交换交叉立方网络在PMC模型下的(t,k)-诊断度研究

doi:10.11959/j.issn.1000-436x.2019099

通信学报 ›› 2019, Vol. 40 ›› Issue (6): 190-202.doi: 10.11959/j.issn.1000-436x.2019099

交换交叉立方网络在PMC模型下的(t,k)-诊断度研究

郭晨^1,²,肖志芳¹,冷明¹(),彭硕¹,王博¹

¹ 井冈山大学电子与信息工程学院，江西吉安 343009
² 江西省农作物生长物联网技术工程实验室，江西吉安 343009

修回日期:2019-01-06 出版日期:2019-06-25 发布日期:2019-07-04
作者简介:郭晨（1979- ），男，江西泰和人，博士，井冈山大学副教授，主要研究方向为网络分析与控制、新型互连网络和系统级故障诊断等。|肖志芳（1985- ），女，江西吉安人，井冈山大学硕士生，主要研究方向为网络分析与控制、云计算和大数据等。|冷明（1975- ），男，江西高安人，博士，井冈山大学教授，主要研究方向为网络分析与控制、云计算和大数据等。|彭硕（1982- ），男，江西吉安人，井冈山大学副教授，主要研究方向为智能算法、数据挖掘和数据分析等。|王博（1980- ），男，江西吉安人，井冈山大学副教授，主要研究方向为神经网络和进化算法。
基金资助:
国家自然科学基金资助项目(61862035);国家自然科学基金资助项目(61562046);国家自然科学基金资助项目(61864003);江西省教育厅科技基金资助项目(GJJ180556);江西省教育厅科技基金资助项目(GJJ180562)

(t,k)-diagnosability of exchanged crossed cube under the PMC model

GUO Chen^1,²,XIAO Zhifang¹,LEMG Ming¹(),PENG Shuo¹,WANG Bo¹

¹ School of Electronic and Information Engineering,Jinggangshan University,Ji’an 343009,China
² Jiangxi Engineering Laboratory of IoT Technologies for Crop Growth,Ji’an 343009,China

Revised:2019-01-06 Online:2019-06-25 Published:2019-07-04
Supported by:
The National Natural Science Foundation of China(61862035);The National Natural Science Foundation of China(61562046);The National Natural Science Foundation of China(61864003);The Science and Technology Project of Jiangxi Provincial Education Department(GJJ180556);The Science and Technology Project of Jiangxi Provincial Education Department(GJJ180562)

摘要/Abstract

摘要：

交换交叉立方网络是新型互连网络拓扑结构研究的最新成果之一，它同时继承了交换超立方网络和交叉立方网络在网络直径、连接边、成本等方面优点，表现出更高的性价比，有望成为多处理器并行计算机的一种更加优化的组织形式。然而，目前，交换交叉立方网络尚未正式引入多处理器并行计算机。影响交换交叉立方网络应用和推广的主要原因之一是其可靠性研究尚不系统，其中以诊断度为代表的运行可靠性的研究最为迫切。基于此，以交换交叉立方网络为研究对象，在得到交换交叉立方网络相关拓扑性质的基础上，通过理论推导和仿真实验证明的方式，首次得出了交换交叉立方网络 ECQ(s,t)在 PMC 模型下的(t,k)-诊断度，进一步补充完善了交换交叉立方网络的可靠性指标，为后续的应用和推广提供了有力的技术支撑。

关键词: 交换交叉立方网络, PMC模型, (t,k)-可诊断, (t,k)-诊断度

Abstract:

Exchanged crossed cube(ECQ) is one of the latest achievements in the research of topology of novel interconnection networks.ECQ is a more optimized form of organization for multi-processor parallel computers,which retains the advantages of exchanged hypercube and crossed cube in terms of the smaller diameter,fewer links,and lower cost factor,and which indicates more balanced consideration.However,so far,ECQ hadn’t been formally introduced into multi-processor parallel computers.One of the main reasons was that its reliability research wasn’t yet systematic.Among them,the operational reliability represented by diagnosability was the most urgent.ECQ was taken as studying object,after topological analyzing,some important topological properties of ECQ were introduced,which determines the (t,k)-diagnosability of ECQ(s,t) under the PMC model by theoretical deduction and simulation experiments.Simulation results show that ECQ reliability complement and improvement,which provides strong technical support for subsequent application and popularization.

