Graph based analysis of 2-D FPGA routing

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 1997

A new class of routing structures with fixed orthogonal wire segments and field programmable switches at the intersections of the wire segments is proposed. In comparison with the conventional two dimensional Field-Programmable Gate Array (FPGA) routing structure, this class of routing structures has the advantage of using a smaller number of programmable switches. Using a probabilistic model, we prove that complete routing can be achieved with a high degree of probability in a routing structure of this class in which the number of tracks in each channel approaches the lower bound asymptotically. A sequential routing algorithm which is based on the solution of the single net routing problem is presented. We take into account the delay introduced by the programmable switches on a routing path and formulate the single net routing problem as a Node-Weighted Steiner Minimum Tree (NWSMT) problem in a bipartite graph G. Since our single net routing problem is NP-complete, a polynomial time approximate algorithm is proposed. We prove that our single net routing algorithm produces an optimal solution for some special classes of bipartite graphs. In general, the solution obtained by our algorithm has aperformance bound of min{A(V\Z), 121-1). On the other hand, we also prove that it is NP-complete to determine a solution which approximates the optimal solution within any constant bound. Experimental results show a reduction of up to 41% in the number of programmable switches when compared with corresponding results for the conventional FPGA routing structure.

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2000

In this paper, the routing problem for twodimensional (2-D) field programmable gate arrays of a Xilinx-like architecture is studied. We first propose an efficient one-step router that makes use of the main characteristics of the architecture. Then we propose an improved approach of coupling two greedy heuristics designed to avoid an undesired decaying effect, a dramatically degenerated router performance on the near completion stages. This phenomenon is commonly observed on results produced by the conventional deterministic routing strategies using a single optimization cost function. Consequently, our results are significantly improved on both the number of routing tracks and routing segments by just applying low-complexity algorithms. On the tested MCNC and industrial benchmarks, the total number of tracks used by the best known two-step global/detailed router is 28% more than that used by our proposed method.

1998

In modern FPGA CAD ow, netlist routing on a particular routing architecture is solved in two steps, global routing based on wire bandwidth constraints of the architecture, and subsequent detailed routing based on the ner switching constraints of the architecture. Detailed routing is difcult and provably NP-complete in popular 2-D mesh architectures such as the Xilinx 4000 series FPGAs 16]. Certain tree based routing architectures, which are desirable for scalability and area universality 11], have known polynomial algorithms and guarantees for detailed routing. In this paper we study approaches to detailed routing for a fat-tree routing architecture with restricted switching topology, in which routing bandwidth scales according to Rent's Rule. We discuss several formulations and frameworks for solving the detailed routing problem, using such techniques as graph coloring, multicomodity ow, and integer linear programming.

Proceedins of the 14th ACM Great Lakes symposium on VLSI - GLSVLSI '04, 2004

In this paper we compare the routing architecture of island-style FPGAs based on field-programmable switch boxes with a maskprogrammable routing structure, in order to assess its position in the design space of routing opportunities available to VLSI IC designers. Although the results presented in this work depend on a few implementation details that will be discussed in the paper, the mask-programmable routing structure shows a large area saving and delay improvement with respect to the field-programmable switch box. As a consequence, we believe that between the two bounds of the design space, i.e., ASICs and FPGAs, there are several hybrid architectural solutions trading off performances, power, area, and programmability, which in the future can be considered for different applications.

ACM Transactions on Reconfigurable Technology and Systems, 2015

Dynamic Partial Reconfiguration (DPaR) enables efficient allocation of logic resources by adding new functionalities or by sharing and/or multiplexing resources over time. Placement and routing (P&R) is one of the most time-consuming steps in the DPaR flow. P&R are two independent NP-complete problems, and, even for medium size circuits, traditional P&R algorithms are not capable of placing and routing hardware modules at runtime. We propose a novel runtime P&R algorithm for Field-Programmable Gate Array (FPGA)-based designs. Our algorithm models the FPGA as an implicit graph with a direct correspondence to the target FPGA. The P&R is performed as a graph mapping problem by exploring the node locality during a depth-first traversal. We perform the P&R using a greedy heuristic that executes in polynomial time. Unlike state-of-the-art algorithms, our approach does not try similar solutions, thus allowing the P&R to execute in milliseconds. Our algorithm is also suitable for P&R in fragmented regions. We generate results for a manufacturer-independent virtual FPGA. Compared with the most popular P&R tool running the same benchmark suite, our algorithm is up to three orders of magnitude faster.

