12888903
Steiner Problems on Directed Acyclic Graphs
Two variations of the minimum-cost Steiner problem on a directed acyclic graph with non-negative weights edges are studied.
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.
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
2008990
Dual-Tree Fast Gauss Transforms
In previous work we presented an efficient approach to computing kernel summations which arise in many machine learning methods such as kernel density estimation. This approach, dual-tree recursion with finite-difference approximation, generalized existing methods for similar problems arising in computational physics in two ways appropriate for statistical problems: toward distribution sensitivity and general dimension, partly by avoiding series expansions. While this proved to be the fastest practical method for multivariate kernel density estimation at the optimal bandwidth, it is much less efficient at larger-than-optimal bandwidths. In this work, we explore the extent to which the dual-tree approach can be integrated with multipole-like Hermite expansions in order to achieve reasonable efficiency across all bandwidth scales, though only for low dimensionalities. In the process, we derive and demonstrate the first truly hierarchical fast Gauss transforms, effectively combining the best tools from discrete algorithms and continuous approximation theory.
23137458
Testing Finite State Machines: Fault Detection
Abstract We present simple randomized algorithms for the fault detection problem : Given a specification in the form of a deterministic finite state machine A and an implementation machine B , determine whether B is equal to A . If A has n states and p inputs, then in randomized polynomial time we can construct with high probability a checking sequence of length O ( pn 4 log n ), i.e., a sequence that detects all faulty machines with at most n states. Better bounds can be obtained in certain cases. The techniques generalize to partially specified finite state machines.
10320854
Conformance testing of protocols specified as communicating FSMs
An approach for conformance testing of protocols specified as a collection of communicating finite state machines (FSMs) with two parts, pruning and a guided random walk procedure, is presented. First the protocol is pruned to various sets of machines; each set provides only one service. This significantly reduces the test sequence length. Then a guided random walk procedure that attempts to cover all transitions in the component FSMs is used. The results of applying the procedure to the full-duplex alternating bit protocol and the asynchronous transfer mode (ATM) adaptation layer convergence protocol are presented. For the ATM adaptation layer, 99% of component FSMs' edges can be covered in a test with 11692 input steps. Previous approaches cannot generate conformance tests for standard protocols (such as ATM adaptation layer) specified as a collection of communicating FSMs.<<ETX>>
32698916
One-Dimensional Regularization with Discontinuities
Regularization is equivalent to fitting smoothing splines to the data so that efficient and reliable numerical algorithms exist for finding solutions. however, the results exhibit poor performance along edges and boundaries. To cope with such anomalies, a more general class of smoothing splines that preserve corners and discontinuities is studied. Cubic splines are investigated in detail, since they are easy to implement and produce smooth curves near all data points except those marked as discontinuities or creases. A discrete regularization method is introduced to locate corners and discontinuities in the data points before the continuous regularization is applied. >
12896882
Faster Gaussian Summation: Theory and Experiment
We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error control scheme integrating any arbitrary approximation method - within the best discretealgorithmic framework using adaptive hierarchical data structures. We rigorously evaluate these techniques empirically in the context of optimal bandwidth selection in kernel density estimation, revealing the strengths and weaknesses of current state-of-the-art approaches for the first time. Our results demonstrate that the new error control scheme yields improved performance, whereas the series expansion approach is only effective in low dimensions (five or less).