CS 598 JGE: Advanced Data Structures (Spring 2011)

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   Pointers    Tables    Bits    Time    Big Data    Related Topics   

Key references for each lecture are highlighted. Other references contain related material—historical developments, applications, later improvements and extensions, and the like—which I may only mention briefly (or not at all) in class. Some sources are cited multiple times. *Starred authors were students when the work was written. (Eventually I hope to post a bibtex file that includes everything listed here; stay tuned!) Several relevant topics that I didn't have time to cover are listed after the schedule.

Fun with Pointers

Tue, Jan 18
Thu, Jan 20
[lecture notes]

Lazy binary and lazy Fibonacci counters
after [Bentley Saxe 1980]

Decomposable searching problems: the Bentley-Saxe logarithmic method; local rebuilding; lazy deamortization; O(P(n)log n/n) worst-case insertion time; anti-data structures for invertible queries; weak deletions; (lazy) global rebuilding; O(P(n)log n/n) worst-case insertion time and O(P(n)/n + D(n)) worst-case deletion time.

Tue, Jan 25

No class today — Jeff is at SODA

Thu, Jan 27
[lecture notes]

A well-balanced tree?
[Andersson, J. Alg. 1999]

Scapegoat trees: O(log n) worst-case search and amortized update time using O(1) extra space

A Self-Adjusting Search Tree
by Jorge Stolfi (1987)

Splay trees: rotations, roller-coasters and zig-zags, weighted amortized analysis, O(log n) amortized time, static optimality theorem, static and dynamic finger properties, working set property, dynamic optimality and other splay tree conjectures

Tue, Feb 1
Thu, Feb 3

[Demaine et al., SODA 2009]

Lower bounds for dynamic binary search trees: arborally satisfied sets, independent rectangle lower bound, Wilber's interleave and alternation lower bounds, SIGNEDGREEDY lower bound, GREEDYFUTURE

Representation of a preferred path in a zipper tree
[Bose et al., SODA 2008]

O(log log n)-competitive binary search trees: tango trees, multisplay trees, chain-splay trees, skip-splay trees, poketrees, zipper trees

Tue, Feb 8
Thu, Feb 10

A multilevel partition of an edge-weighted binary tree, and the resulting topology tree.
[Frederickson 1997]

Dynamic forest maintenance: Link-cut trees; CUT, JOIN, and FINDROOT in O(log n) amortized time; path queries and updates in O(log n) amortized time via lazy propagation; Euler-tour trees; subtree queries and updates in O(log n) amortized time; sketches of topology trees, top trees, rake-compress trees, and self-adjusting top trees.

Tue, Feb 15
Thu, Feb 17

An edge pivots into a planar shortest-path tree as the source node moves along an edge.
After [Chambers Cabello 2007]

Applications of dynamic trees: Maximum flows via network simplex; parametric and multiple-source shortest paths; dynamic graph connectivity

Tue, Feb 22
Thu, Feb 24

Reducing dynamic prefix-sum to dynamic connectivity
[Demaine Pǎtraşcu 2006]

Lower bounds for dynamic connectivity: Cell probe model, prefix sums, reductions, time trees, non-deterministic encoding

Fun with Tables

Tue, Mar 1

Perfect hash browns.
The secret is to get all the moisture out of the potatoes.

Basic hash tables: moments and tail inequalities, chaining, “perfect” hashing, linear probing, cuckoo hashing

Thu, Mar 3

Cuckoo hashing:

Hash functions: (strongly) k-universal hashing, limited independence, tabulation hashing

Tue, Mar 8

The output of a (lower-case) bloom filter.

Bloom filters: basic construction, false positive probability, counting (to support deletions), Bloomier filters

Thu, Mar 10

Periodically covering the plane with balls.
Andoni and Indyk [CACM 2008]

Locality-sensitive hashing

Fun with Bits

Tue, Mar 15
Thu, Mar 17

Bit masks used to solve QBF in polynomial time, on a unit-cost RAM with multiplication.

Unrealistic integer RAMs: Solving anything in #PSPACE in polynomial time and exponential space (sic)

Predecessor search over a finite universe
[Mihai Pătraşcu]

Part of a exponential tree, with the root on the left and children on the right
[Andersson Thorup 2007]

Realistic integer RAMs: transdichotomous RAM, word RAM, AC⁰ RAM
Ordered dictionaries: van Emde Boas trees, x-fast tries, y-fast tries via indirection, fusion trees, exponential search trees

Tue, Mar 22
Thu, Mar 24

Spring break: No class

Tue, Mar 29

Sorting a stack of Indecks notched cards.
From The Last Whole Earth Catalog (1975)

Diagram for Combination Counting
[Hollerith 1890]

A McBee Keysort card.
[Anderson 1949]

Representing 94, without and with a Single Figure notch.
[Anderson 1949]

Fast integer sorting: radix sort, packed sorting, Batcher's bitonic parallel mergesort, signature sort

Thu, Mar 31

A triage tag.
[See also]

Priority queues: atomic heaps, equivalence with sorting, black-box O(1)-time insertion, black-box melding

