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These are the books that I used as an undergrad and they are regarded as being among the definitive algorithmics references:

M.T. Goodrich & R. Tamassia, "Algorithm Design: Foundations, Analysis, and internet Examples" , Wiley, 2002. ISBN 0471383651.

D. Harel, "Algorithmics: The Spirit of Computing" , Second Edition, Addison-Wesley, 1992. ISBN 0201504014.

Background:

E. Kinber & C. Smith, "Theory of Computing: a Gentle Introduction", Prentice-Hall, 2001, ISBN 0

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