Cake-Cutting Algorithms: Be Fair if You Can / Edition 1

by Jack Robertson, William Webb

Overview

The challenge of dividing an asset fairly, from cakes to more important properties, is of great practical importance in many situations. Since the famous Polish school of mathematicians (Steinhaus, Banach, and Knaster) introduced and described algorithms for the fair division problem in the 1940s, the concept has been widely popularized.

This book gathers into one readable and inclusive source a comprehensive discussion of the state of the art in cake-cutting problems for both the novice and the professional. It offers a complete treatment of all cake-cutting algorithms under all the considered definitions of "fair" and presents them in a coherent, reader-friendly manner. Robertson and Webb have brought this elegant problem to life for both the bright high school student and the professional researcher.

Product Details

ISBN-13:	9781568810768
Publisher:	Taylor & Francis
Publication date:	07/15/1998
Edition description:	New Edition
Pages:	177
Product dimensions:	6.00(w) x 9.00(h) x (d)

About the Author

Jack Robertson, William Webb

Table of Contents

Preface 1 Fairly Dividing a Cake 2 Pieces or Crumbs - How Many Cuts Are Needed? 3 Unequal Shares 4 The Serendipity of Disagreement 5 Some Variations on the Theme of ''Fair'' Division 6 Some Combinatorial Observations 7 Interlude: An Inventory of Results 8 Impossibility Theorems 9 Attempting Fair Division with a Limited Number of Cuts 10 Exact and Envy-Free Algorithms 11 A Return to Division for Unequal Shares

What People are Saying About This

From the Publisher

Cake-Cutting Algorithms will engage and challenge both veteran and novice mathematicians...
— Francis Edward Su, American Mathematical Monthly , March 2000

Editorial Reviews

Cake-Cutting Algorithms will engage and challenge both veteran and novice mathematicians...
— Francis Edward Su, American Mathematical Monthly , March 2000

From the Publisher

Examines the many definitions of "fair division" that have been proposed throughout the years and what is known about cake-cutting algorithms as they apply to these definitions. The first seven chapters provide a leisurely survey of the problem, written with the novice in mind, without mathematical formalism. The final four chapters, for the non-casual reader, contain the technical details of proofs for the previous chapters. Exercises and projects are included in most of the chapters and the solutions for all of the exercises are included. Annotation c. by Book News, Inc., Portland, Or.

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