Computational geometry: an introduction
Computational geometry: an introduction
Functional approach to data structures and its use in multidimensional searching
SIAM Journal on Computing
A new approach to the dynamic maintenance of maximal points in a plane
Discrete & Computational Geometry
Dynamic Maintenance of Maxima of 2-d Point Sets
SIAM Journal on Computing
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Introduction to Algorithms
Journal of Computer and System Sciences - Computational biology 2002
Interval Finding and Its Application to Data Mining
ISAAC '96 Proceedings of the 7th International Symposium on Algorithms and Computation
Linear-time algorithm for finding a maximum-density segment of a sequence
Information Processing Letters
Journal of Computer and System Sciences
Information Processing Letters
A dichromatic framework for balanced trees
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
Finding a weight-constrained maximum-density subtree in a tree
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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Let A be a sequence of n real numbers, L1 and L2 be two integers such thatL1 ≤ L2 , and R1 and R2 be two real numbers such that R1 ≤ R2. An interval of A is feasible if its length is between L1 and L2 and its average is between R1 and R2. In this paper, we study the following problems: finding all feasible intervals of A, counting all feasible intervals of A, finding a maximum cardinality set of non-overlapping feasible intervals of A, locating a longest feasible interval of A, and locating a shortest feasible interval of A. The problems are motivated from the problem of locating CpG islands in biomolecular sequences. In this paper, we firstly show that all the problems have an Ω(n log n)-time lower bound in the comparison model. Then, we use geometric approaches to design optimal algorithms for the problems. All the presented algorithms run in an on-line manner and use O(n) space.