Solving graph problems with dynamic computation structures

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Abstract
We introduce dynamic computation structures (DCS), a compilation technique to produce dynamic code for reconfigurable computing. DCS specializes directed graph instances into user-level hardware for reconfigurable architectures. Several problems such as shortest path and transitive closure exhibit the general properties of closed semirings, an algebraic structure for solving directed paths. Motivating our application domain choice of closed semiring problems is the fact that logic emulation software already maps a special case of directed graphs, namely logic netlists, onto arrays of field programmable gate arrays (FPGA). A certain type of logic emulation software called virtual wires further allows an FPGA array to be viewed as a machine-independent computing fabric. Thus, a virtual wires compiler, coupled with front-end commercial behavioral logic synthesis software, enables automatic behavioral compilation into a multi-FPGA computing fabric. We have implemented a DCS front-end compiler to parallelize the entire inner loop of the classic Bellman-Ford algorithm into synthesizable behavioral verilog. Leveraging virtual wire compilation and behavioral synthesis, we have automatically generated designs of 14 to 261 FPGAs from a single graph instance. We achieve speedups proportional to the number of graph edges - - from 10X to almost 400X versus a 125 SPECint SparcStation 10.

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