How evenly should one divide to conquer quickly?
Information Processing Letters
Exact balancing is not always good
Information Processing Letters
Binary trees and uniform distribution of traffic cutback
Journal of Computer and System Sciences
Journal of the ACM (JACM)
Solution of a divide-and-conquer maximin recurrence
SIAM Journal on Computing
Introduction to algorithms
An elementary approach to some analytic asymptotics
SIAM Journal on Mathematical Analysis
Information Processing Letters
Mellin transforms and asymptotics: digital sums
Theoretical Computer Science
A calculus for the random generation of labelled combinatorial structures
Theoretical Computer Science
Mellin transforms and asymptotics
Acta Informatica
Multidimensional Divide-and-Conquer Maximin Recurrences
SIAM Journal on Discrete Mathematics
On the distribution of binary search trees under the random permutation model
Random Structures & Algorithms
Tighter bounds on the solution of a divide-and-conquer maximin recurrence
Journal of Algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The cost distribution of queue-mergesort, optimal mergesorts, and power-of-2 rules
Journal of Algorithms
A sorting problem and its complexity
Communications of the ACM
Improved master theorems for divide-and-conquer recurrences
Journal of the ACM (JACM)
Mathematics for the Analysis of Algorithms
Mathematics for the Analysis of Algorithms
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Notes on merging networks (Prelimiary Version)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Phase changes in random point quadtrees
ACM Transactions on Algorithms (TALG)
On the cost of optimal alphabetic code trees with unequal letter costs
European Journal of Combinatorics
Binary trees with choosable edge lengths
Information Processing Letters
Asymptotic limits of a new type of maximization recurrence with an application to bioinformatics
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
| Hi-index | 5.23 |
We derive asymptotic approximations for the sequence f(n) defined recursively by f(n) = min1≤jn {f(j) + f(n - j)} + g(n), when the asymptotic behavior of g(n) is known. Our tools are general enough and applicable to another sequence F(n) = max1 ≤j{F(j) + F(n - j) + min{g(j),g(n-j)}}, also frequently encountered in divide-and-conquer problems. Applications of our results to algorithms, group testing, dichotomous search, etc. are discussed.