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Welcome to the DSzoo mini wiki at Scratchpad!
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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.
- 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
Aka dictionaries, membership, hashing.
- 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, -dimensional searching)
- maintaining rank space: ordered file maintenance
Geometry in Low Dimensions
- fully decremental
- unique answer
- optimization answer:
- list best
- iterate in order
- aggregation queries:
- (semi)group laws
- count, weighted sum
- 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
- 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
- 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:
- 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 and Hamming norms
Derandomization leads to challenging problems.
- partial match
- near neighbors in and geometric alignment problems.
- 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
Construction time is usually interesting (graph theoretically).
- standard representation problems: below space (connectivity, reachability, shortest paths, s-t mincut)
- spanners and approximate distance oracles: better than storing the graph
- systematic data structures
- 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: