No abstract

The negotiated congestion mechanism forms the basis of most published FPGA routers today, with many routers projecting congestion and any other requirements onto a scalar search space to evaluate candidate paths. In this paper, we study the numerical stability of these scalar projections as the number of iterations increase. We show that in these scalar search spaces the norm of path costs increase exponentially with the number of iterations, leading to floating-point absorption and representation problems in computer arithmetic. We propose a novel two-component totally-ordered monoid space for path candidate evaluation, that guarantees the A* search finds a path with minimum congestion cost, and has linear norm growth with respect to the number of iterations. We demonstrate the efficacy of our new algorithm by testing on hard open routing problems in the FPGA Place and Route Challenge. The router successfully found 18 new routing solutions to instances that were previously unroutable, reducing the lowest track count to route 20 standard FPGA routing benchmarks by 10.2%.

No abstract

As FPGA implementations become more popular in production deployment, improved performance-driven routers are vital in preserving performance upstream from the FPGA design flow. In this paper, a novel long-path timing-driven router, SpiralRoute, is presented. SpiralRoute is a negotiationbased router with a novel path search on a clamped lexicographic spiral cost structure, and provides a guarantee of long-path timing compliance if a legal solution is found. We describe important components of SpiralRoute, including the application of polynomial-time optimal weighted budget distribution to improve connection budget quality, the construction of arbitrary-length lexicographic composition of totally-ordered monoids with order-preserving addition for admissible path search under A*, a trie-of-stacks data structure that allows path candidate extraction and storage to be independent of the size of the index, and a new greedy algorithm for the maintainence of routing tree topology. The efficacy of SpiralRoute is demonstrated by completing 19 instances of long-path timing-driven routing within timing budget that the published timing-driven router VPR 4.30 does not complete. However, SpiralRoute runtimes are slower than VPR 4.30 but we contend that the additional runtime is an acceptable tradeoff for guaranteed solution quality at completion, especially for production circuit routing.

We propose to modify a type of ant algorithm called Population based Ant Colony Optimization (P-ACO)