Book contents
- Frontmatter
- Contents
- Preface
- List of contributors
- 1 Revitalizing the Study of Kinship and Exchange with Network Approaches
- I Representing Kinship Dynamics, Material Flow, and Economic Cooperation
- II Individual Embeddedness and the Larger Structure of Kinship and Exchange Networks
- III Marriage, Exchange, and Alliance: Reconsidering Bridewealth and Dowry
- IV Emergence, Development, and Transformation of Kin-Based Exchange Systems
- 12 Applications of the Minimum Spanning Tree Problem to Network Analysis
- 13 Local Rules and Global Structures: Models of Exclusive Straight Sister-Exchange
- 14 The Capacity and Constraints of Kinship in the Development of the Enga Tee Ceremonial Exchange Network (Papua New Guinea Highlands)
- 15 Between War and Peace: Gift Exchange and Commodity Barter in the Central and Fringe Highlands of Papua New Guinea
- Index
12 - Applications of the Minimum Spanning Tree Problem to Network Analysis
Published online by Cambridge University Press: 05 November 2011
- Frontmatter
- Contents
- Preface
- List of contributors
- 1 Revitalizing the Study of Kinship and Exchange with Network Approaches
- I Representing Kinship Dynamics, Material Flow, and Economic Cooperation
- II Individual Embeddedness and the Larger Structure of Kinship and Exchange Networks
- III Marriage, Exchange, and Alliance: Reconsidering Bridewealth and Dowry
- IV Emergence, Development, and Transformation of Kin-Based Exchange Systems
- 12 Applications of the Minimum Spanning Tree Problem to Network Analysis
- 13 Local Rules and Global Structures: Models of Exclusive Straight Sister-Exchange
- 14 The Capacity and Constraints of Kinship in the Development of the Enga Tee Ceremonial Exchange Network (Papua New Guinea Highlands)
- 15 Between War and Peace: Gift Exchange and Commodity Barter in the Central and Fringe Highlands of Papua New Guinea
- Index
Summary
From a mathematical perspective many problems in anthropology concerned with the analysis of structures, patterns, and configurations are combinatorial in nature. There are three types of combinatorial problems:
The existence problem asks, “Is there a structure of a certain type?”
The counting problem asks, “How many such structures are there?”
The optimization problem asks, “Which is the best structure according to some criterion?” (Roberts 1984).
The minimum spanning tree problem (MSTP) is an optimization problem, well known in many fields; its history is detailed in Graham and Hell (1985). The problem has applications to the design of all kinds of networks, including communication, computer, transportation, and other flow networks. It also has applications to problems of network reliability and classification, among many others. Our purpose here is to describe some applications of the MSTP to anthropology – in particular to problems of size, clustering, and simulation in networks of various kinds. We proceed by presenting in a unified format the three standard MST algorithms of Kruskal (1956), Prim (1957), and Boruvka (1926a,b), describing the advantages and some of the applications of each one.
We first illustrate the MSTP intuitively, as follows. A large corporation with offices in many cities, v1, …, vn, wishes to determine the monthly telephone charge. All the distances d(vi, vj) are known and are distinct.
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- Kinship, Networks, and Exchange , pp. 251 - 260Publisher: Cambridge University PressPrint publication year: 1998