The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Constructing trees in parallel
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Parallel searching in generalized Monge arrays with applications
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Parallel construction of trees with optimal weighted path length
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Sparse dynamic programming II: convex and concave cost functions
Journal of the ACM (JACM)
Parallel construction of optimal alphabetic trees
SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Shortest path in complete bipartite digraph problem and its applications
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
On-line dynamic programming with applications to the prediction of RNA secondary structure
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
On binary searching with non-uniform costs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Heuristic allocation based on a dynamic programming state-space representation
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
The Knuth-Yao quadrangle-inequality speedup is a consequence of total-monotonicity
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A Fast 2-Approximation Algorithm for the Minimum Manhattan Network Problem
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
The Knuth-Yao quadrangle-inequality speedup is a consequence of total monotonicity
ACM Transactions on Algorithms (TALG)
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
A static optimality transformation with applications to planar point location
Proceedings of the twenty-seventh annual symposium on Computational geometry
Binary identification problems for weighted trees
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Synthesis of first-order dynamic programming algorithms
Proceedings of the 2011 ACM international conference on Object oriented programming systems languages and applications
Approximation algorithms for speeding up dynamic programming and denoising aCGH data
Journal of Experimental Algorithmics (JEA)
Approximate dynamic programming using halfspace queries and multiscale Monge decomposition
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A bibliography on computational molecular biology and genetics
Mathematical and Computer Modelling: An International Journal
The binary identification problem for weighted trees
Theoretical Computer Science
Analytical aspects of tie breaking
Theoretical Computer Science
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Dynamic programming is one of several widely used problem-solving techniques in computer science and operation research. In applying this technique, one always seeks to find speed-up by taking advantage of special properties of the problem at hand. However, in the current state of art, ad hoc approaches for speeding up seem to be characteristic; few general criteria are known. In this paper we give a quadrangle inequality condition for rendering speed-up. This condition is easily checked, and can be applied to several apparently different problems. For example, it follows immediately from our general condition that the construction of optimal binary search trees may be speeded up from O(n3) steps to O(n2), a result that was first obtained by Knuth using a different and rather complicated argument.