Instructor : Chandra Chekuri Scribe : Chandra Chekuri 1 Estimating Frequency Moments in Streams

Instructor : Chandra Chekuri Scribe : Rachit Agarwal

Instructor: Chandra Chekuri Scribe: Omid Fatemieh Contents

In a game (N, 〈Si〉, 〈ui〉) players are interested in maximizing ui. In this section we consider games where players incur costs, and hence their goal is to minimize costs. These games are represented as (N, 〈Si〉, 〈ci〉) where ci is the cost function of player i. Recall that we defined a potential function to prove that a load balancing game had a pure Nash equilibrium. In this section we define a...

Approximation algorithms and the hardness of approximation

Chandra Chekuri (Dept. of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL), Joseph Cheriyan (Dept. of Combinatorics and Optimization, University of Waterloo, Waterloo, ON), Ryan O’Donnell (School of Computer Science, Carnegie Mellon University, Pittsburgh, PA), Mohammad R. Salavatipour (Dept. of Computing Science, University of Alberta, Edmonton, AL), David Williamson (...

Instructor : Chandra Chekuri Scribe : Matthew Yancey 1 Matchings in Non - Bipartite Graphs

Proof: We have already seen the easy direction that for any U , ν(G) ≤ |V | 2 − o(G−U)−|U | 2 by noticing that o(G− U)− |U | is the number of nodes from the odd components in G− U that must remain unmatched. Therefore, it is sufficient to show that ν(G) = |V | 2 − maxU⊆V o(G−U)−|U | 2 . Any reference to left-hand side (LHS) or right-hand side (RHS) will be in reference to this inequality. Proof...

Minimizing Average Weighted Completion Time

Sanjeev Khanna University of Pennsylvania 11.