Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Topologically sweeping an arrangement
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
Routing and scheduling on a shoreline with release times
Management Science
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Faster shortest-path algorithms for planar graphs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
The String-to-String Correction Problem
Journal of the ACM (JACM)
A linear space algorithm for computing maximal common subsequences
Communications of the ACM
An Efficient Algorithm for Shortest Paths in Vertical and Horizontal Segments
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Topological Sweeping in Three Dimensions
SIGAL '90 Proceedings of the International Symposium on Algorithms
Single-vehicle Scheduling Problem on a Straight Line with Time Window Constraints
COCOON '95 Proceedings of the First Annual International Conference on Computing and Combinatorics
Approximating Shortest Paths in Arrangements of Lines
Proceedings of the 8th Canadian Conference on Computational Geometry
Improved bounds on planar k-sets and k-levels
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Selected combinatorial research problems.
Selected combinatorial research problems.
Topological Peeling and Implementation
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
An Experimental Study and Comparison of Topological Peeling and Topological Walk
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Optimal Terrain Construction Problems and Applications in Intensity-Modulated Radiation Therapy
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
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In this paper, we study a class of optimal path problems with the following phenomenon: The space complexity of the algorithms for reporting the lengths of single-source optimal paths for these problems is asymptotically smaller than the space complexity of the "standard" treegrowing algorithms for finding actual optimal paths. We present a general and efficient algorithmic paradigm for finding an actual optimal path for such problems without having to grow a single-source optimal path tree. Our paradigm is based on the "marriage-before-conquer" strategy, the prune-and-search technique, and a data structure called clipped trees. The paradigm enables us to compute an actual path for a number of optimal path problems and dynamic programming problems in computational geometry, graph theory, and combinatorial optimization. Our algorithmic solutions improve the space bounds (in certain cases, the time bounds as well) of the previously best known algorithms, and settle some open problems. Our techniques are likely to be applicable to other problems.