Lecturer : David P . Williamson Scribe : Faisal Alkaabneh

Lecture 18 Lecturer : David P . Williamson Scribe : Venus Lo 1 Max Flow in Undirected Graphs

1.1 Max flow We start by reviewing the maximum flow problem. We are given as input an undirected graph G = (V,E); it will be convenient to think of the undirected edges as being directed arcs, so we let ~ E be an arbitrary orientation of edges in E. We also have as input a source vertex s ∈ V and a sink vertex t ∈ V . Normally we also have as input a capacity for each edge in E, but for simplic...

Lecturer: Madhu Sudan Scribe: Ryan O'Donnell

Lecturer : Scott Aaronson Scribe : Tiffany Wang 1

Lecture 17 Lecturer : Ariel Procaccia Scribe : David Kurokawa 1 Setting and Model

To begin, we first rigorously define the model. The cake itself is represented by the real interval [0, 1] and a piece of this cake is a finite union of disjoint intervals X ⊆ [0, 1]. Furthermore, each agent i has a valuation function Vi that represents his/her assessment of pieces of the cake. That is, Vi(X) = x states that the piece X has value x to i. We will assume such Vi have the followin...

Math 262 Lecture 10 : 4 / 29 / 04 lecturer : Lincoln Lu scribe : Chris Calabro

The partial duplication model with parameters (p, t, t0, Gt0) where p ∈ (0, 1), t, t0 ∈ N, t ≥ t0, and Gt0 is an initial undirected graph is the probability distribution on undirected graphs Gt described by the following recursion: If t = t0, then Gt = Gt0 . Otherwise, select a graph Gt−1 = (Vt−1, Et−1) from the partial duplication model with parameters (p, t − 1, t0, Gt0) and construct Gt, ini...