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On optimal irregular switch box designs
 in Field Programmable Logic and Application
, 2004
"... Abstract. In this paper, we develop a unified theory in analyzing optimal switch box design problems, particularly for the unsolved irregular cases, where different pin counts are allowed on different sides. The results drawn from our system of linear Diophantine equations based formulation turn ou ..."
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Abstract. In this paper, we develop a unified theory in analyzing optimal switch box design problems, particularly for the unsolved irregular cases, where different pin counts are allowed on different sides. The results drawn from our system of linear Diophantine equations based formulation turn out to be general. We prove that the divideandconquer (reduction) design methodology can also be applied to the irregular cases. Namely, an optimal arbitrarily large irregular or regular switch box can be obtained by combining small prime switch boxes, which largely reduces the design complexity. We revise the known VPR router for our experiments and show that the design optimality of switch boxes does pay off.
4 logic cell
"... Abstract A switch block with k sides and W terminals per side ((k � W)SB) is said to be universal if every set of 2pin nets satisfying the dimension constraint is simultaneously routable through the switch block. It has been shown that the universal switch blocks (USB) outperform the XC4000typed ..."
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Abstract A switch block with k sides and W terminals per side ((k � W)SB) is said to be universal if every set of 2pin nets satisfying the dimension constraint is simultaneously routable through the switch block. It has been shown that the universal switch blocks (USB) outperform the XC4000typed switch blocks in routability. In this paper, we present a new combinatorial model and routing requirement decomposition theory for analyzing and designing generalized USB models. As a result, we obtain optimum (k � W)USBs for k 6 with all W ’s, k =7�8 with even W ’s; and nearly optimum (k � W)UBSs for k = 7�8 with odd W ’s, which is a revised result on the previously published. vertical channel track ID wire segment 1 2 3 4 C box horizontal channel 1 2
The Exact Channel Density and Compound Design for Generic Universal Switch Blocks
"... A switch block of k sides W terminals on each side is said to be universal (a (k, W)USB) if it is routable for every set of 2pin nets of channel density at most W. The generic optimum universal switch block design problem is to design a (k, W)USB with the minimum number of switches for every pair ..."
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A switch block of k sides W terminals on each side is said to be universal (a (k, W)USB) if it is routable for every set of 2pin nets of channel density at most W. The generic optimum universal switch block design problem is to design a (k, W)USB with the minimum number of switches for every pair of (k, W). This problem was first proposed and solved for k = 4 in Chang et al. [1996], and then solved for even W or for k ≤ 6 in Shyu et al. [2000] and Fan et al. [2002b]. No optimum (k, W)USB is known for k ≥ 7 and odd W ≥ 3. But it is already known that when W is a large odd number, a nearoptimum (k, W)USB can be obtained by a disjoint union of (W − f2(k))/2 copies of the optimum (k, 2)USB and a noncompound (k, f2(k))USB, where the value of f2(k) is unknown for k ≥ 8. In this article, we show that f2(k) = k+3−i 3, where 1 ≤ i ≤ 6 and i ≡ k (mod 6), and present an explicit design for the noncompound (k, f2(k))USB. Combining these two results we obtain the exact designs of (k, W)USBs for all k ≥ 7 and odd W ≥ 3. The new (k, W)USB designs also yield an efficient detailed routing algorithm.
On Optimal Hyperuniversal and Rearrangeable Switch Box Designs
"... Abstract—This paper explores theories on designing optimal multipoint interconnection structures, and proposes a simple switch box design scheme which can be directly applied to field programmable gate arrays (FPGAs), switch box designs, and communication switching network designs. We present a new ..."
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Abstract—This paper explores theories on designing optimal multipoint interconnection structures, and proposes a simple switch box design scheme which can be directly applied to field programmable gate arrays (FPGAs), switch box designs, and communication switching network designs. We present a new hyperuniversal switch box designs with four sides and terminals on each side, which is routable for every multipin netrouting requirement. This new design is proved to be optimum for a I FFF S and close to optimum for T with T &quot;Q switches. We also give a formal analysis and extensive benchmark experiments on routability comparisons between today’s most wellknown FPGA switch boxes like disjoint switch blocks (Xilinx XC4000 Type), Wilton’s switch blocks, Universal switch blocks, and our Hyperuniversal switch boxes. We apply the design scheme to rearrangeable switching network designs targeting for applications of connecting multiple terminals (e.g., teleconferencing). Simply using asided hyperuniversal switch block with a crossbar attached to each side, one can build a threestage onesided polygonal switching network capable of realizing every multipoint connection requirement on terminals. Besides, due to the finegrained decomposition property of our design scheme, the new switch box designs are highly scalable and simple on physical layout and routing algorithm implementations. Index Terms—Field programmable gate arrays (FPGA), hyperrearrangeable, hyperuniversal, routings, switch box, switching network. I.