Tue, Apr 5

A phylogeny of Christian churches reconstructed from memetic analysis (with the Episcopalian meme given a weight of 8)
[Lord and Price 2001]

Least common ancestors: reduction from range minimum queries, reduction to ±1 range minimum queries, induction, the four-Russians trick, heavy-light tree decomposition (again), alphabetic coding, longest common prefix (again), rake-compress trees (again)

Fun with Time

Thu Apr 7

A persistent hash map (via path copying) in Clojure
[Hickey 2008]

Fractional cascading, illustrated by Jorge Stolfi
[Chazelle Guibas 1986]

Partial persistence: fat nodes, path copying, node copying, fractional cascading, planar point location

Tue Apr 12

Overview of project proposals

Thu Apr 14

A Final Thought
[Bender et al. 2002]

AVL dags and version trees
[Fraser and Myers 1987]

Full persistence: Euler tours, ordered list maintenance, virtual scapegoat trees

Replacing the prefix of a pedigree in the compressed path method.
[Fiat Kaplan 2000]

Fingers, prosthetic fingers, tendons, knuckles, and the hand.
[Demaine et al. 2010]

Confluent persistence: Hand, hand, fingers, thumb. Dum ditty, dum ditty, dum dum dum.

Tue Apr 19

Primer timelines [SPOILER!]

Retroactively inserting insertions.
[Demaine et al. 2007]

“You're about to have an idea for a time machine.”
“I am?”

Primer timelines [SPOILER!]
Retroactive data structures: changing the past, rollback, lower bounds via polynomial evaluation, retroactive priority queues via bridges, partial to full retroactivity via √m checkpoints

Fun with Big Data

Thu Apr 21

An obsolete tape robot at Fermi National Lab; each tape cartridge holds about a terabyte.

External-memory data structures: basic definitions and parameters (N, M, and B), fundamental upper and lower bounds (scan, sort, permute, and search), B-trees, sub-constant-time updates via buffering

Tue Apr 26

Answering a 3-sided query: One node in an external-memory priority search tree
[Agarwal et al. 2002]

Answering a 3-sided query: Inside the catalog structure
[Agarwal et al. 2002]

External-memory range searching: external-memory interval trees; external-memory priority search trees; catalog structures for O(B²) points/intervals; external-memory range trees.

Thu Apr 28
Tue May 3

The van Emde Boas layout
[Bender et al. 2000]

A funnel heap
[Brodal Fagerberg 2002]

Cache-oblivious data structures: definitions, tall caches, van Embe Boas layout, exponential layout, funnelsort, funnel heaps, exponential-level priority queues

Fun with Research

Thu May 12
Fri May 13

Chicken chicken chicken.
[Zongker 2002, 2006]

[Vargomax 2007]

Project presentations! — Siebel 4407

Related Topics

Here is a woefully incomplete list of relevant topics that I did not cover this semester.

Fun with Pointers

Other balanced binary trees: AVL trees, balanced binary B-trees (aka half-balanced trees, aka red-black trees), AA-trees (aka left-leaving red-black trees), brother trees, BB(α)-trees, rank-balanced trees, treaps, randomized binary search trees, skip lists, deterministic skip lists, ...

Linkning two pairing heaps
Efficient heaps: Fibonacci heaps, leftist heaps, skew heaps, randomized meldable heaps, pairing heaps, rank-pairing heaps, queaps, soft heaps, fast minimum spanning trees, ...
More dynamic graphs: dynamic minimum spanning trees, sparsification, ...
Kinetic/parametric data structures: kinetic heaps/heaters/hangers/tournaments, convex hulls, Voronoi diagrams, BSP trees, bounding volume hierarchies, parametric shortest paths, ...
Mergeable trees and mergeable dictionaries

[Nelson 1972]
String data structures: KMP automata, PATRICIA trees, suffix trees/arrays/trays/trists, DAWGs, ropes (aka “Model-T enfilades”), ...

Fun with Bits

Word-RAM computational geometry: range searching, point location, Voronoi diagrams, 3SUM, ...
Cell-probe lower bounds: lopsided set disjointness, approximate nearest neighbors, dynamic dictionaries, ...

Fun with Geometry

Practical spatial data structures: quad-/oct-trees, kd-trees, approximate nearest neighbors, dynamic and kinetic kd-trees, well-separated and semi-separated pair decompositions, R-trees, BSP trees, bounding volume hierarchies, ...
Orthogonal range searching: multilevel data structures, range trees, segment trees, interval trees, window lists, fractional cascading, filtering search, pointer-machine lower bounds, ...
Non-orthogonal range searching: ε-nets, cuttings, partition trees, linearization, space-time tradeoffs, semigroup arithmetic lower bounds, ...
Other geometric data structures: point location, Dobkin-Kirkpatrick hierarchies, ray shooting, dynamic convex hulls, parametric search, ...
Approximate nearest-neighbor searching: metric trees, balanced box-decomposition trees, ...

Fun with Big Data

Succinct/implicit data structures
Streaming data structures
Distributed data structures