A Constant-Factor Approximation Algorithm for the Geometric k -MST Problem in the Plane

We show that any rectilinear polygonal subdivision in the plane can be converted into a "guillotine" subdivision whose length is at most twice that of the original subdivision. "Guillotine" subdivisions have a simple recursive structure that allows one to search for "optimal...

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Veröffentlicht in:SIAM journal on computing Jg. 28; H. 3; S. 771 - 781
Hauptverfasser: Mitchell, Joseph S. B., Blum, Avrim, Chalasani, Prasad, Vempala, Santosh
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.1998
Schlagworte:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied mathematics
Applied sciences
Approximation
Artificial intelligence
Bank robberies
Computer science
Computer science; control theory; systems
Dynamic programming
Exact sciences and technology
Graphs
Information retrieval. Graph
Laboratories
Multiplication & division
Network management systems
Orienteering
Pattern recognition. Digital image processing. Computational geometry
Scholarships & fellowships
Theoretical computing
Traveling salesman problem
Computational geometry
Spanning tree
Algorithm complexity
Travelling salesman problem
Dynamic programming
Algorithm
Polynomial time
ISSN:0097-5397, 1095-7111
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Zusammenfassung:We show that any rectilinear polygonal subdivision in the plane can be converted into a "guillotine" subdivision whose length is at most twice that of the original subdivision. "Guillotine" subdivisions have a simple recursive structure that allows one to search for "optimal" such subdivisions in polynomial time, using dynamic programming. In particular, a consequence of our main theorem is a very simple proof that the k-MST problem in the plane has a constant-factor polynomial-time approximation algorithm: we obtain a factor of 2 (resp., 3) for the L1 metric, and a factor of $2\sqrt{2}$ (resp., 3.266) for the L2 (Euclidean) metric in the case in which Steiner points are allowed (resp., not allowed).
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ISSN:0097-5397
1095-7111
DOI:10.1137/S0097539796303299