CSE6140 - Fall 2015
Computational Science & Engineering (CSE)
Algorithms
Homework 4 Solutions
1
Q1: Approximation For Bin Packing (12 points)
a) 4 points - 2 for reduction, 2 for correctness
We prove the decision version of Bin Packing is NP-Complete. The
cse6140-f15-hw3-solns
November 2015
NP-Complete [15 points]
NP-membership: 4 points (2 for stating constraints that need to be satised, 2 for polynomial
time argument)
Reduction: 3 points
Poly-time of reduction: 2 points
Correctness: 3 points each directi
CSE 6140 Assignment 1
due Sept. 14, 2015 at 5 pm on t-square
Please upload 1) a PDF with solutions of Problems 1 and 2; 2) a PDF of your
report for Problem 3; 3) a single zip le of your code, README, results for
Problem 3.
1
Greedy 1
A 30 foot long water
Homework 1 Hints
September 11, 2015
1
Greedy
Visualize the leaks as points l1 , l2 .ln lying along a straight line/pipe,
where ln is the location of the nth leak. Let the length of a strip be s.
Describe what your solution looks like, in terms of where
Homework 5
November 18, 2015
Problem 1
Let G = (V, E) be a ow network with source s, sink t, and integer capacities. Suppose that we are given a
maximum ow in G.
a) Suppose that the capacity of a single edge (u, v) E is increased by 1. Given an O(|V | + |
CSE6140 - Fall 2015
Computational Science & Engineering (CSE)
Algorithms
Homework 4 Solutions
1
Q1: Approximation For Bin Packing (12 points)
a) 4 points - 2 for reduction, 2 for correctness
We prove the decision version of Bin Packing is NP-Complete. The
CSE6140 - Fall 2015
Computational Science & Engineering (CSE)
Algorithms
Homework 4
1
Approximation For Bin Packing (12 points)
Suppose that were given a set of n objects, where the size si of the ith object satises
0 < si < 1. We wish to pack all the obj
CSE 6140:
Computa0onal Science and Engineering
ALGORITHMS
review
Project Presenta0ons
3-4 minutes per team (make sure you do not take more than 4
minutes)
Highlight of approaches you took, and what worked best, ke
CSE6140 Homework 2
September 2015
1
Scheduling with Weights [10 pts]
The deadline for homework 1 is upon us. The TA sits in front of the computer,
with a mountain of emails from students with doubts. Say we have a set of
n emails to answer, where each ema
CSE 6140: C OMPUTATIONAL S CIENCE AND E NGINEERING A LGORITHMS (FALL 2014)
I NSTRUCTOR : P ROF. B ISTRA D ILKINA
Homework 1: Solutions
P ROBLEM 1: S TRING P ROCESSING (DP)
(a) Let Q(i ) be the segmentation quality of string y 1 .y i . Observe that if the
CSE 6140 Assignment 1 Solutions
September 30, 2015
1
Greedy
4 points for the correct algorithm
1 point for correct time complexity
2.5 + 2.5 points for the optimal substructure and greedy choice property proofs
Else for exchange arguments: 2 points for de
CSE 6140 Assignment 1 Solutions
September 30, 2015
1
Greedy
4 points for the correct algorithm
1 point for correct time complexity
2.5 + 2.5 points for the optimal substructure and greedy choice property proofs
Else for exchange arguments: 2 points for de
Homework 5
November 18, 2015
Problem 1
Let G = (V, E) be a ow network with source s, sink t, and integer capacities. Suppose that we are given a
maximum ow in G.
a) Suppose that the capacity of a single edge (u, v) E is increased by 1. Given an O(|V | + |
Homework 3
CSE6140, Fall 2015
October 2015
NP-Complete
Youre conguring a large network of workstations, which well model as an undirected graph G;
the nodes of G represent individual workstations and the edges represent direct communication
links. The wor
Minimum_strips (L, length)cfw_ /L represents an array which records each length eaks
position on the seam, length represents the length of the water pipe
i <- 0 /set the first leak on the seam as the st
minimum_strip(L,n)cfw_ /n represents a set containing each leak,L represents a list of
distances of adjacent leaks in clockwise order
count = 0/ the number of strips
span = 0/ the biggest distance from the start point to the next point
k.sort() / sort the
Minimum_strips (L, length)cfw_ /L represents an array which records each length eaks
position on the seam, length represents the length of the water pipe
i <- 0
/set the first leak on the seam as the start point
S <- Set of repaired leaks
Count<-0 /record
SLS METHODS
Stochastic Local Search (SLS) is a widely used approach to solving hard
combinatorial optimisation problems. Underlying most, if not all, specific SLS
algorithms are general SLS methods that can be applied to many different problems. In this c
CSE6140 Fall2015 Project
November 18, 2015
1
Overview
The Minimum Vertex cover (MVC) problem is a well known NP-complete problem with numerous applications in computational biology, operations research,
the routing and management of resources. In this pro
Programming Assignment
HAO ZHANG
I used Kruskal algorithm to compute the MST. The data structure I use is
Union-Find. And the time complexity for computeMST function is
O(mlgn). m is the number of edges and n is the number of nodes.
Using Union-Find struc
CSE6140 Homework 2
September 2015
1
Scheduling with Weights [10 pts]
The deadline for homework 1 is upon us. The TA sits in front of the computer,
with a mountain of emails from students with doubts. Say we have a set of
n emails to answer, where each ema
GT USERNAME:
NAME:
CSE6140 - MIDTERM SOLUTIONS 2015
Instructions: PLEASE WRITE YOUR NAME and GT ACCOUNT ON EACH PAGE. NUMBER EACH
PAGE.
This is an in-class, closed-book exam. However, you are allowed to use a sheet of notes (both sides of
a letter-sized s
Related work
In 1958, a method called 2-opt exchange was brought up by G.A. Groes to deal with TravelingSalesman problem in his paper A Method for Solving Traveling-Salesman Problems. In this
paper, he proposed: (a) It is applicable to both symmetric and
A High-Speed 2-Opt TSP Solver
for Large Problem Sizes
Martin Burtscher
Department of Computer Science
Overview
CUDA code optimization case study
Uses 2-opt improvement heuristic as example
Will study 6 different implementations
Key findings
Radically chan
In-Class Review
12/1/2016
Outline
1. Tutorials
a.
b.
QRTDs
Boxplots
2. Practice
a.
b.
c.
DP - Pair Sum
NPC - Bin Covering
ILP - Maximum Set Packing
QRTDs - Interpretation
10 Experiments
After 0.6 seconds, our algorithm has a 0.1
chance of solving the prob