On the general motion-planning problem with two degrees of freedom
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
A convex polygon among polygonal obstacles: placement and high-clearance motion
Computational Geometry: Theory and Applications
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An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
Journal of Computer and System Sciences - Computational biology 2002
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
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An optimal algorithm for maximum-sum segment and its application in bioinformatics
CIAA'03 Proceedings of the 8th international conference on Implementation and application of automata
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RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
An algorithm for a generalized maximum subsequence problem
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Optimal algorithms for the average-constrained maximum-sum segment problem
Information Processing Letters
Finding long and similar parts of trajectories
Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Finding long and similar parts of trajectories
Computational Geometry: Theory and Applications
Optimal eviction policies for stochastic address traces
Theoretical Computer Science
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In this paper, we introduce the notion of a constrained Minkowski sumwhich for two (finite) point-sets P,Q⊆ R2 and a set of k inequalities Ax≥ b is defined as the point-set (P ⊕ Q)Ax≥ b= x = p+q | ∈ P, q ∈ Q, , Ax ≥ b. We show that typical subsequenceproblems from computational biology can be solved by computing a setcontaining the vertices of the convex hull of an appropriatelyconstrained Minkowski sum. We provide an algorithm for computing such a setwith running time O(N log N), where N=|P|+|Q| if k is fixed. For the special case (P⊕ Q)x1≥ β, where P and Q consistof points with integer x1-coordinates whose absolute values arebounded by O(N), we even achieve a linear running time O(N). Wethereby obtain a linear running time for many subsequence problemsfrom the literature and improve upon the best known running times forsome of them.The main advantage of the presented approach is that it provides a generalframework within which a broad variety of subsequence problems canbe modeled and solved.This includes objective functions and constraintswhich are even more complexthan the ones considered before.