Data Structures and Algorithms

Abstract

The course provides the foundations for the design and analysis of algorithms.Classic problems ranging from sorting up to problems on graphs are used to discuss common data structures, algorithms and algorithm design paradigms.The course also comprises an introduction to parallel and concurrent programming and the programming model of C++ is discussed in some depth.

Objective

An understanding of the analysis and design of fundamental and common algorithms and data structures. Deeper insight into a modern programming model by means of the programming language C++. Knowledge regarding chances, problems and limits of parallel and concurrent programming.

Content

Data structures and algorithms: mathematical tools for the analysis of algorithms (asymptotic function growth, recurrence equations, recurrence trees), informal proofs of algorithm correctness (invariants and code transformation), design paradigms for the development of algorithms (induction, divide-and-conquer, sweep-line method, backtracking and dynamic programming), classical algorithmic problems (searching, selection and sorting), data structures for different purposes (linked lists, hash tables, balanced search trees, quad trees, heaps, union-find), further tools for runtime analysis (e.g. amortized analysis). The relationship and tight coupling between algorithms and data structures is illustrated with geometric problems (convex hull, line intersections, closest point pairs) graph algorithms (traversals, topological sort, transitive closure, shortest paths, minimum spanning trees, max flow). Programming model of C++: correct and efficient memory handling, generic programming with templates, functional approaches with functors and lambda expressions. Parallel programming: concepts of parallel programming (Amdahl's and Gustavson's laws, task/data parallelism, scheduling), problems of concurrency (data races, bad interleavings, memory reordering), process synchronisation and communication in a shared memory system (mutual exclusion, semaphores, monitors, condition variables), progress conditions (freedom from deadlock, starvation). The concepts provided in the course are motivated and illustrated with practically relevant algorithms and applications. Exercises are carried out in Code-Expert, an online IDE and exercise management system. All required mathematical tools above high school level are covered, including a basic introduction to graph theory.

Resources