Analytic Combinatorics - A Calculus of Discrete Structures
The efficiency of many discrete algorithms crucially depends on quantifying
properties of large structured combinatorial configurations. We survey
methods of analytic combinatorics that are simply based on the idea
of associating numbers to atomic elements that compose combinatorial
structures, then examining the geometry of the resulting functions.
In this way, an operational calculus of discrete structures emerges. Applications
to basic algorithms, data structures, and the theory of random discrete
structures are outlined.
Philippe Flajolet, INRIA, France