Logic programming for combinatorial problems
Artificial Intelligence Review
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Field-programmable interconnection chips (FPIC's) provide the capability of realizing user programmable interconnection for any desired permutation. Such an interconnection is very much desired for supporting rapid prototyping of hardware systems and for providing programmable communication networks for parallel and distributed computing. An FPIC should realize any possible permutation of input to output pins via a set of programmable switches. In this paper, we show that any such architecture requires a minimum of /spl Omega/(n log n) switches, where /spl Omega/ is the number of I/O pins. The result stems from an analysis of the underlying permutation network. In addition, for networks of bounded degree d, we prove an /spl Omega/(log/sub d-1/ n) bound on the routing delay (maximum length of routing paths for specific I/O permutations) and an /spl Omega/(n log/sub d-1/ n) bound on the average utilization of programmable switches used by the FPIC to implement a specific permutation. For the same type of networks, we prove an /spl Omega/(n log/sub d-1/ n) bound on the number of nodes of the network. Furthermore, we design efficient architectures for FPIC's offering a wide variety of routing delays, high average programmable resource utilization, and O(n/sup 2/)-area two-layer layouts. The proposed structures are called hybrid Benes-Crossbar (HBC) architectures and clearly exhibit a tradeoff between performance (routing delay utilization) and area of the layout.