scholarly journals On Rectilinear Distance-Preserving Trees

VLSI Design ◽  
1998 ◽  
Vol 7 (1) ◽  
pp. 15-30
Author(s):  
Gustavo E. Téllez ◽  
Majid Sarrafzadeh

Given a set of terminals on the plane N={s,ν1,…,νn}, with a source terminal s, a Rectilinear Distance-Preserving Tree (RDPT) T(V, E) is defined as a tree rooted at s, connecting all terminals in N. An RDPT has the property that the length of every source to sink path is equal to the rectilinear distance between that source and sink. A Min- Cost Rectilinear Distance-Preserving Tree (MRDPT) minimizes the total wire length while maintaining minimal source to sink linear delay, making it suitable for high performance interconnect applications.This paper studies problems in the construction of RDPTs, including the following contributions. A new exact algorithm for a restricted version of the problem in one quadrant with O(n2) time complexity is proposed. A novel heuristic algorithm, which uses optimally solvable sub-problems, is proposed for the problem in a single quadrant. The average and worst-case time complexity for the proposed heuristic algorithm are O(n3/2) and O(n3), respectively. A 2-approximation of the quadrant merging problem is proposed. The proposed algorithm has time complexity O(α2T(n)+α3) for any constant α > 1, where T(n) is the time complexity of the solution of the RDPT problem on one quadrant. This result improves over the best previous quadrant merging solution which has O(n2T(n)+n3) time complexity.We test our algorithms on randomly uniform point sets and compare our heuristic RDPT construction against a Minimum Cost Rectilinear Steiner (MRST) tree approximation algorithm. Our results show that RDPTs are competitive with Steiner trees in total wire-length when the number of terminals is less than 32. This result makes RDPTs suitable for VLSI routing applications. We also compare our algorithm to the Rao-Shor RDPT approximation algorithm obtaining improvements of up to 10% in total wirelength. These comparisons show that the algorithms proposed herein produce promising results.

VLSI Design ◽  
2007 ◽  
Vol 2007 ◽  
pp. 1-13 ◽  
Author(s):  
Ethiopia Nigussie ◽  
Teijo Lehtonen ◽  
Sampo Tuuna ◽  
Juha Plosila ◽  
Jouni Isoaho

High-performance long-range NoC link enables efficient implementation of network-on-chip topologies which inherently require high-performance long-distance point-to-point communication such as torus and fat-tree structures. In addition, the performance of other topologies, such as mesh, can be improved by using high-performance link between few selected remote nodes. We presented novel implementation of high-performance long-range NoC link based on multilevel current-mode signaling and delay-insensitive two-phase 1-of-4 encoding. Current-mode signaling reduces the communication latency of long wires significantly compared to voltage-mode signaling, making it possible to achieve high throughput without pipelining and/or using repeaters. The performance of the proposed multilevel current-mode interconnect is analyzed and compared with two reference voltage mode interconnects. These two reference interconnects are designed using two-phase 1-of-4 encoded voltage-mode signaling, one with pipeline stages and the other using optimal repeater insertion. The proposed multilevel current-mode interconnect achieves higher throughput and lower latency than the two reference interconnects. Its throughput at 8 mm wire length is 1.222 GWord/s which is 1.58 and 1.89 times higher than the pipelined and optimal repeater insertion interconnects, respectively. Furthermore, its power consumption is less than the optimal repeater insertion voltage-mode interconnect, at 10 mm wire length its power consumption is 0.75 mW while the reference repeater insertion interconnect is 1.066 mW. The effect of crosstalk is analyzed using four-bit parallel data transfer with the best-case and worst-case switching patterns and a transmission line model which has both capacitive coupling and inductive coupling.


2014 ◽  
Vol 626 ◽  
pp. 127-135 ◽  
Author(s):  
D. Jessintha ◽  
M. Kannan ◽  
P.L. Srinivasan

Discrete Cosine Transform (DCT) is commonly used in image compression. In the history of DCT, a milestone was the Distributed Arithmetic (DA) technique. Due to the technology dependency a multiplier-less computation was built with DA based technique. It occupied less area but the throughput is less. Later, due to the technology scaling, multiplier based architectures can be easily adapted for low-power and high-performance architecture. Fixed width multipliers [1]-[7] reduces hardware and time complexity. In this work, Radix 4 fixed width multiplier is adapted with DCT architecture due to low power consumption and saves 30% power. In order to reduce truncation errors caused during fixed width multiplication, an estimation circuit is designed based on conditional probability theory.


