12459424
The Min-Max Voronoi Diagram of Polygons and Applications in VLSI Manufacturing
We study the min-max Voronoi diagram of a set S of polygonal objects, a generalization of Voronoi diagrams based on the maximum distance between a point and a polygon. We show that the min-max Voronoi diagram is equivalent to the Voronoi diagram under the Hausdorff distance function. We investigate the combinatorial properties of this diagram and give improved combinatorial bounds and algorithms. As a byproduct we introduce the min-max hull which relates to the min-max Voronoi diagram in the way a convex hull relates to the ordinary Voronoi diagram.
34901507
A faster algorithm for rubber-band equivalent transformation for planar VLSI layouts
In this paper we consider the problem of transforming a single-layer topological routing of n two-terminal nets into a rubber-band equivalent using rectilinear wires in the presence of rectilinear circuit modules. Given a topological planar VLSI layout sketch with |F| features and |W| noncrossing wire segments connecting n two-terminal nets, we present an O(|F|/spl middot/|W|) time algorithm to do the vertex-disjoint rubber-band equivalent transformation of these n nets if it exists. The algorithm consists of two phases, computing a loose homotopy with four spokes matrices, and computing a vertex-disjoint rubber-band equivalent of the given homotopy, each phase taking O(|F|/spl middot/|W|) time and space. Both complexities are asymptotically optimal in the worst case. From the vertex-disjoint rubber-band equivalent of the given homotopy, one can obtain the detailed routing within the same time complexity. Experimental results are also presented.
37965905
Rectilinear Paths among Rectilinear Obstacles
Given a set of obstacles and two distinguished points in the plane the problem of finding a collision-free path subject to a certain optimization function is a fundamental problem that arises in many fields, such as motion planning in robotics, wire routing in VLSI and logistics in operations research. In this survey we emphasize its applications to VLSI design and limit ourselves to the rectilinear domain in which the goal path to be computed and the underlying obstacles are all rectilinearly oriented, i.e., the segments are either horizontal or vertical. We consider different routing environments, and various optimization criteria pertaining to VLSI design, and provide a survey of results that have been developed in the past, present current results and give open problems for future research.
18326125
Finding Rectilinear Paths Among Obstacles in a Two-Layer Interconnection Model
Finding the best rectilinear path with respect to the bends and teh lengths of paths connecting two given points in the presence of rectilinear obstacles in a two-layer model is studied in this paper. In this model, rectilinear obstacles on each layer are specified separately, and the orientation of routing in each layer is fixed. An algorithm is presented to transform any problem instance in the two-layer model to one in a one-layer model, so that almost all algorithms for finding rectilinear paths among obstacles in the plane can be applied. The transformation algorithm runs in O(e log e) time where e is the number of edges on obstacles lying on both layers. A direct graph-theoretic approach to finding a shortest path in the two-layer model, which is easier to implement is also presented. The algorithm runs in O(e log2 e) time.
16325574
Finding an Approximate Minimum-Link Visibility Path Inside a Simple Polygon
10484740
Labeling Points on a Single Line
In this paper, we consider a map labeling problem where the points to be labeled are restricted on a line. It is known that the 1d-4P and the 1d-4S unit-square label placement problem and the Slope-4P unit-square label placement problem can both be solved in linear time and the Slope-4S unit-square label placement problem can be solved in quadratic time in Ref. [8]. We extend the result to the following label placement problem: Slope-4P fixed-height (width) label or elastic label placement problem and present a linear time algorithm for it provided that the input points are given sorted. We further show that if the points are not sorted, the label placement problems have a lower bound of Ω(n log n), where n is the input size, under the algebraic computation tree model. Optimization versions of these point labeling problems are also considered.
728532
Performance and correctness of the ATM ABR rate control scheme
We study both the correctness and performance of the source/destination protocol of the available bit rate (ABR) service in asynchronous transfer mode (ATM) networks. Although the basic source/destination protocol for congestion management is relatively simple, the protocol specification has to cope with several "real-world" cases such as failures and delayed/lost feedback which may introduce complexity. Rigorous proofs of the correct functioning of the protocol based on a formal specification is necessary. We use a formal extended finite state machine (EFSM) model to show that the ABR source/destination protocol is free of live-locks, so that under all conditions both resource management (RM) and data cells will be transmitted. We also show that the network options of explicit forward congestion indication (EFCI) and explicit rate (ER) interoperate correctly. We use the understanding of the informal English description of the source/destination behavior and of our EFSM model to derive conditions that ensure that the source transmission rate is stable in the presence of delayed or lost feedback RM cells, especially under the operation of a source rule that requires the reduction of the source rate under these conditions. We arrive at bounds on the number of consecutive RM cell losses tolerated while the rate remains stable. We also provide a worst-case analysis of the delay in turning around RM cells at the destination station and the worst-case inter-departure time of forward RM cells from the source.
2522031
The Rectified Gaussian Distribution
A simple but powerful modification of the standard Gaussian distribution is studied. The variables of the rectified Gaussian are constrained to be nonnegative, enabling the use of nonconvex energy functions. Two multimodal examples, the competitive and cooperative distributions, illustrate the representational power of the rectified Gaussian. Since the cooperative distribution can represent the translations of a pattern, it demonstrates the potential of the rectified Gaussian for modeling pattern manifolds.
44869153
Tracking Illegal System Access in a Ubiquitous Environment - Proposal for ATS, a Traceback System Using STOP
In a ubiquitous environment, the boundaries of network topology can change irregularly. In this paper, an Agent-based Traceback System (ATS) is proposed to track attacks that utilize systems within an area of the network topology that has been marked for management purposes. Some of the information exchanged within the proposed system utilizes the previously verified STOP [1]. The additional information provided by utilizing the ATS proposed in this paper will greatly enhance the reliability of the traceback process. In addition, the proposed system is flexible enough to be applied to resource management systems as well.
28781309
Automatic process-oriented control circuit generation for asynchronous high-level synthesis
As an asynchronous design style becomes popular, the request for asynchronous high-level synthesis (AHLS) tools is increasing continuously. In this paper, a method, so called process-oriented method, which generates distributed asynchronous control circuits automatically in a hierarchical and systematic manner is suggested as part of an AHLS tool. Experimental results show that the suggested method is efficient in the aspects of area and performance of derived control circuits.
11856887
Approximation of linear functionals on a banach space with a Gaussian measure
Abstract We study approximation of linear functionals on separable Banach spaces equipped with a Gaussian measure. We study optimal information and optimal algorithms in average case, probabilistic, and asymptotic settings, for a general error criterion. We prove that adaptive information is not more powerful than nonadaptive information and that μ-spline algorithms, which are linear, are optimal in all three settings. Some of these results hold for approximation of linear operators. We specialize our results to the space of functions with continuous r th derivatives, equipped with a Wiener measure. In particular, we show that the natural splines of degree 2 r + I yield the optimal algorithms. We apply the general results to the problem of integration.