Introduction to algorithms
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
On approximating rectangle tiling and packing
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Rectangular tiling in multi-dimensional arrays
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Improved approximation algorithms for rectangle tiling and packing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Slice and dice: a simple, improved approximate tiling recipe
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Maintaining stream statistics over sliding windows: (extended abstract)
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Exact Size of Binary Space Partitionings and Improved Rectangle Tiling Algorithms
SIAM Journal on Discrete Mathematics
On Rectangular Partitionings in Two Dimensions: Algorithms, Complexity, and Applications
ICDT '99 Proceedings of the 7th International Conference on Database Theory
A Linear Time Algorithm for Finding All Maximal Scoring Subsequences
Proceedings of the Seventh International Conference on Intelligent Systems for Molecular Biology
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
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In this paper we consider several variations of the following basic tiling problem: given a sequence of real numbers with two size bound parameters, we want to find a set of tiles such that they satisfy the size bounds and the total weight of the tiles is maximized. This solution to this problem is important to a number of computational biology applications, such as selecting genomic DNA fragments for amplicon microarrays, or performing homology searches with long sequence queries. Our goal is to design efficient algorithms with linear or near-linear time and space in the normal range of parameter values for these problems. For this purpose, we discuss the solution of a basic online interval maximum problem via a sliding window approach and show how to use this solution in a nontrivial manner for many of our tiling problems. We also discuss NPhardness and approximation algorithms for generalization of our basic tiling problem to higher dimensions.