Cake-Cutting Algorithms: Be Fair if You Can

by Robertson, Jack

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Title Statements

Full title :Cake-Cutting Algorithms : Be Fair if You Can.

Edition Statements

Publication Date:1998.

Publication Statements

Publisher(s):Chapman and Hall/CRC
Place of Publication:Natick
Language:eng
Publication Date:1998.

Notes

Includes index.

The Physical Object

Description:1 online resource (192 pages)

Edition Identifiers

ISBN:9781439863855, 1439863857
oclc:on1035519065
LC Classification:T57.6.R63 1998
Dewey Decimal:511.6

Cover; Half Title; Title Page; Copyright Page; Table of Contents; Preface; 1: Fairly Dividing a Cake; 1.1 First Things; 1.2 On to Three Persons -- A False Start; 1.3 On to Three Persons -- Successfully; 1.4 Envy Rears Its Ugly Head; 1.5 EXERCISES; 2: Pieces or Crumbs -- How Many Cuts Are Needed?; 2.1 First Things -- Some Agreements on Assumptions and Notation; 2.2 One Cut Suffices; 2.3 On to the Count; 2.4 Using Fewer Cuts with the Divide and Conquer Algorithm; 2.5 Two Cuts Are Never Enough; 2.6 What is the Best We Can Do for Four Players?; 2.7 Other Information on the Number of Cuts.

2.8 EXERCISES3: Unequal Shares; 3.1 First Things; 3.2 A Better Solution Leading to Ramsey Partitions; 3.3 Cut Near-Halves Algorithm for Unequal Shares; 3.4 More Than Two Players with Unequal Shares; 3.5 Unequal Shares in an Irrational Ratio; 3.6 EXERCISES; 4: The Serendipity of Disagreement; 4.1 First Things; 4.2 Some Other Examples; 4.3 EXERCISES; 5: Some Variations on the Theme of "Fair" Division; 5.1 Other Interpretations of "Fair"; 5.2 Strong Fair Division; 5.3 Envy-Free Division; 5.4 Exact Division; 5.5 Less is More -- The Dirty Work Problem; 5.6 Existence Theorems.

5.7 Classes of Algorithms5.…