Planar Straight Line Graphs

Authored by: Siu-Wing Cheng

Handbook of Data Structures and Applications

Print publication date:  March  2018
Online publication date:  February  2018

Print ISBN: 9781498701853
eBook ISBN: 9781315119335
Adobe ISBN:

10.1201/9781315119335-18

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Abstract

Graphs (Chapter 4) have found extensive applications in computer science as a modeling tool. In mathematical terms, a graph is simply a collection of vertices and edges. Indeed, a popular graph data structure is the adjacency lists representation [1] in which each vertex keeps a list of vertices connected to it by edges. In a typical application, the vertices model entities and an edge models a relation between the entities corresponding to the edge endpoints. For example, the transportation problem calls for a minimum cost shipping pattern from a set of origins to a set of destinations [2]. This can be modeled as a complete directed bipartite graph. The origins and destinations are represented by two columns of vertices. Each origin vertex is labeled with the amount of supply stored there. Each destination vertex is labeled with the amount of demand required there. The edges are directed from the origin vertices to the destination vertices and each edge is labeled with the unit cost of transportation. Only the adjacency information between vertices and edges are useful and captured, apart from the application dependent information.

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