P. Flajolet, R. Kemp, H. Mahmoud, H. Prodinger, Average Case Analysis of Algorithms, Dagstuhl Seminar Report, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....several known proofs that (r; z) is the correct exponential rate for a r . Bender and Richmond [BenRic83] proved this in 1983, under some additional hypotheses, and also derived the leading term asymptotic. A di erent proof in a more general framework is given in [PemWil00a] see also the book [FlaSed00]. When z is a singular point of V, less is known. The preprint [PemWil00b] shows that (r; z) is the correct exponential order when z 2 D is a multiple point and r 2 dir(z) As a consequence, if one assumes a r 0, one has complete knowledge of the exponential order. Another consequence is that ....

Flajolet, P. and Sedgewick, R. (2000). The average case analysis of algorithms. Book Preprint.

....However, we have to ensure, that the effort for object migration pays. It is therefore necessary to analyze at compile time, how stable a certain communication behavior is. Again, code inlining can increase the parts of the program that can be analyzed. Other techniques can be found in [FSZ91, Zim91, ZZ91]. 5.3 Asynchrony of Computation To ease the process of design parallel programs a synchronous execution model is taken where an asynchronous model is correct as well. Since synchronization in a distributed memory system is expensive we try to reduce unnecessary synchronization barriers. Thread ....

P. Flajolet, B. Salvy, and P. Zimmermann. Average case analysis of algorithms. Theoretical Computer Science, 1991.

....the number of recursions or iterations, even if it is constant or a function of the input size that is constant, as well. However, we believe that this case doesn t happen too often in practice. In Fortran programs most of the loops are for loops. For non for loops and recursion techniques like [FSZ91, Zim91, ZZ91] of automatic complexity analysis can be used to derive the number of iterations of a loop and recursive calls of a recursive procedure, respectively. Lemma 3. Let P be a parallel program. If constant folding, loop unwinding, recursion elimination, and procedure inlining is ....

P. Flajolet, B. Salvy, and P. Zimmermann. Average case analysis of algorithms. Theoretical Computer Science, 1991.

....we propose. The oblivious PRAM programs and compilation techniques of [ZL94] are related to our work on shapely programs by their use of static analysis. In the sequential case, Weg75] and [M et88] are examples of syntax directed cost analyses, closely related to our own work. Both [HC88] and [FSZ91] describe average case analyses. However, our work is distinguished by its exploitation of source program structure, concise information about bulk data structures and factoring out of the cost algebra. Note that our work on shape is unrelated to the shape types of Fradet and Le M etayer [FM97] ....

P. Flajolet, B. Salvy, and P. Zimmermann. Average case analysis of algorithms. Theoretical Computer Science, 1991.

....that this bound is tight. Here a probability distribution is given where the average complexity is Theta(log n) 4.4 Automatic Complexity Analysis In recent years automatic complexity analysis systems are developed. The most important of these methods and systems are in [FSZ 88, HC 88, M e 75, FSZ 91, Zi 90] In [FSZ 88, FSZ 91] only uniform input distributions are considered. The method of Flajolet [FSZ 88, FSZ 91] is unable to deal with function composition because the output distribution of a function (or procedure) is usually non uniform. However an application of Theorems 1 and 5 would ....

....a probability distribution is given where the average complexity is Theta(log n) 4.4 Automatic Complexity Analysis In recent years automatic complexity analysis systems are developed. The most important of these methods and systems are in [FSZ 88, HC 88, M e 75, FSZ 91, Zi 90] In [FSZ 88, FSZ 91] only uniform input distributions are considered. The method of Flajolet [FSZ 88, FSZ 91] is unable to deal with function composition because the output distribution of a function (or procedure) is usually non uniform. However an application of Theorems 1 and 5 would allow to estimate the output ....

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Flajolet, P., Salvy, B. and Zimmermann, P. Average Case Analysis of Algorithms, Theoretical Computer Science (79)1, pp. 37 -- 110, 1991

....dealing with the more complex dynamic semantics. To this end we base our approach on so called OO machines, a simple operational semantics for object oriented languages. For reasoning about performance, we develop a calculus by extending complexity analysis techniques for functional programs [25, 8, 6, 27, 7]. For classes we take the viewpoint of amortised complexity: we ignore method identities and instead analyse histories of increasing length, whose amortised complexity accounts for the benefit of previous calls. The most wellknown example for amortised complexity is the UNION FIND data structure ....

