Some results on decomposable and reducible graph properties

Coarse-grained reconfigurable architecture (CGRA) mapping involves three main steps: placement, routing, and timing. The mapping is an NP-complete problem, and a common strategy is to decouple this process into its independent steps. This work focuses on the placement step, and its aim is to propose a technique that is both reasonably fast and leads to high-performance solutions. Furthermore, a near-optimal placement simplifies the following routing and timing steps. Exact solutions cannot find placements in a reasonable execution time as input designs increase in size. Heuristic solutions include meta-heuristics, such as Simulated Annealing (SA) and fast and straightforward greedy heuristics based on graph traversal. However, as these approaches are probabilistic and have a large design space, it is not easy to provide both run-time efficiency and good solution quality. We propose a graph traversal heuristic that provides the best of both: high-quality placements similar to SA and the execution time of graph traversal approaches. Our placement introduces novel ideas based on “you only traverse twice” (YOTT) approach that performs a two-step graph traversal. The first traversal generates annotated data to guide the second step, which greedily performs the placement, node per node, aided by the annotated data and target architecture constraints. We introduce three new concepts to implement this technique: I/O and reconvergence annotation, degree matching, and look-ahead placement. Our analysis of this approach explores the placement execution time/quality trade-offs. We point out insights on how to analyze graph properties during dataflow mapping. Our results show that YOTT is 60.6 , 9.7 , and 2.3 faster than a high-quality SA, bounding box SA VPR, and multi-single traversal placements, respectively. Furthermore, YOTT reduces the average wire length and the maximal FIFO size (additional timing requirement on CGRAs) to avoid delay mismatches in fully pipelined architectures.

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THE CONJUGACY CLASSES OF SOME FINITE METABELIAN GROUPS AND THEIR RELATED GRAPHS

Jurnal Teknologi ◽

10.11113/jt.v79.7608 ◽

2016 ◽

Vol 79 (1) ◽

Author(s):

Nor Haniza Sarmin ◽

Ain Asyikin Ibrahim ◽

Alia Husna Mohd Noor ◽

Sanaa Mohamed Saleh Omer

Keyword(s):

Graph Theory ◽

Conjugacy Class ◽

Dihedral Group ◽

Clique Number ◽

Conjugacy Classes ◽

Quaternion Group ◽

Metabelian Groups ◽

Dominating Number ◽

Graph Properties ◽

Class Graph

In this paper, the conjugacy classes of three metabelian groups, namely the Quasi-dihedral group, Dihedral group and Quaternion group of order 16 are computed. The obtained results are then applied to graph theory, more precisely to conjugate graph and conjugacy class graph. Some graph properties such as chromatic number, clique number, dominating number and independent number are found.

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Reciprocal degree distance and graph properties

Discrete Applied Mathematics ◽

10.1016/j.dam.2018.11.012 ◽

2019 ◽

Vol 258 ◽

pp. 1-7

Author(s):

Mingqiang An ◽

Yinan Zhang ◽

Kinkar Ch. Das ◽

Liming Xiong

Keyword(s):

Graph Properties ◽

Degree Distance

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Modal Expressiveness of Graph Properties

Electronic Notes in Theoretical Computer Science ◽

10.1016/j.entcs.2008.03.064 ◽

2008 ◽

Vol 205 ◽

pp. 31-47 ◽

Cited By ~ 2

Author(s):

Mario R.F. Benevides ◽

L. Menasché Schechter

Keyword(s):

Graph Properties

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Crafting Efficient Neural Graph of Large Entropy

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2019/311 ◽

2019 ◽

Author(s):

Minjing Dong ◽

Hanting Chen ◽

Yunhe Wang ◽

Chang Xu

Keyword(s):

Information Flow ◽

Network Architecture ◽

High Performance ◽

Global Information ◽

High Quality ◽

Network Pruning ◽

Initial Network ◽

Trade Offs ◽

Graph Properties ◽

Deep Cnn

Network pruning is widely applied to deep CNN models due to their heavy computation costs and achieves high performance by keeping important weights while removing the redundancy. Pruning redundant weights directly may hurt global information flow, which suggests that an efficient sparse network should take graph properties into account. Thus, instead of paying more attention to preserving important weight, we focus on the pruned architecture itself. We propose to use graph entropy as the measurement, which shows useful properties to craft high-quality neural graphs and enables us to propose efficient algorithm to construct them as the initial network architecture. Our algorithm can be easily implemented and deployed to different popular CNN models and achieve better trade-offs.

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