Quicksort and Randomized Incremental Constructions

Limited Randomness

7 A Sketch of a Research Immersion Lab/Master Thesis: Randomized Algorithms with Limited Randomness 7 7.1 Experimental Work: Quicksort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 7.2 Experimental Work: Randomized Incremental Constructions . . . . . . . . . . . . . . . . 7 7.3 Theoretical Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Four Results on Randomized Incremental Constructions

Raimund Seidel§ We prove four results on randomized incremental constructions (RIes): • an analysis of the expected behavior under insertion and deletions, • a fully dynamic data structure for convex hull mamtenance in arbitrary dimensions, • a tail estimate for the space complexity of RIes, • a lower bound on the complexity of agame related to RIes.

Blocked Randomized Incremental Constructions

Randomized incremental constructions are widely used in computational geometry, but they perform very badly on large data because of their inherently random memory access patterns. We define an insertion order which removes enough randomness to significantly improve performance, but leaves enough randomness so that the algorithms remain theoretically optimal.

A Noble Randomized Quicksort with a Random Number Generator

Sorting is a well-known computational problem. Sorting means arranging a set of records (or a list of keys) in some (increasing or decreasing) order. Randomized algorithms often have low complexity and are associated to robustness bounds, which are generally less conservative than the classical ones. This paper presents a noble randomized Quicksort with a random number generator. This randomize...

Chapter 13 Introduction to Randomized Algorithms: QuickSort and QuickSelect