction time is usually interesting (graph theoretically).

  • standard representation problems: below n^2 space (connectivity, reachability, shortest paths, s-t mincut)
  • spanners and approximate distance oracles: better than storing the graph
  • systematic data structures

Dynamic Graphs

Fully dynamic problems:

  • dynamic trees (forests, actually)
If the tree is only changed by inserting or deleting leaves, see "Almost Static Trees" above.
  • "easy" problems on undirected graphs: connectivity, MST, mincut
  • reachability in directed graphs
  • hard problems: shortest paths, flow and s-t mincut

The following special cases are often considered:

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