2015 ◽  
Vol 2015 ◽  
pp. 1-20
Author(s):  
Gongyu Wang ◽  
Greg Stitt ◽  
Herman Lam ◽  
Alan George

Field-programmable gate arrays (FPGAs) provide a promising technology that can improve performance of many high-performance computing and embedded applications. However, unlike software design tools, the relatively immature state of FPGA tools significantly limits productivity and consequently prevents widespread adoption of the technology. For example, the lengthy design-translate-execute (DTE) process often must be iterated to meet the application requirements. Previous works have enabled model-based, design-space exploration to reduce DTE iterations but are limited by a lack of accurate model-based prediction of key design parameters, the most important of which is clock frequency. In this paper, we present a core-level modeling and design (CMD) methodology that enables modeling of FPGA applications at an abstract level and yet produces accurate predictions of parameters such as clock frequency, resource utilization (i.e., area), and latency. We evaluate CMD’s prediction methods using several high-performance DSP applications on various families of FPGAs and show an average clock-frequency prediction error of 3.6%, with a worst-case error of 20.4%, compared to the best of existing high-level prediction methods, 13.9% average error with 48.2% worst-case error. We also demonstrate how such prediction enables accurate design-space exploration without coding in a hardware-description language (HDL), significantly reducing the total design time.


2020 ◽  
Vol 79 (Suppl 1) ◽  
pp. 266.2-267
Author(s):  
W. Han ◽  
X. Wang ◽  
L. Li ◽  
S. Wichuk ◽  
E. Hutchings ◽  
...  

Background:Early diagnosis of rheumatoid arthritis (RA) is hampered by suboptimal accuracy of currently available serological biomarkers. Metabolomics may reveal promising biomarker candidates associated with the biomolecular processes of RA. In this work, we applied a high-performance chemical isotope labeling (CIL) LC-MS technique for in-depth profiling of the amine/phenol-submetabolome in serum samples. To avoid false positives and obtain high-confidence biomarker candidates, we analyzed three independent sets of serum samples collected from RA patients and healthy controls to examine the common effects.Objectives:We aimed to identify a metabolite signature with consistently high accuracy for RA.Methods:Serum samples were taken from 3 RA cohorts, which comprised 50, 49, and 131 RA patients, respectively. Within each cohort, there were sex/age-matched healthy controls: 50 in Cohort 1, 50 in Cohort 2, and 100 in Cohort 3. Among these 446 subjects, 75% were females and the average age was 52.5 years. Amine/phenol-containing metabolites were labeled by12C-dansyl chloride to improve the LC-MS detection. For each cohort, a pooled sample was prepared and labeled by13C-dansyl group to serve as the reference sample for relative quantification. Then the individual samples and the pooled sample were mixed 1:1. Finally, an LC-QTOF-MS platform analyzed the mixtures and output the intensity ratios of12C/13C peak pairs.Results:1,149 amine/phenol-containing metabolites were commonly detected across the three sample sets. Among them, 134 were positively identified by our dansyl-labeling standard library, and 141 were matched to predicted retention times and mass values of dansyl-labeled human metabolites. Visualized by the partial least squares discriminant analysis (PLS-DA), the overall amine/phenol-submetabolome demonstrated clear and consistent differences between healthy controls and the RA groups, with cross-validation Q2 = 0.765, 0.745, 0.793, respectively. The selection of significant metabolites was conducted according to the fold change and false-discovery-rate-adjusted Welch’s t-test. Cohort 1 demonstrated 85 metabolites having higher concentrations in the RA samples than the controls, and 89 metabolites with lowered concentrations. The numbers of increased/decreased metabolites in Cohort 2 and 3 were 87/26 and 90/53, respectively. Importantly, there were 59 significantly discriminatory metabolites commonly found in the three data sets (49 increased and 9 decreased). We picked the top three with the highest univariate classification performance to form a biomarker panel. We implemented the linear support vector machine (SVM) to build the classifier and the receiver operating characteristic (ROC) analysis to measure the performance. The area-under-the-curve (AUC) values (95% confidence interval) were 1.000 (1.000-1.000), 0.992 (0.967-1.000) and 0.902 (0.858-0.945) for the three cohorts, respectively. The results revealed the importance of examining multiple sample sets and even in the worst case (Cohort 3), our biomarker candidates could differentiate RA at 82.5% sensitivity and 82.5% specificity. Particularly, in Cohort 3, there were 30 RA patients negative for anti-cyclic citrullinated peptide and rheumatoid factor, and our metabolite panel demonstrated consistently high performance for differentiating these specific subjects from healthy controls.Conclusion:Metabolites showing significant and consistent changes associated with RA have been identified with high discriminative power.Disclosure of Interests:Wei Han: None declared, Xiaohang Wang: None declared, Liang Li: None declared, Stephanie Wichuk: None declared, Edna Hutchings: None declared, Rana Dadashova: None declared, Joel Paschke: None declared, Walter P Maksymowych Grant/research support from: Received research and/or educational grants from Abbvie, Novartis, Pfizer, UCB, Consultant of: WPM is Chief Medical Officer of CARE Arthritis Limited, has received consultant/participated in advisory boards for Abbvie, Boehringer, Celgene, Eli-Lilly, Galapagos, Gilead, Janssen, Novartis, Pfizer, UCB, Speakers bureau: Received speaker fees from Abbvie, Janssen, Novartis, Pfizer, UCB.


