Proceedings Article10.1145/800141.804691
Efficient dynamic programming using quadrangle inequalities
F. Frances Yao
- 28 Apr 1980
- pp 429-435
160
TL;DR: A quadrangle inequality condition for rendering speed-up is given, which follows immediately from the general condition that the construction of optimal binary search trees may be speeded up from O(n) steps to 3 steps, a result that was first obtained by Knuth using a different and rather complicated argument.
read more
Abstract: 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.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Perspectives of Monge properties in optimization
TL;DR: This paper presents a survey on Monge matrices and related Monge properties and their role in combinatorial optimization, and deals with the following three main topics: fundamental combinatorsial properties of Monge structures, applications of MonGE properties to optimization problems and recognition ofMonge properties.
351
Biased Search Trees
TL;DR: Two related classes of biased search trees whose average access time is within a constant factor of the minimum and that are easy to update under insertions, deletions and more radical update operations are described.
The least weight subsequence problem
TL;DR: The least weight subsequence (LWS) problem is introduced, and is shown to be equivalent to the classic minimum path problem for directed graphs, and to be solvable in O(n log n) time generally and, for certain weight functions, in linear time.
Parallel Algorithms for Dynamic Programming Recurrences with More Than O(1) Dependency
Zvi Galil,Kunsoo Park +1 more
TL;DR: This work presents a unifying framework for the parallel computation of dynamic programming recurrences with more than O(1) dependency, and uses two well-known methods, the closure method and the matrix product method, as general paradigms for developing parallel algorithms.
79
On-line dynamic programming with applications to the prediction of RNA secondary structure
TL;DR: An efficient algorithm for Waterman's problem, an on-line two-dimensional dynamic programming problem that is used for the prediction of RNA secondary structure, and an O(n + h log min{h, n2h}) time algorithm for the sparse convex case, where h is the number of possible base pairs in the RNA structure.
72
References
•Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
- 01 Jan 1974
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
10.6K
Algorithm 97: Shortest path
TL;DR: The procedure was originally programmed in FORTRAN for the Control Data 160 desk-size computer and was limited to te t ra t ion because subroutine recursiveness in CONTROL Data 160 FORTRan has been held down to four levels in the interests of economy.
4.3K
Recognition and parsing of context-free languages in time n3*
TL;DR: A recognition algorithm is exhibited whereby an arbitrary string over a given vocabulary can be tested for containment in a given context-free language and it is shown that it is completed in a number of steps proportional to the “cube” of the number of symbols in the tested string.
1.1K
•Proceedings Article
On a General Method for Maximizing and Minimizing among Certain Geometric Problems (Extended Abstract)
David P. Dobkin,Lawrence Snyder +1 more
- 01 Jan 1979
TL;DR: In this paper, the authors consider the problem of finding an initial solution with respect to a fixed bounding point and then iteratively transforming this solution into a new solution for a new point.
77