Key words: exchanged crossed cube, PMC model, (t,k)-diagnosable, (t,k)-diagnosability

中图分类号:

TP301

郭晨,肖志芳,冷明,彭硕,王博. 交换交叉立方网络在PMC模型下的(t,k)-诊断度研究[J]. 通信学报, 2019, 40(6): 190-202.

GUO Chen,XIAO Zhifang,LEMG Ming,PENG Shuo,WANG Bo. (t,k)-diagnosability of exchanged crossed cube under the PMC model[J]. Journal on Communications, 2019, 40(6): 190-202.

图/表 16

表1

图1

图2

图3

图4

图5

图6

图7

图8

图9

表2

表3

图10

表4

表5

表6

仿真实验数据与理论推导结果"

ECQ(s,)t		(t ₁,k)-可诊断（仿真结果）		$(⌊ 2^{\frac{s + t + 2 + δ}{4}} ⌋, s + 1)$ +可诊断（理论结果）
s	t	t₁	k	$⌊ 2^{\frac{s + t + 2}{4}} ⌋$	$⌊ 2^{\frac{s + t + 2 + 1}{4}} ⌋$	s+ 1
1	1	2	2	2	2	2
1	2	2	2	2	2	2
1	3	3	2	2	3	2
1	4	3	2	3	4	2
1	5	4	2	4	4	2
2	2	3	3	2	3	3
2	3	3	3	3	4	3
2	4	4	3	4	4	3
2	5	5	3	4	5	3
3	3	4	4	4	4	4
3	4	5	4	4	5	4
3	5	6	4	5	6	4
4	4	6	5	5	6	5
4	5	7	5	6	8	5
5	5	9	6	8	9	6

