## Geometric Shortest Paths and Network Optimization (1998)

Venue: | Handbook of Computational Geometry |

Citations: | 146 - 12 self |

### BibTeX

@INPROCEEDINGS{Mitchell98geometricshortest,

author = {Joseph S.B. Mitchell},

title = {Geometric Shortest Paths and Network Optimization},

booktitle = {Handbook of Computational Geometry},

year = {1998},

pages = {633--701},

publisher = {Elsevier Science Publishers B.V. North-Holland}

}

### Years of Citing Articles

### OpenURL

### Abstract

Introduction A natural and well-studied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to be the sum of the weights of the edges that comprise it. Efficient algorithms are well known for this problem, as briefly summarized below. The shortest path problem takes on a new dimension when considered in a geometric domain. In contrast to graphs, where the encoding of edges is explicit, a geometric instance of a shortest path problem is usually specified by giving geometric objects that implicitly encode the graph and its edge weights. Our goal in devising efficient geometric algorithms is generally to avoid explicit construction of the entire underlying graph, since the full induced graph may be very large (even exponential in the input size, or infinite). Computing an optimal