6.851: Advanced Data Structures (Fall'17)

Prof. Erik Demaine     TAs: Adam Hesterberg, Jayson Lynch


[Home] [Lectures] [Problem Sets] [Project] [Coauthor] [Accessibility]

Lecture 20 Video     [previous] [next] [completion form]

[+] Dynamic graphs: Euler tour trees, decremental connectivity in trees in O(1), fully dynamic connectivity in O(lg2 n), survey

This lecture continues our theme of dynamic graphs. Beyond surveying results for several such problems, we'll focus on dynamic connectivity, where you can insert and/or delete edges, and the query is to determine whether two vertices are in the same connected component (i.e., have a path between them). We'll cover a few different results for this problem:

  1. Link-cut trees (from last lecture) already solve trees in O(lg n).
  2. Euler-tour trees are a simpler way to solve trees in O(lg n), which allow us to aggregate over subtrees instead of paths.
  3. If we just insert or just delete edges, we can solve trees in O(1), using our friend leaf trimming plus some simple bit-vector tricks.
  4. For general graphs, we'll see how to support updates in O(lg2 n) and queries in O(lg n / lg lg n).

This will be our culmination of data structures for dynamic graphs; the next (final) lecture is about matching lower bounds.

Download Video: 360p, 720p

Lecture notes, page 1/8[previous page][next page][PDF]

Lecture notes, page 1/8[previous page][next page][PDF]

The video above should play if your web browser supports either modern Flash or HTML5 video with H.264 or WebM codec. The lecture notes should advance automatically. If you have any trouble with playback, email Erik.