CPSC 327 Course Information

At the heart of computer science is the development of efficient algorithms for solving problems, and the choice of data structure to implement that algorithm can have a significant impact on the simplicity and efficiency of a program.

This course continues the study of data structures, their applications, and the algorithms associated with them. Topics include abstract data types, dictionaries, graphs, searching, and sorting. The design and analysis of algorithms is also covered, with topics such as efficiency and complexity, NP-completeness, dynamic programming, and amortized analysis.


Instructor	Stina Bridgeman bridgeman@hws.edu Lansing 312, x3614

Office Hours	M 1-2pm, W 4-5:30pm, Th 9:30-11am, F 1:30-2:30pm or by appointment (schedule)

Class Hours and Meeting Place	MWF 11:15-12:10pm Lansing 300

Course Web Page	http://math.hws.edu/~bridgeman/courses/327/s06/ You are expected to regularly consult the course web page for announcements, assignments, and most handouts.

Text	Algorithm Design: Foundations, Analysis, and Internet Examples Goodrich & Tamassia Wiley, 2001 ISBN 0-471-38365-1 book website Additional material will be handed out or posted on the course webpage.

Prerequisites	CPSC 225 and CPSC 229

Rationale & Aims	This course explores a topic at the very core of computer science: designing efficient solutions to problems, and implementing those solutions in efficient and organized ways. The course has three main goals: to develop a toolbox of known data structures and algorithms which can be used to solve many common problems to develop a toolbox of strategies for solving new problems, where a "canned" data structure or algorithm might not be sufficient to gain a working knowledge of algorithmic efficiency, to inform the algorithm- and program-design process by providing a basis for comparing solutions and defining good solutions These skills will build on the programming skills introduced and refined in CPSC 124/225, with the ultimate goal of producing stronger problem-solvers and programmers.

Course Content Overview	The course material falls into five main units: Algorithm Analysis: You've thought of several algorithms for solving a particular problem - which is the best? Time- and space-efficiency will be discussed, and big-Oh notation will be introduced - concepts which will be the fundamental tools used in the rest of the course. There will also be a quick review of several basic data structures (including stacks, queues, vectors, and lists) with an emphasis on applying the new algorithm analysis tools to compare possible implementations of these data structures. Objectives: describe and discuss different ways in which the efficiency of an algorithm can be determined define big-Oh notation define the difference between best case, worst case, and average case running time determine the (best, worst, average) running time of an algorithm arrange algorithms from fast to slow based on their asymptotic running times compare and contrast the time- and space-efficiency of array vs. linked list implementations of stacks, queues, vectors, and lists and discuss situations in which each implementation is most appropriate Searching, Sorting, and Selection: Searching, sorting, and selection (picking the kth smallest or largest item) problems are extremely common, so it is worth considering how to solve these problems efficiently. This section will expand the toolbox of known data structures and algorithms with a number of new data structures (including balanced search trees and hashtables) and algorithms (including sorting and selection algorithms). These three problems will also serve as a case study of how different data structures and algorithms can greatly affect a program's efficiency, and will provide a motivation for introducing some additional tools for algorithm analysis. Objectives: define, implement, and discuss the running time of data structures supporting searching included unordered lists, ordered lists, binary search trees, balanced trees, and hashtables define, implement, and discuss the running time of sorting algorithms including insertion sort, selection sort, mergesort, quicksort, and bucket sort define, implement, and discuss the running time of quick-select write and solve recurrence relations to determine the running time of recursive algorithms Algorithm Design: The next unit will examine three fundamental techniques of algorithm design (greedy algorithms, divide-and-conquer, and dynamic programming), along with examples of applications of each technique. This continues to build the toolbox of known solutions, but more importantly begins to build a repertoire of strategies for solving new problems. Objectives: define the greedy method, and define and recognize problems where the greedy method is applicable give examples of greedy algorithms define divide-and-conquer, and define and recognize problems where divide-and-conquer is appropriate give examples of divide-and-conquer algorithms define dynamic programming, and define and recognize problems where dynamic programming is appropriate give examples of dynamic programming algorithms develop greedy, divide-and-conquer, and dynamic programming algorithms for new problems, and prove their correctness determine the running time of algorithms of each type Graphs: The graph is a data structure with a wide variety of applications. We'll define a graph ADT, consider how that ADT might be implemented, and introduce a number of common graph algorithms (including traversal, shortest path, and minimum spanning tree) and their applications. Objectives: define what a graph is and give examples of applications define typical operations present in a graph ADT discuss implementation alternatives for the graph ADT (including edge list, adjacency list, and adjacency matrix) and their tradeoffs define and implement basic graph algorithms (e.g. depth-first search, breath-first search, locating biconnected components, transitive closure), determine their running times, and discuss their applications define and implement basic algorithms for weighted graphs (e.g. single-source shortest path, all-pairs shortest path, minimum spanning tree), determine their running times, and discuss their applications Complexity and NP-Completeness: After a semester-long focus on the efficiency of algorithms, some questions might come to mind: Are some problems fundamentally harder to solve than others? Are there problems that can't be solved? We'll delve briefly back into more theoretical topics to examine these questions (and what "hard" actually means), and to look at some of the hardest problems in computer science. Objectives: define P, NP, NP-hard, and NP-complete and give examples of relevant problems describe several important NP-complete problems (e.g. 3SAT, vertex cover, clique, knapsack, TSP) discuss and apply algorithmic strategies (e.g. backtracking, branch-and-bound) for dealing with NP-complete problems If time permits, some additional data structures (such as sets and heaps) and algorithms for different domains (such as text processing, computational geometry, and network security) will be considered.

Assignments and Evaluation	This course is a problem-solving course. Many of the assignments will be written, but some will involve programming or use of the computer for experimental studies. Homework: To encourage discussion and keeping up with the course material (and to enable rapid feedback), homework problems will be assigned frequently and will generally be due at the beginning of the next class period after they are assigned (rather than having large weekly problem sets). Of the problems assigned each day, only a few will be designated as problems to hand in for grading. (The rest should be worked for additional practice and review.) Late homeworks will not be accepted, but the three lowest individual problem scores will be dropped when computing the homework component of the final grade. Programming Exercises: Some exercises will involve implementation and/or experimental comparison of different data structures and algorithms. Programming assignments will generally have a longer deadline than homework problems (e.g. due a week or so after being assigned). Exams: There will be two midterm exams and a final exam. All will be take-home exams, and will emphasize applying concepts rather than simple recall. More information about the exams will be provided closer to the exam dates. Late Policy and Collaboration: See the course policies for the late policy and collaboration policy. Final Grades: Final grades in this course will be computed as follows: Homework and programming exercises: 50% Midterm exams: 30% (15% each) Final exam: 20% On-time attendance and class participation (see the course policies) are expected, though they are not formally factored into your final grade. However, missing class - for any reason - often results in lower grades because important material was missed. Similarly, not participating in class even if you are physically present may mean that you aren't actively following the material and thus may be missing more sophisticated or subtle points. Whether or not your grade is impacted for these reasons is up to you - it is your responsibility to get notes from another student or otherwise catch up on missed material. Also note that class participation and the number of unexecused absences are considered when deciding whether or not to round up a final grade which is just below a grade-level cutoff. See the course policies for the definition of unexcused and excused absences. Extra Credit: There will be opportunities for extra credit at various points during the semester.