CS 601 (Autumn 2009): Quiz 2 solutions
November 3, 2009
For each item i we have a 0/1 integer variable xi , where xi = 1 indicates that item i is picked while xi = 0 indicates that it is not picked. The integer LP is as follows.
Greedy algorithm for Set cover
Input: Collection C of sets S1 ; :; Sm over a universe U . Weight wi for each set Si . Output: a subcollection C H of smallest possible total weight whose union is also U . Whatever we need to minimize, can naturally be thou
A linear programming problem in \canonical form" is dened as follows. The input consists of an m n matrix A, m 1 vector b, and an n 1 vector c. The output is an n 1 vector x ! 0 that is feasible, i.e. such tha
CS601: HW 4 Solutions
3 Sept, 2009
1 (a) Prove Independent Set p Diverse Subset Sol. Given an instance of Independent Set problem, a graph G = (V, E ), we can convert to an instance of Diverse Subset problem as follows: For each vertex vi add a customer c
Randomizd algorithm for 3 SAT
The obvious algorithm is to try out all 2n assignments. For
(2n) time. Since the problem is extremely important, exponential time algorithms have also been looked at, and the goal is minimize the e
Prateek Sharma - 09305910 November 10, 2009
Problem 1 - 3-Coloring
We use similar techniques like we did for the MAX-3-SAT randomized algorithm. Pick any vertex and assign a color randomly. Since there are 3 colors, the
Global Min Cut
How easy is it to disconnect a network? This problem is formalized as the min-cut problem. It also arises as a subproblem in many optimization problems.
Input: Undirected graph G = (v; E ). Output: Smallest set of
Here are some of the typical uses of randomness in parallel computation. The rst use is for coordinating processors; usually random methods are faster than deterministic ones, or in someways inferior. For example, if two processors conten
You have about one minute per mark. Keep this in mind while deciding how long you need to write. Crisp answers will receive more credit. You need not repeat anything proved in the book or in class (just state as much), unless the question explici
CS601: HW 6 Solutions
October 6, 2009
1 (a) KT11.1 Give an example where the greedy algorithm does not use the minimum possible weights. Sol. Weights: 4,3,2,1 K = 5. Optimal is 2 but greedy uses 3 trucks.
1 (b) Show that greedy algorithm is at most twice