Maximum independent set for intervals by divide and conquer with pruning

Suppose a given set of n intervals contains a maximum independent set of k disjoint intervals. This brief note demonstrates that “divide and conquer with pruning” produces an easy, output‐sensitive O(n log k)‐time algorithm to compute such a maximum independent set. © 2006 Wiley Periodicals, Inc. NE...

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Vydáno v:Networks Ročník 49; číslo 2; s. 158 - 159
Hlavní autor: Snoeyink, Jack
Médium: Journal Article
Jazyk:angličtina
Vydáno: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.03.2007
John Wiley & Sons
Témata:
Applied sciences
Computer science; control theory; systems
Computer systems and distributed systems. User interface
divide and conquer
Exact sciences and technology
interval graph
maximum independent set
output-sensitive algorithm
Software
Interval graph
Filtering
Independent set
Pruning(tree)
divide and conquer
maximum independent set
Divide and conquer method
output- sensitive algorithm
ISSN:0028-3045, 1097-0037
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Abstract Suppose a given set of n intervals contains a maximum independent set of k disjoint intervals. This brief note demonstrates that “divide and conquer with pruning” produces an easy, output‐sensitive O(n log k)‐time algorithm to compute such a maximum independent set. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 49(2), 158–159 2007
AbstractList Suppose a given set of n intervals contains a maximum independent set of k disjoint intervals. This brief note demonstrates that “divide and conquer with pruning” produces an easy, output‐sensitive O ( n log k )‐time algorithm to compute such a maximum independent set. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 49(2), 158–159 2007
Suppose a given set of n intervals contains a maximum independent set of k disjoint intervals. This brief note demonstrates that “divide and conquer with pruning” produces an easy, output‐sensitive O(n log k)‐time algorithm to compute such a maximum independent set. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 49(2), 158–159 2007
Author Snoeyink, Jack
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Issue 2
Keywords Interval graph
Filtering
Independent set
Pruning(tree)
divide and conquer
maximum independent set
Divide and conquer method
output- sensitive algorithm
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References S. Masuda, K. Nakajima, An optimal algorithm for finding a maximum independent set of a circular-arc graph, SIAM J Comput 17 ( 1988), 41-52.
G. K. Manacher, T. A. Mankus, A simple linear time algorithm for finding a maximum independent set of circular arcs using intervals alone, Networks 39(2) ( 2002), 68-72.
U. I. Gupta, D. T. Lee, J. Y.-T. Leung, Efficient algorithms for interval graphs and circular-arc graphs, Networks 12 ( 1982), 459-467.
H. Edelsbrunner, W. Shi, An O(n log 2h) time algorithm for the three-dimensional convex hull problem, SIAM J Comput 20 ( 1991), 259-277.
1982; 12
1997
2002; 39
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– reference: U. I. Gupta, D. T. Lee, J. Y.-T. Leung, Efficient algorithms for interval graphs and circular-arc graphs, Networks 12 ( 1982), 459-467.
– reference: S. Masuda, K. Nakajima, An optimal algorithm for finding a maximum independent set of a circular-arc graph, SIAM J Comput 17 ( 1988), 41-52.
– reference: G. K. Manacher, T. A. Mankus, A simple linear time algorithm for finding a maximum independent set of circular arcs using intervals alone, Networks 39(2) ( 2002), 68-72.
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  start-page: 459
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  start-page: 259
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  end-page: 277
  article-title: An ( log ) time algorithm for the three‐dimensional convex hull problem
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  start-page: 68
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  article-title: A simple linear time algorithm for finding a maximum independent set of circular arcs using intervals alone
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Snippet Suppose a given set of n intervals contains a maximum independent set of k disjoint intervals. This brief note demonstrates that “divide and conquer with...
Suppose a given set of n intervals contains a maximum independent set of k disjoint intervals. This brief note demonstrates that “divide and conquer with...
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SubjectTerms Applied sciences
Computer science; control theory; systems
Computer systems and distributed systems. User interface
divide and conquer
Exact sciences and technology
interval graph
maximum independent set
output-sensitive algorithm
Software
Title Maximum independent set for intervals by divide and conquer with pruning
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