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.