Computing the largest empty rectangle
SIAM Journal on Computing
A note on finding a maximum empty rectangle
Discrete Applied Mathematics
Fast algorithms for computing the largest empty rectangle
SCG '87 Proceedings of the third annual symposium on Computational geometry
Dynamic programming with convexity, concavity and sparsity
Theoretical Computer Science - Selected papers of the Combinatorial Pattern Matching School
Sparse dynamic programming I: linear cost functions
Journal of the ACM (JACM)
A Linear Time Algorithm for Finding All Maximal Scoring Subsequences
Proceedings of the Seventh International Conference on Intelligent Systems for Molecular Biology
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Powers of Geometric Intersection Graphs and Dispersion Algorithms
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Algorithms for Transposition Invariant String Matching
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Mining for empty spaces in large data sets
Theoretical Computer Science - Database theory
Discovering interesting holes in data
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
Subquadratic algorithms for 3SUM
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Disjoint segments with maximum density
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
Computing maximum-scoring segments in almost linear time
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
On locating disjoint segments with maximum sum of densities
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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We derive fast algorithms for the problem of finding, on the real line, a prescribed number of intervals of maximum total length that contain at most some prescribed number of points from a given point set. Basically this is a typical dynamic programming problem, however, for input sizes much bigger than the two parameters we can improve the obvious time bound by selecting a restricted set of candidate intervals that are sufficient to build some optimal solution. As a byproduct, the same idea improves an algorithm for a similar subsequence problem recently brought up by Chen, Lu and Tang at IWBRA 2005. The problems are motivated by the search for significant patterns in certain biological data. While the algorithmic idea for the asymptotic worst-case bound is rather evident, we also consider further heuristics to save even more time in typical instances. One of them, described in this paper, leads to an apparently open problem of computational geometry flavour (where we are seeking a subquadratic algorithm) which might be interesting in itself.