We examine the problem of detecting negative cycles in a dynamic graph, which is a fundamental problem that arises in electronic design automation and systems theory.We introduce the concept of adaptive negative cycle detection, in which a graph changes over time, and negative cycle detection needs to be done periodically, but not necessarily after every individual change. Such scenarios arise, for example, during iterative design space exploration for hardware and software synthesis. We present an algorithm for this problem, called the Adaptive Bellman-Ford (ABF) algorithm, based on a novel extension of the well known Bellman-Ford algorithm. The ABF algorithm allows us to systematically adapt information for a given graph to a modified version of the graph. We show that the ABF algorithm significantly outperforms previously available approaches for dynamic graphs, which either recompute negative cycle information from scratch whenever a graph is modified, or process the modifications one at a time ("incrementally").As an application of the ABF technique, we show that it can be used to obtain a very fast implementation of Lawler's technique for the computation of the maximum-cycle mean (MCM) of a graph, especially for a certain important kind of sparse graph. We further illustrate the application of the ABF technique to design-space exploration by developing automated search techniques for scheduling iterative data-flow graphs.

We consider the problem of representing timing information associated with functions in a dataflow graph used to represent a signal processing system in the context of high-level hardware (architectural) synthesis. This information is used for synthesis of appropriate architectures for implementing the graph. Conventional models for timing suffer from shortcomings that make it difficult to represent timing information in a hierarchical manner, especially for multirate signal processing systems.We identify some of these shortcomings, and provide an alternate model that does not have these problems. We show that with some reasonable assumptions on the way hardware implementations of multirate systems operate, we can derive general hierarchical descriptions.of multirate systems similarly to single rate systems. Several analytical results such as the computation of the iteration period bound, that previously applied only to single rate systems can also easily be extended to multirate systems under the n e w assumptions.We have applied our model to several multirate signal processing applications, and obtained favorable results. We present results of the timing information computed for several multirate DSP applications that show how the new treatment can streamline the problem of performance analysis and synthesis of such systems.

Abstract-The problem of representing timing information associated with functions in a dataflow graph is considered. This information is used for constraint analysis during behavioral synthesis of appropriate architectures for implementing the graph. Conventional models for timing suffer from shortcomings that make it difficult to represent timing information in a hierarchical manner for sequential and multirate systems. Some of these shortcomings are identified, and an alternate timing model that does not have these problems for hardware implementations is provided.We introduce the concept of timing pairs to model delay elements in sequential and multirate circuits and show how this allows us to derive hierarchical timing information for complex circuits. The resulting compact representation of the timing information can be used to streamline system performance analysis. In addition, several analytical results that previously applied only to single rate systems can now be extended to multirate systems.We present an algorithm to compute the timing parameters and have used this to compute timing parameters for a number of benchmark circuits. The results obtained on several ISCAS benchmark circuits as well as several multirate dataflow graphs corresponding to useful signal processing applications are presented. These results show that the new representation model can result in large reductions in the amount of information required to represent timing for hierarchical systems.

Two dimensional mesh motion compensation produces blocking free prediction in contrast to block matching motion compensation by generating a smooth full motion field from the set of node motion vectors. This is clearly not appropriate across moving object boundaries where motion discontinuities exist. In this paper, we address this problem by proposing an adaptive interpolation scheme for patches that contain multiple motions (i.e., patches around motion boundaries). Simulation results show improvements over standard 2-D mesh motion compensation at a fraction of computational increase.

We propose an efficient high-performance scaling algorithm based on the oriented polynomial image model. We develop a simple classification scheme that classifies the region around a pixel as an oriented or nonoriented block. Based on this classification, a nonlinear oriented interpolation is performed to obtain high quality video scaling. In addition, we also propose a generalization that can perform scaling for arbitrary scaling factors. Based on this algorithm, we develop an efficient architecture for image scaling. Specifically, we consider an architecture for scaling a Quarter Common Intermediate Format (QCIF) image to 4CIF format. We show the feasibility of the architecture by describing the various computation units in a hardware description language (Verilog) and synthesizing the design into a netlist of gates. The synthesis results show that an application specific integrated circuit (ASIC) design which meets the throughput requirements can be built with a reasonable silicon area.Index Terms-Adaptive scaling, oriented polynomial interpolation, video zoom, VLSI architecture.