Data Structures and Algorithms 1

The design and analysis of data structures and efficient algorithms has gained considerable importance in recent years. The concept of "algorithm" is central in computer science, and "efficiency" is central in the world of money. I have organized the material in three volumes and nine chapters. Vol. 1: Sorting and Searching (chapters I to III) Vol. 2: Graph Algorithms and NP-completeness (chapters IV to VI) Vol. 3: Multi-dimensional Searching and Computational G- metry (chapters VII and VIII) Volumes 2 and 3 have volume 1 as a common basis but are indepen dent from each other. Most of volumes 2 and 3 can be understood without knowing volume 1 in detail. A general kowledge of algorith mic principles as laid out in chapter 1 or in many other books on algorithms and data structures suffices for most parts of volumes 2 and 3. The specific prerequisites for volumes 2 and 3 are listed in the prefaces to these volumes. In all three volumes we present and analyse many important efficient algorithms for the fundamental computa tional problems in the area. Efficiency is measured by the running time on a realistic model of a computing machine which we present in chapter I. Most of the algorithms presented are very recent inven tions; after all computer science is a very young field. There are hardly any theorems in this book which are older than 20 years and at least fifty percent of the material is younger than 10 years.

I. Foundations.- 1. Machine Models: RAM and RASP.- 2. Randomized Computations.- 3. A High Level Programming Language.- 4. Structured Data Types.- 5. Recursion.- 6. Order of Growth.- 7. Secondary Storage.- 8. Exercises.- 9. Bibliographic Notes.- II. Sorting.- 1. General Sorting Methods.- 2. Sorting by Distribution.- 3. The Lower Bound on Sorting, Revisited.- 4. The Linear Median Algorithm.- 5. Exercises.- 6. Bibliographic Notes.- III. Sets.- 1. Digital Search Trees.- 2. Hashing.- 3. Searching Ordered Sets.- 4. Weighted Trees.- 5. Balanced Trees.- 6. Dynamic Weighted Trees.- 7. A Comparison of Search Structures.- 8. Subsets of a Small Universe.- 9. Exercises.- 10. Bibliographic Notes.- IX. Algorithmic Paradigms.