Cake cutting algorithms: be fair if you can
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Natick, Mass.
Peters
1998
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 181 S. graph. Darst. |
| ISBN: | 1568810768 |
Staff View
MARC
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| 246 | 1 | 3 | |a Cake-cutting algorithms |
| 264 | 1 | |a Natick, Mass. |b Peters |c 1998 | |
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Record in the Search Index
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\ J
Contents
Preface «
1 Fairly Dividing a Cake 1
1.1 First Things 1
1.2 On to Three Persons — A False Start 5
1.3 On to Three Persons — Successfully 7
1.4 Envy Rears Its Ugly Head 11
1.5 EXERCISES 14
2 Pieces or Crumbs — How Many Cuts Are Needed? 17
2.1 First Things — Some Agreements on Assumptions and Notation 17
2.2 One Cut Suffices 22
2.3 On to the Count 23
2.4 Using Fewer Cuts with the Divide and Conquer Algorithm . 25
2.5 Two Cuts Are Never Enough 28
2.6 What is the Best We Can Do for Four Players? 29
2.7 Other Information on the Number of Cuts 31
2.8 EXERCISES 32
V
vi CONTENTS
3 Unequal Shares 35
3.1 First Things 35
3.2 A Better Solution Leading to Ramsey Partitions 36
3.3 Cut Near-Halves Algorithm for Unequal Shares 42
3.4 More Than Two Players with Unequal Shares 45
3.5 Unequal Shares in an Irrational Ratio 46
3.6 EXERCISES 48
4 The Serendipity of Disagreement 49
4.1 First Things 49
4.2 Some Other Examples 50
4.3 EXERCISES 57
5 Some Variations on the Theme of "Fair" Division 61
5.1 Other Interpretations of "Fair" 61
5.2 Strong Fair Division 62
5.3 Envy-Free Division 65
5.4 Exact Division 68
5.5 Less is More — The Dirty Work Problem 73
5.6 Existence Theorems 75
5.7 Classes of Algorithms 76
5.8 EXERCISES 77
6 Some Combinatorial Observations 83
6.1 Applying Graph Theory to Fair Division 83
6.2 What Can Be Done with n Arbitrary Pieces? 88
6.3 EXERCISES 91
7 Interlude: An Inventory of Results 93
7.1 Algorithms for Fair Division 93
7.2 Number of Cuts for Fair Division 95
8 Impossibility Theorems 99
8.1 Resetting the Stage 99
8.2 More Than n - 1 Cuts Are Required for n Players, n 3 . 102
8.3 No Finite Algorithm Can Accomplish Exact Division 103
8.4 PROJECTS 105
CONTENTS vii
9 Attempting Fair Division with a Limited Number of Cuts 107
9.1 The Problem 107
9.2 Simple Fair Division for a Small Number of Players 108
9.3 What Can Be Done with k Cuts? 114
9.4 Divide and Conquer Revisited 120
9.5 EXERCISES 122
9.6 PROJECTS 123
10 Exact and Envy-Free Algorithms 125
10.1 Resetting the Stage 125
10.2 Near-Exact Division 126
10.3 Envy-Free Division 128
10.4 Super Envy-Free Division 136
10.5 EXERCISES 138
10.6 PROJECTS 138
11 A Return to Division for Unequal Shares 141
11.1 Resetting the Stage 141
11.2 Ramsey Partitions and Fair Division 141
11.3 Cut and Choose for Unequal Shares 145
11.4 Envy-Free Division for Three Players with Unequal Shares . . . 149
11.5 EXERCISES 154
11.6 PROJECT 154
Solutions 155
References 173
Index 179 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV024446248 |
| illustrated | Illustrated |
| indexdate | 2024-09-06T00:06:35Z |
| institution | BVB |
| isbn | 1568810768 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018422963 |
| oclc_num | 37820010 |
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| owner | DE-83 DE-188 DE-19 DE-BY-UBM |
| owner_facet | DE-83 DE-188 DE-19 DE-BY-UBM |
| physical | X, 181 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Peters |
| record_format | marc |
| spelling | Robertson, Jack 1937- Verfasser (DE-588)138721564 aut Cake cutting algorithms be fair if you can Jack Robertson ; William Webb Cake-cutting algorithms Natick, Mass. Peters 1998 X, 181 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Optimierungsproblem (DE-588)4390818-4 gnd rswk-swf Verteilter Algorithmus (DE-588)4200453-6 gnd rswk-swf Optimierungsproblem (DE-588)4390818-4 s Verteilter Algorithmus (DE-588)4200453-6 s DE-604 Webb, William 1944- Verfasser (DE-588)1037733606 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018422963&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Robertson, Jack 1937- Webb, William 1944- Cake cutting algorithms be fair if you can Optimierungsproblem (DE-588)4390818-4 gnd Verteilter Algorithmus (DE-588)4200453-6 gnd |
| subject_GND | (DE-588)4390818-4 (DE-588)4200453-6 |
| title | Cake cutting algorithms be fair if you can |
| title_alt | Cake-cutting algorithms |
| title_auth | Cake cutting algorithms be fair if you can |
| title_exact_search | Cake cutting algorithms be fair if you can |
| title_full | Cake cutting algorithms be fair if you can Jack Robertson ; William Webb |
| title_fullStr | Cake cutting algorithms be fair if you can Jack Robertson ; William Webb |
| title_full_unstemmed | Cake cutting algorithms be fair if you can Jack Robertson ; William Webb |
| title_short | Cake cutting algorithms |
| title_sort | cake cutting algorithms be fair if you can |
| title_sub | be fair if you can |
| topic | Optimierungsproblem (DE-588)4390818-4 gnd Verteilter Algorithmus (DE-588)4200453-6 gnd |
| topic_facet | Optimierungsproblem Verteilter Algorithmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018422963&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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