Efficient Generation of Plane Triangulations without Repetitions

Li, Zhangjian; Nakano, Shin-ichi

doi:10.1007/3-540-48224-5_36

Cited by 37 publications

(34 citation statements)

References 7 publications

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“…The algorithm uses O(m) space and generates such graphs in O (1) time per graph on average without duplications. Li and Nakano [6] presented an efficient algorithm that enumerates all biconnected rooted triangulated plane graphs in constant time per each. Nakano [11] presented an algorithm with the same time complexity to generate all triconnected rooted triangulated plane graphs.…”

Section: Introductionmentioning

confidence: 99%

Listing Triconnected Rooted Plane Graphs

Zhuang

Nagamochi

2010

Combinatorial Optimization and Applications

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A plane graph is a drawing of a planar graph in the plane such that no two edges cross each other. A rooted plane graph has a designated outer vertex. For given positive integers n ≥ 1 and g ≥ 3, let G 3 (n, g) denote the set of all triconnected rooted plane graphs with exactly n vertices such that the size of each inner face is at most g. In this paper, we give an algorithm that enumerates all plane graphs in G 3 (n, g). The algorithm runs in constant time per each by outputting the difference from the previous output.

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Section: Introductionmentioning

confidence: 99%

Listing Triconnected Rooted Plane Graphs

Zhuang

Nagamochi

2010

Combinatorial Optimization and Applications

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“…The algorithm does not output entire triangulations but the difference from the previous triangulation. The algorithm of [LN01] generates all based triangulations as follows. Given n and r, we first define a tree T such that the inner vertices of T correspond to the biconnected based plane triangulations having at most n − 1 vertices including at most n − r inner vertices, the leaves of T correspond to the biconnected based plane triangulations having exactly n vertices including exactly r vertices on the outer face, and the edges of T correspond to some relation between the biconnected based plane triangulations.…”

Section: Introductionmentioning

confidence: 99%

“…By modifying the algorithm, we can also generate without duplications all biconnected (non-based) plane triangulations having exactly n vertices including exactly r vertices on the outer face in O(r 2 n) time per triangulation on average [LN01]. If we maintain output triangulations in a database to avoid the duplication, then the space complexity will be exponential.…”

Section: Introductionmentioning

confidence: 99%

“…So to obtain an efficient algorithm, we have to check the occurrence of duplication without any database, hence this is a non-trivial modification. Another algorithm with O(n 2 ) time per triangulation is also claimed in [M98] without detail but using a complicated theoretical linear-time plane graph isomorphism algorithm [HW74], while the algorithm in [LN01] is simple and does not need the isomorphism algorithm.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, we proposed an algorithm to generate all biconnected "based" plane triangulations having exactly n vertices including exactly r vertices on the outer face [LN01]. A based plane triangulation means a plane triangulation with one designated "base" edge on the outer face.…”

Section: Introductionmentioning

confidence: 99%

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More Efficient Generation of Plane Triangulations

Nakano

Uno

2004

Graph Drawing

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Listing all rectangular drawings with certain properties

Takagi

Nakano

2004

Systems & Computers in Japan

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SUMMARYA plane drawing of a plane graph is called a rectangular drawing if every face (including the outer face) is a rectangle. An algorithm to generate all based rectangular drawings with maximum degree three is known. In this paper by generalizing the algorithm we give a simple algorithm to generate all based rectangular drawings having n faces without the degree constraint. The algorithm generates without duplications all rectangular drawings having exactly n faces in O(n) time per drawing. By modifying the algorithm we give three more algorithms to generate all rectangular drawings with certain properties. Those algorithms use O(n) space in total.

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Efficient Generation of Plane Triangulations without Repetitions

Cited by 37 publications

References 7 publications

Listing Triconnected Rooted Plane Graphs

Listing Triconnected Rooted Plane Graphs

More Efficient Generation of Plane Triangulations

Listing all rectangular drawings with certain properties

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