Theoretical: How many substrings / subsequences does a string of length n have? Give examples of typical alphabets.

Practical: Compute the reverse complement of a given string, compute the resulting protein, given the DNA or RNA sequence (genetic code supplied).

Theoretical: What is the difference between global and local alignment, when are they applied? Give the definition of the cell D(i,j) for global and of the cell L(i,j) for local alignment (as opposed to how they are computed). Give the recursion for the computation. Give the running times and space requirements of these algorithms. Why are these preferable to the exhaustive search algorithm? Recursive formula for number of alignments. Explain space-saving variant of N-W algorithm.

Practical: Compute the score of a given alignment, for given scoring function; compute sim(s,t) using the DP algorithm of Needleman-Wunsch; compute an optimal alignment/all optimal alignments using the DP-table. Connection between the table and alignments: write down the alignment represented by a path in the table and vice versa; find all optimal local alignments using the DP-algorithm of Smith-Waterman.

Theoretical: Problem specification, in particular of the affine gap penalty variant: what is meant by "gap open" and "gap extend". Running times of algorithms (in particular affine gap). Which version of the basic DP-algorithm would you choose for a given problem (e.g. for computing overlaps, deciding whether t is substring of s, ...).

Practical: Score given alignment using different variants (e.g. affine gap penalty, semiglobal).

Topics: Edit distance (unit cost and general cost), q-gram distance.

Theoretical: Define unit cost edit distance. How do we have to choose the scoring function in order to have a parallel between edit distance and alignment? Explain and analyse the DP algorithm for edit distance. Define the q-gram distance.

Practical: Compute the edit distance between two strings, using the DP-algorithm. Give the series of edit operations corresponding to an alignment and vice versa. Compute the q-gram distance between two strings.

Topics: Definition of MSA, projections (=induced alignments), SP-score. Theorem about optimal MSA and optimal projections. Its use for upper and lower bounds.

Theoretical: What are induced alignments (=projections)? What is the SP-score? Explain and analyse the DP algorithm. Is it feasible? Complexity status of MSA with SP-score. What other algorithms exist (star al., progr. al.), be able to sketch them (without analysis). Are they exact? If not, what can we say about the quality of the alignment produced?

Practical: Score a multiple alignment with the SP-score. Give the induced alignments of an MSA.

Topics: Motivation for different match and mismatch scores. PAM scoring matrices. Computation of PAM scoring matrices. BLOSUM matrices (sketched only).

Theoretical: Explain how the PAM scoring matrices are computed. Explain the biological motivation. What is the underlying idea? What data were used? What does the number k mean in PAMk? What is the difference between the probability matrix and the scoring matrix? What do the entries represent? Interpret their values. Why do we use a "log-odds" matrix? What are the main differences between PAM and BLOSUM matrices?

Practical: Use a given PAMk or BLOSUM-k matrix (supplied) to score an alignment.

Topics: BLAST.

Theoretical: What is a heuristic? Explain the underlying ideas of BLAST. What is the advantage over the DP-algorithms? What is the primary application? Why are heuristics used and not the DP-algorithms?

Practical: Given a small example (a query and a db sequence), explain how BLAST works on the example: list some high-scoring words, show where there is a hit, show how to extend it.

Topics: Overlap graphs. SCS.

Theoretical: Define the SCS problem. Why do we assume substring-freeness? Why does this not change the problem? Complexity status of SCS problem.

Practical: Given a set of strings (=fragments, reads), construct the overlap graph.

Topics: De Bruijn graphs: definition (full de Bruijn graphs, and de Bruijn subgraphs). De Bruijn graph of a string or of a set of strings. Walks in de Bruijn graphs. Sequencing by Euler tours/paths in de Bruijn graphs.

Theoretical: What does an Euler tour / path in the de Bruijn graph of a string correspond to? How do we compute an Euler tour / path? Complexity of algorithm.

Practical: Given a set of reads, apply the algorithm for reconstructing the target sequence. Given the alphabet and k, draw / complete the de Bruijn graph of order k.