An Improved Augmented Line Segment based Algorithm for the Generation of Rectilinear Steiner Minimum Tree

2017 ◽  
Vol 7 (3) ◽  
pp. 1262 ◽  
Author(s):  
Vani V ◽  
G.R. Prasad
Keyword(s):  
Line Segment ◽  
Vlsi Design ◽  
Intersection Point ◽  
Global Routing ◽  
Good Reduction ◽  
Wire Length ◽  
Line Segments ◽  
Main Application ◽  
The Cost ◽  
Steiner Minimum Tree

An improved Augmented Line Segment Based (ALSB) algorithm for the construction of Rectilinear Steiner Minimum Tree using augmented line segments is proposed. The proposed algorithm works by incrementally increasing the length of line segments drawn from all the points in four directions. The edges are incrementally added to the tree when two line segments intersect. The reduction in cost is obtained by postponing the addition of the edge into the tree when both the edges (upper and lower L-shaped layouts) are of same length or there is no overlap. The improvement is focused on reduction of the cost of the tree and the number of times the line segments are augmented. Instead of increasing the length of line segments by 1, the line segments length are doubled each time until they cross the intersection point between them. The proposed algorithm reduces the wire length and produces good reduction in the number of times the line segments are incremented. Rectilinear Steiner Minimum Tree has the main application in the global routing phase of VLSI design. The proposed improved ALSB algorithm efficiently constructs RSMT for the set of circuits in IBM benchmark.

scholarly journals Obstacle aware delay optimized rectilinear steiner minimum tree routing

2019 ◽  
Vol 16 (2) ◽  
pp. 640
Author(s):  
Shyamala G ◽  
G R Prasad
Keyword(s):  
Integrated Circuit ◽  
Large Scale ◽  
Vlsi Design ◽  
Global Routing ◽  
Buffer Insertion ◽  
Device Layer ◽  
Wire Length ◽  
Delay Constraints ◽  
Tree Routing ◽  
Steiner Minimum Tree

<p><span>This work presents a method to solve the problem of constructing Rectilinear Steiner Minimum Tree (RSMT) for a group of pins in the presence of obstacles. In modern </span><span>very large-scale integrated circuit</span><span> (VLSI) designs, the obstacles, generally blocks the metal and the device layer. Therefore routing on top of blockage is a possible solution but buffers cannot be placed over the obstacle. Modern VLSI design OARSMT construction has long wire length, which results in signal violation. To address this issue a slew constraint interconnect need to be considered in routing over obstacle. This is called the Obstacle-Avoiding Rectilinear Steiner minimum trees (OARSMT) problem with slew constraints over obstacles. The drawback of traditional OARSMT is that they only consider slew constraint, and delay constraints are neglected. It induces high routing resources overhead due to buffer insertion and does not solve global routing solution. This work presents an Obstacle Aware Delay Optimized Rectilinear Steiner Minimum Tree (OADORSMT) Routing to address the delay, slew constraint and reduce the routing resources. Experiments are conduced to evaluate the performance of proposed approach over existing approach in term of wire length and worst negative slack. The experiments are conducted for small and large nets considering fixed and varied obstacles and outcome shows the proposed efficiency over existing approaches. The OADORSMT is designed in such a way where it can be parallelized to obtain better efficiency.</span></p>

Less is more: Simple stimuli provoke more variable search strategies.

2020 ◽  
Author(s):  
Anna Nowakowska ◽  
Alasdair D F Clarke ◽  
Jessica Christie ◽  
Josephine Reuther ◽  
Amelia R. Hunt
Keyword(s):  
Line Segment ◽  
Search Strategies ◽  
Complex Objects ◽  
Search Behaviour ◽  
Line Segments ◽  
Surface Level ◽  
Efficient Search ◽  
Less Is More ◽  
Dramatic Shift

We measured the efficiency of 30 participants as they searched through simple line segment stimuli and through a set of complex icons. We observed a dramatic shift from highly variable, and mostly inefficient, strategies with the line segments, to uniformly efficient search behaviour with the icons. These results demonstrate that changing what may initially appear to be irrelevant, surface-level details of the task can lead to large changes in measured behaviour, and that visual primitives are not always representative of more complex objects.

