TY - GEN
T1 - A real elementary approach to the master recurrence and generalizations
AU - Yap, Chee
PY - 2011
Y1 - 2011
N2 - The master theorem provides a solution to a well-known divide-and-conquer recurrence, called here the master recurrence. This paper proves two cook-book style generalizations of this master theorem. The first extends the treated class of driving functions to the natural class of exponential-logarithmic (EL) functions. The second extends the result to the multiterm master recurrence. The power and simplicity of our approach comes from re-interpreting integer recurrences as real recurrences, with emphasis on elementary techniques and real induction.
AB - The master theorem provides a solution to a well-known divide-and-conquer recurrence, called here the master recurrence. This paper proves two cook-book style generalizations of this master theorem. The first extends the treated class of driving functions to the natural class of exponential-logarithmic (EL) functions. The second extends the result to the multiterm master recurrence. The power and simplicity of our approach comes from re-interpreting integer recurrences as real recurrences, with emphasis on elementary techniques and real induction.
UR - http://www.scopus.com/inward/record.url?scp=79955751693&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79955751693&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-20877-5_3
DO - 10.1007/978-3-642-20877-5_3
M3 - Conference contribution
AN - SCOPUS:79955751693
SN - 9783642208768
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 14
EP - 26
BT - Theory and Applications of Models of Computation - 8th Annual Conference, TAMC 2011, Proceedings
T2 - 8th Annual Conference on Theory and Applications of Models of Computation, TAMC 2011
Y2 - 23 May 2011 through 25 May 2011
ER -