A Surjective Mapping from Permutations to Room-to-Room Floorplans

Fujimaki, Ryo; Takahashi, Toshihiko

doi:10.1093/ietfec/e90-a.4.823

Cited by 6 publications

(4 citation statements)

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“…, G p of the edges of the embedded graph G in the proof of Theo- Floorplanning is a fundamental issue in circuit layout [106,43,69,62,51,108,32,8,17,58,24,57,91,68,84,4]. Motivated by VLSI physical design, various representations of floorplans were proposed [110,109,33]. Designing a floorplan to meet a certain criterion is NP-complete in general [87,44,100], so heuristic techniques such as simulated annealing [102,101,17] are practically useful.…”

Section: Related Workmentioning

confidence: 99%

Linear-Time Compression of Bounded-Genus Graphs into Information-Theoretically Optimal Number of Bits

Lu¹

2014

SIAM J. Comput.

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A compression scheme A for a class G of graphs consists of an encoding algorithm Encode A that computes a binary string Code A (G) for any given graph G in G and a decoding algorithm Decode A that recovers G from Code A (G). A compression scheme A for G is optimal if both Encode A and Decode A run in linear time and the number of bits of Code A (G) for any n-node graph G in G is information-theoretically optimal to within lower-order terms. Trees and plane triangulations were the only known nontrivial graph classes to admit optimal compression schemes. Based upon Goodrich's separator decomposition for planar graphs and Djidjev and Venkatesan's planarizers for bounded-genus graphs, we give an optimal compression scheme for any hereditary (i.e., closed under taking subgraphs) class G under the premise that any n-node graph of G to be encoded comes with a genus-o( n log 2 n ) embedding. By Mohar's linear-time algorithm that embeds a bounded-genus graph on a genus-O(1) surface, our result implies that any hereditary class of genus-O(1) graphs admits an optimal compression scheme. For instance, our result yields the first-known optimal compression schemes for planar graphs, plane graphs, graphs embedded on genus-1 surfaces, graphs with genus 2 or less, 3-colorable directed plane graphs, 4-outerplanar graphs, and forests with degree at most 5. For nonhereditary graph classes, we also give a methodology for obtaining optimal compression schemes. From this methodology, we give the first-known optimal compression schemes for triangulations of genus-O(1) surfaces and floorplans.

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Section: Related Workmentioning

confidence: 99%

Linear-Time Compression of Bounded-Genus Graphs into Information-Theoretically Optimal Number of Bits

Lu¹

2014

SIAM J. Comput.

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“…FT Squeeze [5] FT Squeeze can represent any rec-dissection of n rooms by a permutation II of size TI [5], and can be decoded in O(n) time [6], [7].…”

Section: Rectangular Dissectionmentioning

confidence: 99%

“…In a few years, 2.5-dimensional FT Squeeze [8], which is ob tained by expanding FT Squeeze [5] and represents stacked-recdissection with a permutation and a sequence, was proposed.…”

Section: Introductionmentioning

confidence: 99%

A novel representation for 3D-LSI floorplan: Merged FT Squeeze

Ohta

Fujiyoshi

2012

2012 IEEE 3rd Latin American Symposium on Circuits and Systems (LASCAS)

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Since semiconductor manufacturing technology has improved, LSIs which consist of several silicon chips (silicon layers) have been put to practical use. Then, signal delay and power consumption are reduced, because wires on different silicon layers are connected each other by bonding wires in the LSI. To reduce signal delay and power consumption further, Through Silicon Via (TSV), which connects wires on adjacent silicon layers as penetration wiring instead of bonding wires, is investigated actively. And it will come into practical use in several years. To make floorplans with considering positions of TSVs, representation of floorplans which implies positional relation of modules on different silicon layers, is required. In this paper, we propose a new representation for three-dimensional floorplans, inspired by FT Squeeze, representation of two-dimensional floorplans. Effectiveness of the proposed representation is confirmed by experiments.

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“…For application in VLSI physical design, several encodings of rectangular drawings have been published: For example, H-Sequence [2], EQ-Sequence [3], FT-Squeeze [5], and so on. The bit length of codes is a mesure of encoding schemes [4].…”

Section: Introductionmentioning

confidence: 99%

A Compact Code for Rectangular Drawings with Degree Four Vertices

Takahashi

2014

Journal of Information Processing

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A subdivision of a rectangle into rectangular faces with horizontal and vertical line segments is called a rectangular drawing or floorplan. Several encodings of rectangular drawings have been published; however, most of them deal with rectangular drawings without vertices of degree four. Recently, Saito and Nakano developed two compact encodings for general rectangular drawings, that is, which allows vertices of degree four. The two encodings respectively need 6 f − 2n 4 + 6 bits and 5 f − 5 bits for rectangular drawings with f inner faces and n 4 degree four vertices. The best encoding of the two depends on the number of vertices of degree four, that is, the former is the better if 2n 4 > f + 11; otherwise the latter is the better. In this paper, we propose a new encoding of general rectangular drawings with 5 f − n 4 − 6 bits for f ≥ 2, which is the most compact regardless of n 4 .

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A Surjective Mapping from Permutations to Room-to-Room Floorplans

Cited by 6 publications

References 0 publications

Linear-Time Compression of Bounded-Genus Graphs into Information-Theoretically Optimal Number of Bits

Linear-Time Compression of Bounded-Genus Graphs into Information-Theoretically Optimal Number of Bits

A novel representation for 3D-LSI floorplan: Merged FT Squeeze

A Compact Code for Rectangular Drawings with Degree Four Vertices

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