The quarter-state-sequence floorplan representation

Sakanushi, Keishi; Kajitani, Yoji; Mehta, Dinesh P.

doi:10.1109/tcsi.2003.809442

Cited by 36 publications

(10 citation statements)

References 22 publications

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“…In [13], a representation called quarter-state-sequence (QSS) was presented. It uses a Q sequence that represents the configuration of one of the corners of the mosaic floorplan.…”

Section: Mosaic Floorplansmentioning

confidence: 99%

A simple optimal binary representation of mosaic floorplans and Baxter permutations

2014

Theoretical Computer Science

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A floorplan is a rectangle subdivided into smaller rectangular sections by horizontal and vertical line segments. Each section in the floorplan is called a block. Two floorplans are considered equivalent if and only if there is a one-to-one correspondence between the blocks in the two floorplans such that the relative position relationship of the blocks in one floorplan is the same as the relative position relationship of the corresponding blocks in another floorplan. The objects of Mosaic floorplans are the same as floorplans, but an alternative definition of equivalence is used. Two mosaic floorplans are considered equivalent if and only if they can be converted to each other by sliding the line segments that divide the blocks.Mosaic floorplans are widely used in VLSI circuit design. An important problem in this area is to find short binary string representations of the set of n-block mosaic floorplans. The best known representation is the Quarter-State Sequence which uses 4n bits. This paper introduces a simple binary representation of n-block mosaic floorplan using 3n − 3 bits. It has been shown that any binary representation of n-block mosaic floorplans must use at least (3n − o(n)) bits. Therefore, the representation presented in this paper is optimal (up to an additive lower order term).Baxter permutations are a set of permutations defined by prohibited subsequences. Baxter permutations have been shown to have one-to-one correspondences to many interesting objects in the so-called Baxter combinatorial family. In particular, there exists a simple one-to-one correspondence between mosaic floorplans and Baxter permutations. As a result, the methods introduced in this paper also lead to an optimal binary representation of Baxter permutations and all objects in the Baxter combinatorial family.

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“…In [13], a representation called quarter-state-sequence (QSS) was presented. It uses a Q sequence that represents the configuration of one of the corners of the mosaic floorplan.…”

Section: Mosaic Floorplansmentioning

confidence: 99%

A simple optimal binary representation of mosaic floorplans and Baxter permutations

2014

Theoretical Computer Science

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“…Associated rooms of room 6 are room 8, 7, and room 7 which is left-most room among these rooms becomes the next room of room 6. We can identify the sequence of rooms tracing the next rooms, and we name this sequence Abe order [7]. In this paper, we define the i-th room of Abe order as i, and it's right-bottom prime seg as seg i.…”

Section: Segment-state Sequence 21 Preliminariesmentioning

confidence: 99%

S-sequence: a new floorplan representation method preserving room abutment relationships

Ishimaru

Sakanushi

Kobayashi

et al.

2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512)

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In this paper, we propose Segment-State Sequence (S-sequence), a new encoding method of floorplan with different abutment relationships between rooms. As one of the availability of proposed method, we present necessary and sufficient conditions to abut two modules facing to the same segment partitioning a floorplan, and an abutment judgment which checks whether pairs of modules abut on the floorplan or not by using S-sequence. Since our algorithm checks abutment relationships of the rooms before decoding, we need not decode S-sequence which does not meet abutment constraints in Simulated Annealing process. Consequently, we can optimize floorplan satisfying abutment constraints rapidly. In experiments, we implemented floorplan optimization algorithm with S-sequence and abutment judgment method, and the results show that the proposed algorithm optimized floorplan satisfying abutment constraints rapidly.

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“…For Abe-labelling and related properties, we refer to [20]. An important feature of Abe-labelling is that every room is visited exactly once and ends at the bottom-right room so that every room has a unique Abe-label.…”

Section: T-junction Floorplan and Codingmentioning

confidence: 99%

“…[4], BSG [6,7] in 1994 is considered the first success. Various ABLR-system generators followed: SP [5] and TCG [13] for general topological structures, O-tree [9] and B*-tree [12] for topology and physical dimension mixed structures, Q-seq [10,20] and CBL [11] and Prime-graph [15] for T-junction floorplans.…”

Section: Introductionmentioning

confidence: 99%

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Theory of T-junction floorplans in terms of single-sequence

Zhang¹,

Kajitani²

2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512)

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In a placement, two rectangles on a plane are non-overlapping if and only if the relationship between them is one of ABLR (above, below, left-of, right-of)-relations. From the standpoint that a system of ABLR-relations is specified by the designer to confine the placement, the first concern is its consistency, i.e. if there is a corresponding placement. The second is an efficient way to construct a corresponding placement. The third is a handy coding of the ABLR-system all the way. In this paper, the first concern is solved by an existence condition of the primal-and dual-orders of rectangles. The second is answered by a linear time construction algorithm of a T-junction floorplan. This is new in its speed and generality with respect to the number of rooms. The third is by a new coding Single-Sequence SS. Its unique suitability to handle the T-junction floorplan is remarkable. Using the merit that SS can control the distribution of empty rooms, a novel application is suggested to space-planning, a recent trend in VLSI physical design to budget the space for congestion relief and interference separation (though the detail is not contained here for the space).

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The quarter-state-sequence floorplan representation

Cited by 36 publications

References 22 publications

A simple optimal binary representation of mosaic floorplans and Baxter permutations

A simple optimal binary representation of mosaic floorplans and Baxter permutations

S-sequence: a new floorplan representation method preserving room abutment relationships

Theory of T-junction floorplans in terms of single-sequence

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