beside prvious answers

• Genome assembly algorthims generally
• De-brujin graph assembly
• RNA secondary structure prediction
• Motif Finding

more could be found in

Bioinformatic Algorithms Books

http://www.renyi.hu/~miklosi/AlgorithmsOfBioinformatics.pdf

http://www.comp.nus.edu.sg/~ksung/algo_in_bioinfo/

https://www.cl.cam.ac.uk/~pl219/Bioinformatics2015.pdf

I would strongly recommend you to follow which is specific for bioinformatics algorithm. One of the most useful and toughest course I have ever done. It's freely available from world's renowned universities.

https://www.coursera.org/specializations/bioinformatics.

Cheers Chirag

For alignment:

• Burrows Wheeler ( read this paper : http://www.cs.jhu.edu/~langmea/resources/bwt_fm.pdf )
• Smith-Waterman
• Needleman-Wunsch

Here are a few problems worth exploring:

• Pairwise sequence alignment
• Clustering, phylogenetic tree building
• Multiple sequence alignment
• Dynamic programming on trees
• Genome assembly
• Genome Rearrangements

I suggest this book: Beginning Perl for Bioinformatics, By James Tisdall, Publisher: O'Reilly Media. There are many examples in it and easy to understand biological stuff for computer science students.

Could anyone here say sth about the Burrows Wheeler Transform ? Thanks .