Filters








38,908 Hits in 6.1 sec

Complexity Lower Bounds for Approximation Algebraic Computation Trees

Felipe Cucker, Dima Grigoriev
1999 Journal of Complexity  
The goal of this paper is to prove lower bounds for approximated computations. As it is customary for lower bounds, we consider some form of algebraic tree as our computational model (cf.  ...  We prove lower bounds for approximate computations of piecewise polynomial functions which, in particular, apply for round-o computations of such functions.  ...  , and Yao 1998 ] for the discussion and the exponential lower bound for ternary rathen than the usual binary computation trees).  ... 
doi:10.1006/jcom.1999.0519 fatcat:2pvxuqrnhzcrncvkh4hbbondxq

Page 2762 of Mathematical Reviews Vol. , Issue 99d [page]

1991 Mathematical Reviews  
(E-PAMP-I; Pamplona) Lower bounds for Diophantine approximations. (English summary) Algorithms for algebra (Eindhoven, 1996). J. Pure Appl. Algebra 117/118 (1997), 277-317.  ...  lower bound is shown for the depth of randomized algebraic decision trees that recognize the knapsack problem and an Q(nlogn) lower bound for the element distinctness problem.  ... 

Page 7812 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
The transforma- tion of comparison model lower bounds, which are usually easier to obtain, to the parallel-random-access-machine, unifies some known lower bounds and gives new lower bounds for several  ...  In this latter case, a lower bound of the complexity is given versus the total number of vertices in all obstacles.  ... 

Page 514 of Mathematical Reviews Vol. , Issue 99a [page]

1991 Mathematical Reviews  
Symbolic Comput. 13 (1992), no. 3, 231- 233; MR 93b:13020] strongly reduces the gap between the upper bound and the lower bound for this problem.  ...  An Ackermannian upper bound for PIMP over the integers has been given vy G. Gallo and B. Mishra [Appl. Algebra Engrg. Comm. Comput. 5 (1994), no. 6, 343-370; MR 95i:13026].  ... 

Lower bounds for algebraic computation trees

Michael Ben-Or
1983 Proceedings of the fifteenth annual ACM symposium on Theory of computing - STOC '83  
A topological method is given for obtaining lower bounds for the height of algebraic computation trees, and algebraic decision trees.  ...  Using this method we are able to generalize, and present in a uniform and easy way, almost all the known nonlinear lower bounds for algebraic computations.  ...  Since our algebraic computation tree model can handle the operation of taking square roots most of the lower bounds from Shamos's work can be extended to lower bounds on the complexity of solving the problems  ... 
doi:10.1145/800061.808735 dblp:conf/stoc/Ben-Or83 fatcat:lwhhw5siejedjagvnnvadm2oeq

Page 7109 of Mathematical Reviews Vol. , Issue 97K [page]

1997 Mathematical Reviews  
Such a lower bound result for the depth of algebraic decision trees was proved before by J. L. Montafia, J. E. Morais and L. M. Pardo [Appl. Algebra Engrg. Comm.  ...  N., Jr.] (1-PAS-C; University Park, PA) Complexity lower bounds for computation trees with elementary transcendental function gates. (English summary) Theoret. Comput.  ... 

On the complexity of approximating Euclidean traveling salesman tours and minimum spanning trees [chapter]

Gautam Das, Sanjiv Kapoor, Michiel Smid
1996 Lecture Notes in Computer Science  
In the algebraic computation tree model, the complexities of both these problems are shown to be (n log n=r), for all n and r such that r < n and r is larger than some constant.  ...  We consider the problems of computing r-approximate traveling salesman tours and r-approximate minimum spanning trees for a set of n points in IR d , where d 1 is a constant.  ...  This algorithm ts in the algebraic computation tree model. Hence, the lower bound of Theorem 1 is tight.  ... 
doi:10.1007/3-540-62034-6_38 fatcat:uirglv2cm5dkhom3sljlzy3qly

On the Complexity of Approximating Euclidean Traveling Salesman Tours and Minimum Spanning Trees

