## 139 Citations

### Lower Bounds on Algebraic Random Access Machines (Extended Abstract)

- MathematicsICALP
- 1995

We prove general lower bounds for set recognition on random access machines (RAMs) that operate on real numbers with algebraic operations {+, −, ×, /}, as well as RAMs that use the operations {+, −,…

### On the complexity of computing the measure of ∪[ai,bi]

- Computer ScienceCACM
- 1978

The decision tree complexity of computing the measure of the union of n (possibly overlapping) intervals is shown to be &OHgr;(n log n), even if comparisons between linear functions of the interval…

### How Good Is the Adversary Lower Bound?

- MathematicsMFCS
- 1977

The relationship between adversary argument and so called information theory argument is indicated and the efficiency of adversary argument relative to the type of comparisons involved in the computation of a problem is investigated.

### Topological Lower Bounds in Complexity Theory

- Computer Science, Mathematics
- 2015

This thesis shows that c′(n,k) ≥ n log₃(n/6k) of the k-of-EACH PROBLEM on n elements, and improves upon a lower bound, due to Linusson [12], on the linear decision tree complexity.

### An exponential lower bound on the size of algebraic decision trees for Max

- Mathematics, Computer Sciencecomputational complexity
- 1998

The proof gives an exponential lower bound on the size of the polyhedral decision problem MAX= for testing whether the j-th number is the maximum among a list of n real numbers.

### A Survey of Analysis Techniques for Discrete Algorithms

- Computer ScienceCSUR
- 1977

This survey includes an introduction to the concepts of problem complexity, analysis of algorithms to find bounds on complexity, average-case behavior, and approximation algomthms The major techmques…

### Applications of Ramsey's Theorem to Decision Trees Complexity (Preliminary Version)

- Computer Science, MathematicsFOCS
- 1984

It is proved that the queries of any k-bounded decision tree that solves an order invariant problem over a large enough input dornain can be replaced with k- bounded queries whose outcome depends only on the relative order of the inputs.

## References

SHOWING 1-10 OF 18 REFERENCES

### A Lower Bound of the ½n² on Linear Search Programs for the Knapsack Problem

- Computer Science, MathematicsJ. Comput. Syst. Sci.
- 1978

### Lower bounds on the size of Boolean formulas: Preliminary Report

- Computer ScienceSTOC
- 1975

It is shown that every Boolean expression for C(n)k, allowing all of the 16 binary connectives, has size exceeding &egr;n log n/log log n, &egR;> 0.

### Computing the Maximum and the Median

- MathematicsSWAT
- 1971

The new results are: (a) the maximum of a set of n integers cannot be computed in fewer than n-1 comparisons if comparisons of only linear functions of the integers are permitted, but the maximum can be compute in log2 n comparisons.

### A Lower Bound on the Number of Additions in Monotone Computations

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1976

### Depth-First Search and Linear Graph Algorithms

- MathematicsSIAM J. Comput.
- 1972

The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components…

### On some generalizations of binary search

- Computer ScienceSTOC '74
- 1974

Applications of these new search methods to an open problem in the theory of computation are discussed yielding new insight into the Lba problem.

### Gaussian elimination is not optimal

- Mathematics
- 1969

t. Below we will give an algorithm which computes the coefficients of the product of two square matrices A and B of order n from the coefficients of A and B with tess than 4 . 7 n l°g7 arithmetical…

### Convex Polytopes

- MathematicsThe Mathematical Gazette
- 1969

Graphs, Graphs and Realizations Before proceeding to the graph version of Euler’s formula, some notation will be introduced. A (finite) abstract graph G consists of two sets, the set of vertices V =…

### Algebraic Geometry

- MathematicsNature
- 1973

Introduction to Algebraic Geometry.By Serge Lang. Pp. xi + 260. (Addison–Wesley: Reading, Massachusetts, 1972.)