Explanation for Neon Color Effect in Achromatic Line Segments on Chromatic Inducers Based on the Multiple Interpretation Hypothesis

2005 ◽  
Vol 101 (1) ◽  
pp. 267-282
Author(s):  
Seiyu Sohmiya
Keyword(s):  
Visual System ◽  
Line Segment ◽  
Color Contrast ◽  
Achromatic Color ◽  
Line Segments ◽  
Color Effect ◽  
Complementary Color ◽  
Multiple Interpretation ◽  
Color Induction ◽  
Simultaneous Color Contrast

In van Tuijl's neon configurations, an achromatic line segment on a blue inducer produces yellowish illusory color in the illusory area. This illusion has been explained based on the idea of the complementary color induced by the blue inducer. However, it is proposed here that this illusion can be also explained by introducing the assumption that the visual system unconsciously interprets an achromatic color as information that is constituted by transparent and nontransparent colors. If this explanation is correct, not only this illusion, but also the simultaneous color contrast illusion can be explained without using the idea of the complementary color induction.

ALPHA-REGULAR STICK UNKNOTS

2012 ◽  
Vol 21 (06) ◽  
pp. 1250059 ◽  
Author(s):  
CHRISTOPHER FRAYER ◽  
CHRISTOPHER SCHAFHAUSER
Keyword(s):  
Line Segment ◽  
Line Segments

Suppose Pn is a regular n-gon in ℝ2. An embedding f : Pn ↪ ℝ3 is called an α-regular stick knot provided the image of each side of Pn under f is a line segment of length 1 and any two consecutive line segments meet at an angle of α. The main result of this paper proves the existence of α-regular stick unknots for odd n ≥ 7 with α in the range [Formula: see text]. All knots constructed will have trivial knot type, and we will show that any non-trivial α-regular stick knot must have [Formula: see text].

Automatically Evolving Texture Image Descriptors using the Multi-tree Representation in Genetic Programming using Few Instances

2020 ◽  
pp. 1-34
Author(s):  
Harith Al-Sahaf ◽  
Ausama Al-Sahaf ◽  
Bing Xue ◽  
Mengjie Zhang
Keyword(s):  
Genetic Programming ◽  
Feature Vector ◽  
Local Binary Patterns ◽  
Texture Image ◽  
Tree Representation ◽  
Line Segments ◽  
Image Descriptor ◽  
Image Descriptors ◽  
The Cost

The performance of image classification is highly dependent on the quality of the extracted features that are used to build a model. Designing such features usually requires prior knowledge of the domain and is often undertaken by a domain expert who, if available, is very costly to employ. Automating the process of designing such features can largely reduce the cost and efforts associated with this task. Image descriptors, such as local binary patterns, have emerged in computer vision, and aim at detecting keypoints, e.g., corners, line-segments and shapes, in an image and extracting features from those keypoints. In this paper, genetic programming (GP) is used to automatically evolve an image descriptor using only two instances per class by utilising a multi-tree program representation. The automatically evolved descriptor operates directly on the raw pixel values of an image and generates the corresponding feature vector. Seven well-known datasets were adapted to the few-shot setting and used to assess the performance of the proposed method and compared against six hand-crafted and one evolutionary computation-based image descriptor as well as three convolutional neural network (CNN) based methods. The experimental results show that the new method has significantly outperformed the competitor image descriptors and CNN-based methods. Furthermore, different patterns have been identified from analysing the evolved programs.

APT

Fog Computing ◽  
2018 ◽  
pp. 158-182
Author(s):  
Dan Jen ◽  
Michael Meisel ◽  
Daniel Massey ◽  
Lan Wang ◽  
Beichuan Zhang ◽  
...  
Keyword(s):  
Performance Evaluation ◽  
Service Providers ◽  
The Internet ◽  
Global Routing ◽  
Internet Routing ◽  
Internet Address ◽  
Routing Table ◽  
The Cost ◽  
Edge Networks ◽  
Extensive Performance

The global routing system has seen a rapid increase in table size and routing changes in recent years, mostly driven by the growth of edge networks. This growth reflects two major limitations in the current architecture: (a) the conflict between provider-based addressing and edge networks' need for multihoming, and (b) flat routing's inability to provide isolation from edge dynamics. In order to address these limitations, we propose A Practical Tunneling Architecture (APT), a routing architecture that enables the Internet routing system to scale independently from edge growth. APT partitions the Internet address space in two, one for the transit core and one for edge networks, allowing edge addresses to be removed from the routing table in the transit core. Packets between edge networks are tunneled through the transit core. In order to automatically tunnel the packets, APT provides a mapping service between edge addresses and the addresses of their transit-core attachment points. We conducted an extensive performance evaluation of APT using trace data collected from routers at two major service providers. Our results show that APT can tunnel packets through the transit core by incurring extra delay on up to 0.8% of all packets at the cost of introducing only one or a few new or repurposed devices per AS.

