Improved Parallel Legalization Schemes for Standard Cell Placement with Obstacles

In standard cell placement, a circuit is given consisting of cells with a standard height, (different widths) and the problem is to place the cells in the standard rows of a chip area so that no overlaps occur and some target function is optimized. The process is usually split into at least two phases. In a first pass, a global placement algorithm distributes the cells across the circuit area, while in the second step, a legalization algorithm aligns the cells to the standard rows of the power grid and alleviates any overlaps. While a few legalization schemes have been proposed in the past for the basic problem formulation, few obstacle-aware extensions exist. Furthermore, they usually provide extreme trade-offs between time performance and optimization efficiency. In this paper, we focus on the legalization step, in the presence of pre-allocated modules acting as obstacles. We extend two known algorithmic approaches, namely Tetris and Abacus, so that they become obstacle-aware. Furthermore, we propose a parallelization scheme to tackle the computational complexity. The experiments illustrate that the proposed parallelization method achieves a good scalability, while it also efficiently prunes the search space resulting in a superlinear speedup. Furthermore, this time performance comes at only a small cost (sometimes even improvement) concerning the typical optimization metrics

Improved Parallel Legalization Schemes for Standard Cell Placement with Obstacles

In standard cell placement, a circuit is given consisting of cells with a standard height, (different widths) and the problem is to place the cells in the standard rows of a chip area so that no overlaps occur and some target function is optimized. The process is usually split into at least two phases. In a first pass, a global placement algorithm distributes the cells across the circuit area, while in the second step, a legalization algorithm aligns the cells to the standard rows of the power grid and alleviates any overlaps. While a few legalization schemes have been proposed in the past for the basic problem formulation, few obstacle-aware extensions exist. Furthermore, they usually provide extreme trade-offs between time performance and optimization efficiency. In this paper, we focus on the legalization step, in the presence of pre-allocated modules acting as obstacles. We extend two known algorithmic approaches, namely Tetris and Abacus, so that they become obstacle-aware. Furthermore, we propose a parallelization scheme to tackle the computational complexity. The experiments illustrate that the proposed parallelization method achieves a good scalability, while it also efficiently prunes the search space resulting in a superlinear speedup. Furthermore, this time performance comes at only a small cost (sometimes even improvement) concerning the typical optimization metrics

A Neuropsychological Approach of Developmental Dyscalculia and a Screening Test Via a Web Application

Traditional definitions of Developmental Dyscalculia state that a child must substantially underachieve on mathematical abilities tests relative to the level expected given age, education and intelligence. However, cognitive developmental neuropsychological studies nowadays suggest that not only core numerical but also cognitive skills of children with developmental dyscalculia present deficits. The main aim of the research protocol was to construct a battery of six tests that can be delivered by computer in order to screen children’s arithmetic and cognitive skills. The hypothesis of the study was that children that are already diagnosed by paper and pencil tests as dyscalculic will present lower scores and larger time latencies not only in arithmetical but also in executive function tasks. A total of 134 right handed children (74 male and 60 female, age range 8 – 12 years) participated in this study. The students with disorders in mathematics (N= 67, 37 male and 30 female age range 8 – 12 years M= 10.15 SD=1.10) had a statement of dyscalculia after assessment at a Centre of Diagnosis, Assessment and Support, as it is required by Greek Law. A comparison group without any learning disabilities was individually matched with the dyscalculic group according to age, sex and grade (N=67, 37 male and 30 female, age range 8 – 12 years old, M=10.24 SD=1.12). Statistical analysis revealed that children with dyscalculia had statistically significant lower mean scores of correct answers and larger time latencies in all tasks compared to their average peers that participated in the comparison group.

A Neuropsychological Approach of Developmental Dyscalculia and a Screening Test Via a Web Application

Traditional definitions of Developmental Dyscalculia state that a child must substantially underachieve on mathematical abilities tests relative to the level expected given age, education and intelligence. However, cognitive developmental neuropsychological studies nowadays suggest that not only core numerical but also cognitive skills of children with developmental dyscalculia present deficits. The main aim of the research protocol was to construct a battery of six tests that can be delivered by computer in order to screen children’s arithmetic and cognitive skills. The hypothesis of the study was that children that are already diagnosed by paper and pencil tests as dyscalculic will present lower scores and larger time latencies not only in arithmetical but also in executive function tasks. A total of 134 right handed children (74 male and 60 female, age range 8 – 12 years) participated in this study. The students with disorders in mathematics (N= 67, 37 male and 30 female age range 8 – 12 years M= 10.15 SD=1.10) had a statement of dyscalculia after assessment at a Centre of Diagnosis, Assessment and Support, as it is required by Greek Law. A comparison group without any learning disabilities was individually matched with the dyscalculic group according to age, sex and grade (N=67, 37 male and 30 female, age range 8 – 12 years old, M=10.24 SD=1.12). Statistical analysis revealed that children with dyscalculia had statistically significant lower mean scores of correct answers and larger time latencies in all tasks compared to their average peers that participated in the comparison group.

A Neuropsychological Approach of Developmental Dyscalculia and a Screening Test Via a Web Application

Traditional definitions of Developmental Dyscalculia state that a child must substantially underachieve on mathematical abilities tests relative to the level expected given age, education and intelligence. However, cognitive developmental neuropsychological studies nowadays suggest that not only core numerical but also cognitive skills of children with developmental dyscalculia present deficits. The main aim of the research protocol was to construct a battery of six tests that can be delivered by computer in order to screen children’s arithmetic and cognitive skills. The hypothesis of the study was that children that are already diagnosed by paper and pencil tests as dyscalculic will present lower scores and larger time latencies not only in arithmetical but also in executive function tasks. A total of 134 right handed children (74 male and 60 female, age range 8 – 12 years) participated in this study. The students with disorders in mathematics (N= 67, 37 male and 30 female age range 8 – 12 years M= 10.15 SD=1.10) had a statement of dyscalculia after assessment at a Centre of Diagnosis, Assessment and Support, as it is required by Greek Law. A comparison group without any learning disabilities was individually matched with the dyscalculic group according to age, sex and grade (N=67, 37 male and 30 female, age range 8 – 12 years old, M=10.24 SD=1.12). Statistical analysis revealed that children with dyscalculia had statistically significant lower mean scores of correct answers and larger time latencies in all tasks compared to their average peers that participated in the comparison group.