....proof. Xi For methods, we aim at worst case complexities. The rules in Table 6 are the same as in the work on automatic complexity analysis based on recurrences [25, 8, 27, 26] In case of recursion we obtain usually a linear recurrence system. Solution methods of these systems are described in [6, 7, 27]. A generalization of these rules to methods with more than one parameter is straightforward. Fig. 6 shows parts of the complexity proof of push. The termination function of the loop is defined as Psi(self ) ssize Gamma i. Remember that only array accesses to stack are counted. Observe that ....

P. Flajolet, B. Salvy, and P. Zimmermann. Average case analysis of algorithms. Theoretical Computer Science, 1991.

....dealing with the more complex dynamic semantics. To this end we base our approach on so called OO machines, a simple operational semantics for object oriented languages. For reasoning about performance, we develop a calculus by extending complexity analysis techniques for functional programs [24,8,6,26,7]. For classes we take the viewpoint of amortized complexity: we ignore method identities and instead analyse histories of increasing length, whose amortized complexity accounts for the benefit of previous calls. The most well known example for amortized complexity is the UNION FIND data structure ....

....recurrences of order 1. For methods, we aim at worst case complexities. The rules are the same as in the work on automatic complexity analysis based on recurrences [24,8,26,25] In case of recursion we obtain usually a linear recurrence system. Solution methods of these systems are described in [6,7,26]. Fig. 4 shows parts of the complexity proof of push. The termination function of the loop is defined as Psi(self ) ssize Gamma i. 4. Object Complexity It is sometimes important to understand the cost of operations of an object. This kind of complexity is similar to the complexity of ....

P. Flajolet, B. Salvy, and P. Zimmermann. Average case analysis of algorithms. Theoretical Computer Science, 1991.

....that this bound is tight. Here a probability distribution is given where the average complexity is Theta(log n) 4.4 Automatic Complexity Analysis In recent years automatic complexity analysis systems are developed. The most important of these methods and systems are in [FSZ 88, HC 88, M e 75, FSZ 91, Zi 90] In [FSZ 88, FSZ 91] only uniform input distributions are considered. The method of Flajolet [FSZ 88, FSZ 91] is unable to deal with function composition because the output distribution of a function (or procedure) is usually non uniform. However an application of Theorems 1 and 5 would ....

....Here a probability distribution is given where the average complexity is Theta(log n) 4.4 Automatic Complexity Analysis In recent years automatic complexity analysis systems are developed. The most important of these methods and systems are in [FSZ 88, HC 88, M e 75, FSZ 91, Zi 90] In [FSZ 88, FSZ 91] only uniform input distributions are considered. The method of Flajolet [FSZ 88, FSZ 91] is unable to deal with function composition because the output distribution of a function (or procedure) is usually non uniform. However an application of Theorems 1 and 5 would allow to estimate the ....

[Article contains additional citation context not shown here]

Flajolet, P., Salvy, B. and Zimmermann, P. Average Case Analysis of Algorithms, Theoretical Computer Science (79)1, pp. 37 -- 110, 1991

....Such a program would be non oblivious for the compiler although it may be oblivious. However, we believe that this case doesn t happen too often in practice. In Fortran programs most of the loops are for loops. For non for loops and recursion techniques of automatic complexity analysis like [FSZ91, Zim90a, Zim90b, ZZ91] can be used to derive the number of iterations of a loop and recursive calls of a recursive procedure, respectively. When these numbers are known, recursion can be eliminated by inlining the recursive calls. Finally, we remove dead code, especially conditional branches ....

P. Flajolet, B. Salvy, and P. Zimmermann. Average case analysis of algorithms. Theoretical Computer Science, 1991.

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P. Flajolet, R. Kemp, H. Mahmoud, H. Prodinger, Average Case Analysis of Algorithms, Dagstuhl Seminar Report, 1997.

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P. Flajolet, R. Kemp, H. Prodinger, and R. Sedgewick, Average Case Analysis of Algorithms, Dagstuhl Seminar Report 9527, 1995. 17

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P. Flajolet, R. Kemp, H. Prodinger, Average Case Analysis of Algorithms, Dagstuhl Seminar Report 68, 1993.

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