G. Das, S. Kapoor, M. Smid
1997 Algorithmica  
In the algebraic computation tree model, the complexities of both these problems are shown to be (n log n=r), for all n and r such that r < n and r is larger than some constant.  ...  We consider the problems of computing r-approximate traveling salesman tours and r-approximate minimum spanning trees for a set of n points in IR d , where d 1 is a constant.  ...  This algorithm ts in the algebraic computation tree model. Hence, the lower bound of Theorem 1 is tight.  ... 
doi:10.1007/pl00009183 fatcat:ly5rdng3ebgefasnd7vxzvd3dm

Page 4807 of Mathematical Reviews Vol. , Issue 86j [page]

1986 Mathematical Reviews  
We show an ex- ponential lower bound on the decision tree complexity of some Boolean function having linear formula size and linear one-time- 68Q Theory of computing 86j:68048 only branching program complexity  ...  Complexity sets, 10. Matrix multiplication, 11. Bilinear transformations, 12. Complex- ity of algebras. 13. The exponent of matrix multiplication, 14. The rank and approximate rank, 15.  ... 

Computing Complex Iceberg Cubes by Multiway Aggregation and Bounding [chapter]

LienHua Pauline Chou, Xiuzhen Zhang
2004 Lecture Notes in Computer Science  
Our bounding techniques are as general as the Divide and Approximate pruning techniques for complex constraints and yet our multiway aggregation is as efficient as Star-cubing.  ...  Citation: Chou, P and Zhang, X 2004, 'Computing complex iceberg cubes by multiway aggregation and bounding', in Y Kambayashi et al. (ed.) Data Warehousing and  ...  The bounding techniques are general and can prune for complex nonmonotone constraints defined with distributive and algebraic functions.  ... 
doi:10.1007/978-3-540-30076-2_11 fatcat:fjigbfl2zvdt7fve5rrrpylxpm

A lower bound for the integer element distinctness problem

Anna Lubiw, András Rácz
1991 Information and Computation  
A lower bound of Q(n log n) is proved for the integer element distinctness problem-Given  ...  ALGEBRAIC COMPUTATION TREES In this section we carry over Theorem 5-lower bounds for rational version of problems-to the algebraic computation tree model. THEOREM 6.  ...  One of the motivations for proving lower bounds on decision/computation trees is the hope of carrying these lower bounds over to RAM?  ... 
doi:10.1016/0890-5401(91)90034-y fatcat:kikxwteekjfvhmlrav7zcj6y7y

Page 2810 of Mathematical Reviews Vol. , Issue 93e [page]

1993 Mathematical Reviews  
Frederic Green (1-CLRK) 93e:68026 68Q20 68725 Hirsch, Michael D. (1-PRIN-CS) Lower bounds for the nonlinear complexity of algebraic computation trees with integer inputs. Comput.  ...  Complexity 1 (1991), no. 3, 257-268. Summary: “A. C. C. Yao [SIAM J. Comput. 20 (1991), no. 4, 655-668; MR 92g:68042] proved some lower bounds for algebraic computation trees with integer inputs.  ... 

Page 5370 of Mathematical Reviews Vol. , Issue 94i [page]

1994 Mathematical Reviews  
Some lower and upper bounds for algebraic decision trees of various degrees are found. It is shown that over GF(2) decision trees of degree d are more powerful than trees of degree < d.  ...  Summary: “We consider the complexity of computing Boolean functions with algebraic decision trees over GF(2) and R.  ... 

Page 1848 of Mathematical Reviews Vol. , Issue 98C [page]

1998 Mathematical Reviews  
Yao [“An exponential lower bound on the size of the algebraic decision trees for MAX”, Preprint; per bibl.] have recently shown that if the degree of the query polynomials is bounded by a constant, then  ...  As for the lower bound, the problem is shown to be I}-hard.  ... 

Page 2536 of Mathematical Reviews Vol. , Issue 83f [page]

1983 Mathematical Reviews  
This elegant concept is strictly connected with obtaining the lower bounds for time complexity in models of decision trees.  ...  There are many techniques to derive lower bounds in models of linear decision trees.  ... 
« Previous Showing results 1 — 15 out of 38,908 results