• Corpus ID: 11800023

Chapter 33 Backwards analysis

  title={Chapter 33 Backwards analysis},
  author={Sariel Har-Peled}
The idea of backwards analysis (or backward analysis) is a technique to analyze randomized algorithms by imagining as if it was running backwards in time, from output to input. Most of the more interesting applications of backward analysis are in Computational Geometry, but nevertheless, there are some other applications that are interesting and we survey some of them here. 



Probabilistic Algorithms

It remains to identify complexity classes that correspond to these randomized algorithms, and check how they relate to traditional classes.

Closest-Point Problems in Computational Geometry

  • M. Smid
  • Computer Science, Mathematics
    Handbook of Computational Geometry
  • 2000

Net and prune: a linear time algorithm for euclidean distance problems

We provide a general framework for getting linear time constant factor approximations (and in many cases FPTAS's) to a copious amount of well known and well studied problems in Computational

Fast C-K-R Partitions of Sparse Graphs

The main ingredient is a fast algorithm for sampling the probabilistic partitions of Calinescu, Karloff, and Rabani in sparse graphs.

Simple Randomized Algorithms for Closest Pair Problems

A conceptually simple, randomized incremental algorithm for finding the closest pair in a set of n points in D-dimensional space, where D ≥ 2 is a fixed constant that runs in O(n) expected time.

Clustering Motion

A linear time algorithm is presented for computing a 2-approximation to the k-center clustering of a set of n points in ℝd, that slightly improves the algorithm of Feder and Greene, that runs in Θ(n log k) time (which is optimal in the algebraic decision tree model).

Fast Clustering with Lower Bounds: No Customer too Far, No Shop too Small

A constant factor approximation algorithm is given for the LowerBoundedCenter problem that runs in O(n \log n) time when the input points lie in the d-dimensional Euclidean space R^d, where d is a constant.

Backwards Analysis of Randomized Geometric Algorithms

The theme of this chapter is a rather simple method that has proved very potent in the analysis of the expected performance of various randomized algorithms and data structures in computational

On the greedy permutation and counting distances

  • On the greedy permutation and counting distances
  • 2014

Probabilistic algorithms Algorithms and Complexity: New Directions and Recent Results

  • Probabilistic algorithms Algorithms and Complexity: New Directions and Recent Results
  • 1976