A Duplicate Chinese Document Image Retrieval System Based on Line Segment Feature in Character Image Block

2011 ◽  
pp. 14-23
Author(s):  
Yung-Kuan Chan ◽  
Tung-Shou Chen ◽  
Yu-An Ho
Keyword(s):  
Image Retrieval ◽  
Line Segment ◽  
Document Image ◽  
Experimental Results ◽  
Document Images ◽  
Rapid Progress ◽  
Image Block ◽  
Line Segments ◽  
Image Retrieval System ◽  
On Line

With the rapid progress of digital image technology, the management of duplicate document images is also emphasized widely. As a result, this paper suggests a duplicate Chinese document image retrieval (DCDIR) system, which uses the ratio of the number of black pixels to that of white pixels on the scanned line segments in a character image block as the feature of the character image block. Experimental results indicate that the system can indeed effectively and quickly retrieve the desired duplicate Chinese document image from a database.

Basic Geometric Constructions

2021 ◽  
pp. 217-226
Author(s):  
Mark Powell ◽  
Arunima Ray
Keyword(s):  
Dimensional Space ◽  
Intersection Point ◽  
Important Application ◽  
Geometric Constructions ◽  
Clifford Torus ◽  
The Cost ◽  
Regular Homotopy ◽  
Associated Surfaces

Basic geometric constructions, including tubing, boundary twisting, pushing down intersections, and contraction followed by push-off are presented. These moves are used repeatedly later in the proof. New, detailed pictures illustrating these constructions are provided. The Clifford torus at an intersection point between two surfaces in 4-dimensional space is described. The chapter closes with an important application of some of these moves called the Geometric Casson Lemma. This lemma upgrades algebraically dual spheres to geometrically dual spheres, at the cost of introducing more self-intersections. It is also shown that an immersed Whitney move is a regular homotopy of the associated surfaces.

Plate and line segment processes

1978 ◽  
Vol 15 (03) ◽  
pp. 494-501 ◽  
Author(s):  
N. A. Fava ◽  
L. A. Santaló
Keyword(s):  
Line Segment ◽  
Integral Geometry ◽  
Random Variables ◽  
Random Processes ◽  
Line Segments ◽  
Expected Values

Random processes of convex plates and line segments imbedded in R 3 are considered in this paper, and the expected values of certain random variables associated with such processes are computed under a mean stationarity assumption, by resorting to some general formulas of integral geometry.

ON THE STEINER RATIO IN $\mathcal{R}_{n}$

2011 ◽  
Vol 03 (04) ◽  
pp. 473-489
Author(s):  
HAI DU ◽  
WEILI WU ◽  
ZAIXIN LU ◽  
YINFENG XU
Keyword(s):  
Euclidean Space ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Dimensional Euclidean Space ◽  
Minimum Length ◽  
Steiner Ratio ◽  
Line Segments ◽  
Finite Set ◽  
Steiner Minimum Tree ◽  
Set Of Points

The Steiner minimum tree and the minimum spanning tree are two important problems in combinatorial optimization. Let P denote a finite set of points, called terminals, in the Euclidean space. A Steiner minimum tree of P, denoted by SMT(P), is a network with minimum length to interconnect all terminals, and a minimum spanning tree of P, denoted by MST(P), is also a minimum network interconnecting all the points in P, however, subject to the constraint that all the line segments in it have to terminate at terminals. Therefore, SMT(P) may contain points not in P, but MST(P) cannot contain such kind of points. Let [Formula: see text] denote the n-dimensional Euclidean space. The Steiner ratio in [Formula: see text] is defined to be [Formula: see text], where Ls(P) and Lm(P), respectively, denote lengths of a Steiner minimum tree and a minimum spanning tree of P. The best previously known lower bound for [Formula: see text] in the literature is 0.615. In this paper, we show that [Formula: see text] for any n ≥ 2.

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