An FPGA Task Placement Algorithm Using Reflected Binary Gray Space Filling Curve

Alternative Algorithm for Hilbert's Space-Filling Curve

A space-filling curve

In mathematics classes where the natural numbers are studied, several surprising results can be shown about the relative “sizes” of infinite sets, such as the fact the there is a oneto-one mapping between the natural numbers N and the even numbers, showing that they are both countably infinite, with the “same size”. Similar logic also shows that there is a mapping from the natural numbers N ont...

On binary reflected Gray codes and functions

The Binary Reflected Gray Code function b is defined as follows: If m is a nonnegative integer, then b(m) is the integer obtained when initial zeros are omitted from the binary reflected Gray code of length m. This paper examines this Gray code function and its inverse and gives simple algorithms to generate both. It also simplifies Conder’s result that the jth letter of the kth word of the bin...

A space-filling curve

In mathematics classes where the natural numbers are studied, several surprising results can be shown about the relative “sizes” of infinite sets, such as the fact the there is a oneto-one mapping between the natural numbers N and the even numbers, showing that they are both countably infinite, with the “same size”. Similar logic also shows that there is a mapping from the natural numbers N ont...

An Algorithm for Dynamically Reconfigurable FPGA Placement

In this paper, we introduce a new placement problem movitated by the Dynamically Reconfigurable FPGA (DRFPGA) architectures. Unlike traditional placement, the problem for DRFPGAs must consider the precedence constraints among logic components. For the placement, we develop an effective metric that can consider wirelength, register requirement, and power consumption simultaneously. With the cons...