14112648
Reduction design for generic universal switch blocks
A k-side switch block with W terminals per side is said to be a universal switch block ((k, W)-USB) if every set of the nets satisfying the routing constraint (i.e., the number of nets on each side is at most W) is simultaneously routable through the switch block. The (4, W)-USB was originated by designing better switch modules for 2-D FPGAs, such as Xilinx XC4000-type FPGAs, whereas the generic USBs can be applied in multidimensional or some nonconventional 2-D FPGA architectures. The problem we study in this article is to design (k, W)-USBs with the minimum number of switches for any given pair of (k, W). We provide graph models for routing requirements and switch blocks and develop a series of decomposition theorems for routing requirements with the help of a new graph model. The powerful decomposition theory leads to the automatic generation of routing requirements and a detailed routing algorithm, as well as the reduction design method of building large USBs by smaller ones. As a result, we derive a class of well-structured and highly scalable optimum (k, W)-USBs for k ≤ 6, or even Ws, and near-optimum (k, W)-USBs for k ≥ 7 and odd Ws. We also give routing experiments to justify the routing improvement upon the entire chip using the USBs. The results demonstrate the usefulness of USBs.
16244697
OBDD Minimization Based on Two-Level Representation of Boolean Functions
In this paper, we analyze the basic properties of some Boolean function classes and propose a low complexity OBDD variable ordering algorithm, which is exact (optimum) to some classes of functions and very effective to general two-level form functions. We show that the class of series-parallel functions, which can be expressed by a factored form where each variable appears exactly once, can yield exact OBDD variable orderings in polynomial time. We also study the thin Boolean functions whose corresponding OBDDs can be represented by the form of thin OBDDs in which the number of nonterminal nodes is equal to the number of input variables. We show,that a thin Boolean function always has an essential prime cube cover and the class of series-parallel functions is a proper subset of thin Boolean functions. We propose a heuristic viewing OBDDs as evaluation machines with function cube covers as their inputs and apply a queuing principle in the algorithm design. Our heuristic, the augmented Dynamic Shortest Cube First algorithm, is proven to be optimum for the series-parallel functions and also be very effective for general two-level form functions. Experimental results on a large number of two-level form benchmark circuits show that the algorithm yields an OBDD total size reduction of over 51 percent with only 7 percent CPU time compared to the well-known network-based Fan-in Heuristic implemented in the SIS package. Comparing to the known exact results, ours is only 49 percent larger in size while only uses 0.001 percent CPU time.
62726183
Further improve circuit partitioning using GBAW logic perturbation techniques
Efficient circuit partitioning is gaining more importance with the increasing size of modern circuits. Conventionally, circuit partitioning is solved by modeling a circuit as a hypergraph for the ease of applying graph algorithms. However there exists room for further improvement on even optimum hypergraph partitioning results, if logic information can be applied for perturbation. In this paper we present a multi-way partitioning framework which can couple any excellent hypergraph partitioner and a noval logic perturbation based technique (GBAW) for further improvement over very excellent partitioning results. Our approach can integrate with any graph partitioner. We performed experiments on 2-, 3-, 4-, and 5-way partitionings for various circuits of different sizes from MCNC benchmarks. We have chosen the state-of-the-art hMetis-Kway to obtain high quality initial solutions for the experiments. Our experiments showed that this partitioning approach can achieve a further 15% reduction in cut size for 2-way partitioning with an area penalty of only 0.33%. The good results demonstrated the effectiveness of this new partitioning technique.
594928
Graph based analysis of 2-D FPGA routing
In this paper, we study the two-dimensional FPGA, Xilinx-like routing architectures and present the first known computational complexity results for them. The routing problem is formulated as a two-dimensional interval packing problem and is proved to be NP-complete with or without doglegs. Next, we consider other routing structures obtained from the industrial one by arbitrarily changing switch box connection topology while maintaining the same connection flexibility. There is an exponentially large number of such routing structures. We further prove that there does not exist a better routing architecture among the members of this large domain. In addition, we prove that there is no constant bound on the mapping ratio of a track number required by a detailed routing to a global routing channel density for the studied architectures. Finally, we show two directions of changing the routing architectures which yield polynomial time mapping solutions and constant bounded mapping ratios. Our theoretical analysis is intended to give some insight to, and understanding of this new routing problem's fundamental properties.
