15096399
A Faster One-Dimensional Topological Compaction Algorithm with Jog Insertion
Abstract. We consider the problem of one-dimensional topological compaction with jog insertions. By combining both geometric and graph-theoretic approaches we present a faster and simpler algorithm to improve over previous results. The compaction algorithm takes as input a sketch consisting of a set F of features and a set W of wires, and minimizes the horizontal width of the sketch while maintaining its routability. The algorithm consists of the following steps: constructing a horizontal constraint graph, computing all possible jog positions, computing the critical path, relocating the features, and reconstructing a new sketch homotopic to the input sketch, which is suitable for detailed routing. The algorithm runs in O(|F| ⋅ |W|) worst-case time and space, which is asymptotically optimal in the worst case. Experimental results are also presented.
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.
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.
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.
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.
16325574
Finding an Approximate Minimum-Link Visibility Path Inside a Simple Polygon
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.
5759098
An Efficient Algorithm for Minimizing Real-Time Transition Systems
We address the problem of performing simultaneously reachability analysis and minimization of real-time transition systems represented by timed automata, i.e., automata extended with a finite set of clock variables. The transitions of the automaton may depend on the values of the clocks and may reset some of the clocks. An efficient algorithm is presented for minimizing a system with respect to a given initial partition that respects the enabling conditions of the transitions of the timed automaton. Our algorithm generates the portion of the minimized system that is reachable from a given initial configuration in time polynomial in the input and the size of the minimal reachable system.
3246222
An Efficient Algorithm for Minimizing Real-time Transition Systems
We address the problem of performing simultaneously reachability analysis and minimization of real-time transition systems represented by timed automata , i.e., automata extended with a finite set of clock variables. The transitions of the automaton may depend on the values of the clocks and may reset some of the clocks. An efficient algorithm is presented for minimizing a system with respect to a given initial partition that respects the enabling conditions of the transitions of the timed automaton. Our algorithm generates the portion of the minimized system that is reachable from a given initial configuration in time polynomial in the input and the size of the minimal reachable system.
45853491
Testing Finite-State Machines: State Identification and Verification
We study the complexity of two fundamental problems in the testing of finite-state machines. 1) Distinguishing sequences (state identification). We show that it is PSPACE-complete to determine whether a finite-state machine has a preset distinguishing sequence. There are machines that have distinguishing sequences, but only of exponential length. We give a polynomial time algorithm that determines whether a finite-state machine has an adaptive distinguishing sequence. (The previous classical algorithms take exponential time.) Furthermore, if there is an adaptive distinguishing sequence, then we give an efficient algorithm that constructs such a sequence of length at most n(n/spl minus/1)/2 (which is the best possible), where n is the number of states. 2) Unique input output sequences (state verification). It is PSPACE-complete to determine whether a state of a machine has a unique input output sequence. There are machines whose states have unique input output sequences but only of exponential length. >
9141097
Passive tool dynamics rendering for nonlinear bilateral teleoperated manipulators
In a previous paper (see ibid., p. 3278-83), a control law renders a 2n-degree of freedom (DOF) nonlinear teleoperator (consisting of n-DOF master and slave robots) as a n-DOF common passive mechanical tool which has the usual robotic dynamics. In this paper, we develop a control methodology to endow the resulting n-DOF common passive mechanical tool with useful passive tool dynamics which incorporates inertia scaling, guidance/avoidance system while preserving energetic passivity of the closed-loop system. A fictitious energy storage is used to scale the apparent inertia of the teleoperator. The passive velocity field control for a velocity field tracking and artificial potential function are utilized for guidance/avoidance system. Thus, with the control law proposed previously, the control law renders the 2n-DOF teleoperator as a n-DOF common passive mechanical tool which has programmable apparent inertia and moves under the effects of velocity/potential field tailored to task objectives and obstacles in the workspace.