9084389
Restricted track assignment with applications
Consider a set of intervals S = {I1, I2, …, In}, where Ii = (li, ri), li, and ri are real numbers, and li < ri. We study a restricted track assignment problem (RTAP): if an interval Ia contains another interval Ib, then Ia must be assigned to a higher track than Ib, and the goal is to minimize the number of tracks used. The problem RTAP is shown to be NP-hard. An approximation algorithm that produces a solution within twice of the optimal is also presented and the bound is shown to be tight. The algorithm runs in O(n log n) time and requires linear space. The proposed approximation algorithm is employed to solve the problem of finding a maximum-weighted independent set in a circle graph, and related problems.
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.
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.
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.
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.
19220261
Path protection and blocking probability minimization in optical networks
We study the problem of shared path protection in optical networks from the viewpoint of blocking probability minimization. Unlike the worst-case approach common in other studies, which typically deals with one failure at a time and requires recomputation of the protection paths after every failure, our framework assumes a fixed path protection strategy for every connection that does not change in response to failures in other connections, which is more realistic for networks with high failure rates. We study backup-path strategy configurations that minimize the blocking probability and derive various properties. We show that configurations which do not have partial overlaps among connections backup paths are optimal in a rather general sense. We discuss the minmax optimal configuration properties and present an efficient algorithm for finding it in a case of special interest, while showing it to be NP-hard in general. In addition, we discuss the properties of the game resulting if each connection chooses its backup path selfishly; we show it to belong to the class of potential games, well-studied in the game theory literature, and derive several further properties resulting from its specific structure.
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.
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.
10647129
A new zero-crossing-based discontinuity detector
General zero-crossing-based discontinuity detectors in two dimensions, which include Marr-Hildreth (1980), residual, difference of Gaussians, and other detectors as special cases, are discussed. Mathematical justification for this class of detectors is presented. An optimal detector that maximizes the signal-to-noise ratio is derived. Preliminary experimental results for real images are reported.
6967475
Protocol System Integration, Interface and Interoperability
Heterogeneous network protocol systems are integrated together to fulfill complex tasks and their interoperability is a major hurdle for the network reliability and quality of services. We identify a new equivalence relation of states that preserves the integrated system interface behaviors. Based on this state equivalence we study the minimization of the system components with respect to their interfaces and design an efficient polynomial time minimization algorithm. We apply our technique to GMPLS protocols and obtain a significant state space reduction. We discuss integrated protocol system verification and interoperability testing with the minimized state system without resorting to the global state space information.