14594559
Detecting Critical Configuration of Six Points
When space points and camera optical center lie on a twisted cubic, no matter how many corresponding pairs there are from space points to their image points, camera projection matrix cannot be uniquely determined, in other words, the configuration of camera and space points in this case is critical for camera parameter estimation. In practice, it is important to detect this critical configuration before the estimated camera parameters are used. In this work, a new method is introduced to detect this critical configuration, which is based on an effective criterion function constructed from an invariant relationship between six space points and their corresponding image points. The advantage of this method is that no explicit computation on camera projection matrix or optical center is needed. Simulations show it is quite robust and stable against noise. Experiments on real data show the criterion function can be faithfully trusted for camera parameter estimation.
11461597
A unification of network coding and tree-packing (routing) theorems
Given a network of lossless links with rate constraints, a source node, and a set of destination nodes, the multicast capacity is the maximum rate at which the source can transfer common information to the destinations. The multicast capacity cannot exceed the capacity of any cut separating the source from a destination; the minimum of the cut capacities is called the cut bound. A fundamental theorem in graph theory by Edmonds established that if all nodes other than the source are destinations, the cut bound can be achieved by routing. In general, however, the cut bound cannot be achieved by routing. Ahlswede et al. established that the cut bound can be achieved by performing network coding, which generalizes routing by allowing information to be mixed. This paper presents a unifying theorem that includes Edmonds' theorem and Ahlswede et al.'s theorem as special cases. Specifically, it shows that the multicast capacity can still be achieved even if information mixing is only allowed on edges entering relay nodes. This unifying theorem is established via a graph theoretic hardwiring theorem, together with the network coding theorems for multicasting. The proof of the hardwiring theorem implies a new proof of Edmonds' theorem.
11776269
Geometric invariants and applications under catadioptric camera model
This paper presents geometric invariants of points and their applications under central catadioptric camera model. Although the image has severe distortions under the model, we establish some accurate projective geometric invariants of scene points and their image points. These invariants, being functions of principal point, are useful, from which a method for calibrating the camera principal point and a method for recovering planar scene structures are proposed. The main advantage of using these in variants for plane reconstruction is that neither camera motion nor the intrinsic parameters, except for the principal point, is needed. The theoretical correctness of the established invariants and robustness of the proposed methods are demonstrated by experiments. In addition, our results are found to be applicable to some more general camera models other than the catadioptric one
13420664
Music Classification Using Significant Repeating Patterns
With the popularity of multimedia applications, a large amount of music data has been accumulated on the Internet. Automatic classification of music data becomes a critical technique for providing an efficient and effective retrieval of music data. In this paper, we propose a new approach for classifying music data based on their contents. In this approach, we focus on monophonic music features represented as rhythmic and melodic sequences. Moreover, we use repeating patterns of music data to do music classification. For each pattern discovered from a group of music data, we employ a series of measurements to estimate its usefulness for classifying this group of music data. According to the patterns contained in a music piece, we determine which class it should be assigned to. We perform a series of experiments and the results show that our approach performs on average better than the approach based on the probability distribution of contextual information in music.
16403469
PSALM: A Data Model for Pervasive Visualization
In this poster, we investigate how to achieve visualization in a pervasive visualization environment, especially on new platforms such as PDAs, cell phones, and other mobile devices that have very limited resources and usually are not considered appropriate platforms for visualization. We will use a clinic application as an example and our target application. In this system, patient data, such as CT and MRI, are stored in a central server in the hospital and physicians can access these data using a cell phone for a quick preview, a pocket PC or laptop for some initial diagnosis, and a powerful workstation for any further diagnosis.