A Linear Algorithm for Analysis of Minimum Spanning and Shortest Path Trees of Planar Graphs

A Linear Algorithm for Analysis of Minimum Spanning and Shortest Path Trees of Planar Graphs (1992)

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by Heather Booth , Jeffery Westbrook

Venue:	Algorithmica
Citations:	16 - 0 self

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Datum	Value	Source
TITLE	A Linear Algorithm for Analysis of Minimum Spanning and Shortest Path Trees of Planar Graphs	user correction - Legacy Corrections
AUTHOR NAME	Heather Booth	user correction - Legacy Corrections
AUTHOR AFFIL	y	user correction - Legacy Corrections
AUTHOR NAME	Jeffery Westbrook	user correction - Legacy Corrections
AUTHOR AFFIL	; z; Department of Computer Science, University of Tennessee, Knoxville; Department of Computer Science, Yale University, New Haven; was done while the author was at the Department of Computer Science	user correction - Legacy Corrections
AUTHOR ADDR	; TN 37996. This research; Princeton, NJ 08544.	user correction - Legacy Corrections
ABSTRACT	We give a linear time and space algorithm for analyzing trees in planar graphs. The algorithm can be used to analyze the sensitivity of a minimum spanning tree to changes in edge costs, to find its replacement edges, and to verify its minimality. It can also be used to analyze the sensitivity of a singlesource shortest path tree to changes in edge costs, and to analyze the sensitivity of a minimum cost network flow. The algorithm is simple and practical. It uses the properties of a planar embedding, combined with a heap-ordered queue data structure. Let G = (V; E) be a planar graph, either directed or undirected, with n vertices and m = O(n) edges. Each edge e 2 E has a real-valued cost cost(e). A minimum spanning tree of a connected, undirected planar graph G is a spanning tree of minimum total edge cost. If G is directed and r is a vertex from which all other vertices are reachable, then a shortest path tree from r is a spanning tree that contains a minimum-cost path from r to every...	user correction - Legacy Corrections
YEAR	1992	user correction - Legacy Corrections
VENUE	Algorithmica	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	341--352	INFERENCE
VOLUME	11	INFERENCE
TECH	Technical Report YALEU/DCS/TR-763	INFERENCE
CITATIONS	20 found	ParsCit 1.0