995590
k best cuts for circular-arc graphs
Given a set ofn nonnegativeweighted circular arcs on a unit circle, and an integerk, thek Best Cust for Circular-Arcs problem, abbreviated as thek-BCCA problem, is to find a placement ofk points, calledcuts, on the circle such that the total weight of the arcs that contain at least one cut is maximized.We first solve a simpler version, thek Best Cuts for Intervals (k-BCI) problem, inO(kn+n logn) time andO(kn) space using dynamic programming. The algorithm is then extended to solve a variation, called thek-restricted BCI problem, and the space complexity of thek-BCI problem can be improved toO(n). Based on these results, we then show that thek-BCCA problem can be solved inO(I(k,n)+nlogn) time, whereI(k, n) is the time complexity of thek-BCI problem. As a by-product, thek Maximum Cliques Cover problem (k>1) for the circular-arc graphs can be solved inO(I(k,n)+nlogn) time.
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.
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.
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.
16325574
Finding an Approximate Minimum-Link Visibility Path Inside a Simple Polygon
2585986
Fast multiplication of a recursive block Toeplitz matrix by a vector and its application
We present an algorithm for multiplying an N × N recursive block Toeplitz matrix by a vector with cost O (N log N). Its application to optimal surface interpolation is discussed.
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.
7389460
Fault Detection of Hierarchical Networks with Probabilistic Testing Algorithms
As communications networks are expanding to larger areas the control and maintenance of routing information are becoming a formidable task. To cope with its size and complexity and to make the network reliable and scalable hierarchical network has been proposed with new features to support the information infrastructure. However, the network hierarchy adds more complications to the network design and implementations and that hampers the network reliability and quality of services. Conformance testing is known to be a powerful tool for network fault detection yet most of the works in the published literature are on networks without hierarchy. We present probabilistic algorithms for testing hierarchical networks along with the added features. Based on a formal model of the networks, we provide a formal analysis that shows that our probabilistic algorithms guarantee a high fault coverage with a feasible number of tests. To further reduce the number of tests we identify test equivalence classes and that enables us to significantly reduce the number of tests yet without losing the fault coverage. Experimental results on Internet OSPF protocol are reported.
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.
7765148
A formal approach for passive testing of protocol data portions
Passive testing is a process of detecting faults in a system under test by passively observing its input/output behaviors only without interrupting its normal operations, and proves to be a promising technique for network fault management. We study passive testing of data portions of network protocols and present two algorithms, using an event-driven extended finite state machine model. Experimental results on the Internet routing protocol OSPF (open shortest path first) are reported.