Proceedings of ASP-DAC'95/CHDL'95/VLSI'95 with EDA Technofair, 1995

In this paper we analyze the properties of the Xilinx-like regular segmentation schemes for 2-D Field Programmable Gate Arrays (FPGAs). We introduce a new notion of architectural level routing decaying effect caused by wiring segmentation. We discuss its routing properties and propose a relative prime number based segmentation scheme for 2-D FPGA architectures. A new FPGA design concept of applying architectural coupling to achieve better routability is also introduced and experimentally justified

Proceedings of the 2003 ACM/SIGDA eleventh international symposium on Field programmable gate arrays, 2003

The routing channels of an FPGA consist of wire segments of various types providing the tradeoff between performance and routability. In the routing architectures of recently developed FPGAs (e.g., Virtex-II), there are more versatile wire types and richer connections between them than those of the older generations of FPGAs (e.g. XC4000). To fully exploit the potential of the new routing architectures, it is beneficial to perform wire type assignment for all channels as an intermediate stage between global routing and detailed routing. In this paper, we present a wire-type assignment algorithm that is based on iteratively applying min-cost maxflow technique to simultaneously route many nets. At each stage of the network flow computation, we have guaranteed optimal result in terms of routability and delay cost. We use the routing architecture of the Virtex-II FPGAs from Xilinx as a target architecture in our experiments. Experimental results show that our algorithm outperforms the traditional sequential net-by-net approach.

IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2000

Multi-FPGA systems (MFSs) are used as custom computing machines, logic emulators and rapid prototyping vehicles. A key aspect of these systems is their programmable routing architecture which is the manner in which wires, FPGAs and Field-Programmable Interconnect Devices (FPIDs) are connected. Several routing architectures for MFSs have been proposed and previous research has shown that the partial crossbar is one of the best existing architectures [Kim96] [Khal97]. In this paper we propose a new routing architecture, called the Hybrid Complete-Graph and Partial-Crossbar (HCGP) which has superior speed and cost compared to a partial crossbar. The new architecture uses both hardwired and programmable connections between the FPGAs. We compare the performance and cost of the HCGP and partial crossbar architectures experimentally, by mapping a set of 15 large benchmark circuits into each architecture. A customized set of partitioning and inter-chip routing tools were developed, with particular attention paid to architecture-appropriate inter-chip routing algorithms. We show that the cost of the partial crossbar (as measured by the number of pins on all FPGAs and FPIDs required to fit a design), is on average 20% more than the new HCGP architecture and as much as 25% more. Furthermore, the critical path delay for designs implemented on the partial crossbar were on average 20% more than the HCGP architecture and up to 43% more. Using our experimental approach, we also explore a key architecture parameter associated with the HCGP architecture: the proportion of hard-wired connections versus programmable connections, to determine its best value.

2011 21st International Conference on Field Programmable Logic and Applications, 2011

We propose a new FPGA routing approach that, when combined with a low-cost architecture change, results in a 34% reduction in router run-time, at the cost of a 3% area overhead, with no increase in critical path delay. Our approach begins with traditional PathFinder-style routing, which we run on a coarsened representation of the routing architecture. This leads to fast generation of a partial routing solution where signals are assigned to groups of wire segments rather than individual wire segments. A Boolean satisfiability (SAT)-based stage follows, generating a legal routing solution from the partial solution. Our approach points to a new research direction: reducing FPGA CAD run-time by exploring FPGA architectures and algorithms together.

IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2003

Multi-FPGA systems are used as custom computing machines to solve compute intensive problems and also in the verification and prototyping of large circuits. In this paper, we address the problem of routing multi-terminal nets in a multi-FPGA system that uses partial crossbars as interconnect structures. First, we model the multi-terminal routing problem as a partitioned bin packing problem and formulate it as an integer linear programming problem where the number of variables is exponential. A fast heuristic is applied to compute an upper bound on the routing solution. Then, a column generation technique is used to solve the linear relaxation of the initial master problem in order to obtain a lower bound on the routing solution. This is followed by an iterative branch-and-price procedure that attempts to find a routing solution somewhere between the two established bounds. In this regard, the proposed algorithm guarantees an exact routing solution by searching a branch-and-price tree. Due to the tightness of the bounds, the branch-and-price tree is small resulting in shorter execution times. Experimental results are provided for different netlists and board configurations in order to demonstrate the algorithm's performance. The obtained results show that the algorithm finds an exact routing solution in a very short time.