2008 ◽  
Vol Vol. 10 no. 3 (Graph and Algorithms) ◽  
Author(s):  
Dariusz Dereniowski ◽  
Adam Nadolski

Graphs and Algorithms International audience We study two variants of edge-coloring of edge-weighted graphs, namely compact edge-coloring and circular compact edge-coloring. First, we discuss relations between these two coloring models. We prove that every outerplanar bipartite graph admits a compact edge-coloring and that the decision problem of the existence of compact circular edge-coloring is NP-complete in general. Then we provide a polynomial time 1:5-approximation algorithm and pseudo-polynomial exact algorithm for compact circular coloring of odd cycles and prove that it is NP-hard to optimally color these graphs. Finally, we prove that if a path P2 is joined by an edge to an odd cycle then the problem of the existence of a compact circular coloring becomes NP-complete.


2012 ◽  
Vol 239-240 ◽  
pp. 1557-1560
Author(s):  
Hai Yan Zhou ◽  
Li Ping Wen

The problem of the great group of a figure is the famous NP-difficult problem. There exists an algorithm of solving the great group of figure or only applying to some of the special figure .There need time price is index level, and is low efficiency. It puts forward a kind of solving the minimax group partition algorithm with the most magnanimous nodes for elicitation information. This algorithm can be applied to any simple figure, and the maximum time complexity of algorithm is O(sn3).


2012 ◽  
Vol 16 (6) ◽  
pp. 974-979 ◽  
Author(s):  
Joo-Ha Lee ◽  
Young-Soo Yoon ◽  
Joong-Hoon Kim

Author(s):  
William C. Regli ◽  
Satyandra K. Gupta ◽  
Dana S. Nau

Abstract While automated recognition of features has been attempted for a wide range of applications, no single existing approach possesses the functionality required to perform manufacturability analysis. In this paper, we present a methodology for taking a CAD model of a part and extracting a set of machinable features that contains the complete set of alternative interpretations of the part as collections of MRSEVs (Material Removal Shape Element Volumes, a STEP-based library of machining features). The approach handles a variety of features including those describing holes, pockets, slots, and chamfering and filleting operations. In addition, the approach considers accessibility constraints for these features, has an worst-case algorithmic time complexity quadratic in the number of solid modeling operations, and modifies features recognized to account for available tooling and produce more realistic volumes for manufacturability analysis.


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