Computer Science 549 Computational Biology
Prof. Steven Skiena
Fall 2013
Homework 1
Due Thursday, October 3, 2013
September 17, 2013
Each of the problems should be solved on a separate sheet of paper to facilitate grading. Limit
the solution of each probl
Lecture 22: The NP-Completeness Challenge Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
Problem of the Day
Show that the Hitting Set problem is NP-complete: Input: A coll
Lecture 21: Other Reductions Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
Problem of the Day
Show that the Dense subgraph problem is NP-complete: Input: A graph G, and i
Lecture 20: Satisability Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
Problem of the Day
Suppose we are given a subroutine which can solve the traveling salesman decisio
Lectures 12, 13, and 14:
Gene Prediction
Steven Skiena
Department of Computer Science
State University of New York
Stony Brook, NY 117944400
http:/www.cs.sunysb.edu/skiena
Sequence Annotation
As new DNA sequence data becomes available, we seek to
identify
Lectures 8, 9, 10, and 11:
Homology Searching
Steven Skiena
Department of Computer Science
State University of New York
Stony Brook, NY 117944400
http:/www.cs.sunysb.edu/skiena
String Comparison
The two killer apps of modern string processing algorithms
h
Lectures 21, 22, and 23:
Phylogenic Trees and Evolution
Steven Skiena
Department of Computer Science
State University of New York
Stony Brook, NY 117944400
http:/www.cs.sunysb.edu/skiena
Phylogenic Trees
In any evolutionary process, speciation events caus
Lectures 15, 16, 17, and 18:
Microarrays
Steven Skiena
Department of Computer Science
State University of New York
Stony Brook, NY 117944400
http:/www.cs.sunysb.edu/skiena
Faster, Better, Cheaper
Biology used to be a hypothesis driven science.
But one of
Lectures 19, 20, and 21:
RNA and Protein Folding
Steven Skiena
Department of Computer Science
State University of New York
Stony Brook, NY 117944400
http:/www.cs.sunysb.edu/skiena
Shape and Structure of Molecules
The primary molecules of biological intere
Lectures 1, 2, and 3:
Preliminaries
Steven Skiena
Department of Computer Science
State University of New York
Stony Brook, NY 117944400
http:/www.cs.sunysb.edu/skiena
Administrivia
Make sure I get your name and email address written clearly,
as well as wh
Lectures 4, 5, 6, and 7:
Sequence Assembly
Steven Skiena
Department of Computer Science
State University of New York
Stony Brook, NY 117944400
http:/www.cs.sunysb.edu/skiena
Sequencing the Human Genome
The sequencing the human genome was a tremendous scie
SUNY at Stony Brook CSE 549 Computational Biology Final Exam Name: ID #: INSTRUCTIONS: This is a closed book, closed mouth exam. You may use either pen or pencil. Check to see that you have 6 exam pages plus this cover. Use only the space alloted. Do not
1.
a) Same protein may vary in different organisms
b) Yak Genome Sequences can be found here:
http:/www.ncbi.nlm.nih.gov/nuccore/AGSK00000000
c) Follow this link for statistics: http:/www.ncbi.nlm.nih.gov/genomes/static/gpstat.html
2. Descriptive
3. Descr
HW 2 Key:
Q4.
Let S[i,j] be the shortest string which is a super-sequence of B1[1 . i] and B2[1 . j].
S[0,0] = 0, S[i,0] = i, and S[0,j] = j.
Recurrence Formula:
S[i,j] = Min cfw_
S[i-1,j-1] + 1 ; if B1[i] = B2[j]
S[i-1,j] + 1
S[i,j-1] + 1
Runtime: O(nm)
Computer Science 549 Computational Biology
Prof. Steven Skiena
Fall 2013
Homework 2
Due Tuesday, November 5, 2013
October 15, 2013
Type and print your answer, which is appreciated, or handwrite clearly and neatly. Each of the
problems should be solved on
Lecture 19: Introduction to NP-Completeness Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
Reporting to the Boss
Suppose you fail to nd a fast algorithm. What can you tell
Lecture 15: Backtracking Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
Problem of the Day
The single-destination shortest path problem for a directed graph is to nd the s
Lecture 17: Edit Distance Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
Problem of the Day
Suppose you are given three strings of characters: X, Y , and Z, where |X| = n,
Lecture 2: Asymptotic Notation Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
Problem of the Day
The knapsack problem is as follows: given a set of integers S = cfw_s1, s2
Lecture 1: Introduction to Algorithms Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
What Is An Algorithm?
Algorithms are the ideas behind computer programs. An algorithm
Lecture 5: Dictionaries Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
Dictionary / Dynamic Set Operations
Perhaps the most important class of data structures maintain a s
Lecture 6: Hashing Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
Dictionary / Dynamic Set Operations
Perhaps the most important class of data structures maintain a set of
Lecture 4: Elementary Data Structures Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
Problem of the Day
True or False? 1. 2n2 + 1 = O(n2 ) 2. n = O(log n) 3. log n = O( n)
Lecture 3: Program Analysis Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
Problem of the Day
Find two functions f (n) and g(n) that satisfy the following relationship. If
Lecture 7: Heapsort / Priority Queues Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
Problem of the Day
Take as input a sequence of 2n real numbers. Design an O(n log n) a
Lecture 11: Breadth-First Search Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
Problem of the Day
Present correct and efcient algorithms to convert between the following
Lecture 8: Mergesort / Quicksort Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
Problem of the Day
Given an array-based heap on n elements and a real number x, efciently d
Lecture 12: Depth-First Search Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
Problem of the Day
Prove that in a breadth-rst search on a undirected graph G, every edge in
Lecture 9: Linear Sorting Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
Problem of the Day
The nuts and bolts problem is dened as follows. You are given a collection of n
Lecture 10: Graph Data Structures Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 117944400 http:/www.cs.sunysb.edu/skiena
Sort Yourselves
Sort yourselves in alphabetical order so I can return the midterms efcient