表6

参考文献 22

[1]	LAI P L , TAN J M , CHANG C P ,et al. Conditional diagnosability measures for large multiprocessor systems[J]. IEEE Transactions on Computers, 2005,54(2): 165-175.
[2]	PREPARATA F P , METZE G , CHIEN R T . On the connection assignment problem of diagnosable systems[J]. IEEE Transactions Electronic Computers, 1967,16(12): 848-854.
[3]	ARAKI T , SHIBATA Y . (t,k)-diagnosable system:a generalization of the PMC models[J]. IEEE Transactions on Computers, 2003,52(7): 971-975.
[4]	CHANG G Y . Conditional (t,k)-diagnosis under the PMC model[J]. IEEE Transactions Parallel and Distributed Systems, 2011,22(11): 1797-1803.
[5]	CHANG G Y , CHEN G H , CHANG G J . (t,k)-diagnosis for matching composition networks[J]. IEEE Transactions Computers, 2006,55(1): 88-92.
[6]	CHEN C A , HSIEH S Y . (t,k)-diagnosis for component-composition graphs under the MM* model[J]. IEEE Transactions Computers, 2011,60(12): 1704-1717.
[7]	CHEN C A , CHANG G Y , HSIEH S Y . Conditional (t,k)-diagnosis in graphs by using the comparison diagnosis model[J]. IEEE Transactions Computers, 2015,64(6): 1622-1632.
[8]	WEI C C , CHEN C A , HSIEH S Y . Conditional (t,k)-diagnosis in regular and irregular graphs under the comparison diagnosis model[J]. IEEE Transactions Dependable and Secure Computing, 2016,PP(99): 1-7.
[9]	CHEN C A , HSIEH S Y . Component-composition graphs:(t,k)-diagnosability and its application[J]. IEEE Transactions on Computers, 2013,62(6): 1097-1110.
[10]	熊茜, 梁家荣, 马强 . 交换超立方网络的(t,k)故障诊断度研究[J]. 通信学报, 2016,37(3): 190-198.
	XIONG X , LIANG J R , MA Q . Research on (t,k)-diagnosability for exchanged hypercube network[J]. Journal on Communications, 2016,37(3): 190-198.
[11]	梁家荣, 陈秒江 . 基于比较模型的扩展立方体网络的(t,k)-诊断度研究[J]. 通信学报, 2017,38(8): 9-18.
	LIANG J R , CHEN M J . Research on(t,k)-diagnosability for augmented cube network under the comparison model[J]. Journal on Communications, 2017,38(8): 9-18.
[12]	FENG N T . A survey of interconnection networks[J]. Computer, 1981,14(12): 12-27.
[13]	LI K , MU Y , K LI . Exchanged crossed cube:a novel interconnection network for parallel computation[J]. IEEE Transactions on Parallel and Distributed Systems, 2013,24(11): 2211-2219.
[14]	PETER K K , HSU W J , PAN Y . The exchanged hypercube[J]. IEEE Transactions on Parallel and Distributed Systems, 2005,6(9): 866-874.
[15]	EFE K . The crossed cube architecture for parallel compution[J]. IEEE Transactions on Parallel and Distributed Systems, 1992,3(5): 513-646.
[16]	PENG S L , LIN C K , TAN J J M ,et al. The g-good-neighbor conditional diagnosability of hypercube under PMC model[J]. Applied Mathematics and Computation, 2012,218(21): 10406-10412.
[17]	NING W , FENG X , WANG L . The connectivity of exchanged crossed cube[J]. Information Processing Letters, 2015,115(2): 394-396.
[18]	郭晨, 冷明, 彭硕 ,等. 交换交叉立方网络在MM模型下的条件诊断度研究[J]. 通信学报, 2017,38(9): 106-124.
	GUO C , LENG M , PENG S ,et al. Conditional diagnosability of exchanged crossed cube under the MM model[J]. Journal on Communications, 2017,38(9): 106-124.
[19]	HAKIMI S L , AMIN A T . Characterization of connection assignment of diagnosable systems[J]. IEEE Transactions on Computers, 1974,23(1): 86-88.
[20]	张大方, 江招生 . 基于集团的系统级故障诊断研究[J]. 计算机学报, 1998,21(4): 308-314.
	ZHANG D F , JIANG Z S . The research of the system-level fault diagnosis based on the body[J]. Chinese Journal of Computers, 1998,21(4): 308-314.
[21]	郭晨, 梁家荣, 葛志辉 ,等. 基于互测PMC模型的条件诊断算法[J]. 电子学报, 2015,43(2): 255-261.
	GUO C , LIANG J R , GE Z H ,et al. A conditional diagnosis algorithm based on ex-test PMC model[J]. ACTA Electronica Sinica, 2015,43(2): 255-261.
[22]	YE L C , LIANG J R . Five-round adaptive diagnosis in hamiltonian networks[J]. IEEE Transactions Parallel ＆ Distributed Systems, 2015,26(9): 2459-2464.

u	v	σ (u,v)
00	01	0 1
1	0	0/1
1	1	0/1

节点编号	节点地址值	节点编号	节点地址值	节点编号	节点地址值	节点编号	节点地址值
0	00000	8	01000	16	10000	24	11000
1	00001	9	01001	17	10001	25	11001
2	00010	10	01010	18	10010	26	11010
3	00011	11	01011	19	10011	27	11011
4	00100	12	01100	20	10100	28	11100
5	00101	13	01101	21	10101	29	11101
6	00110	14	01110	22	10110	30	11110
7	00111	15	01111	23	10111	31	11111

交换交叉立方网络在PMC模型下的(t,k)-诊断度研究

(t,k)-diagnosability of exchanged crossed cube under the PMC model

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参考文献 22

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序号																节点编号
序号	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31
1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1
5	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0
6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	1
#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#
2³²-1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0
2³²	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1

[1]	郭晨,冷明,彭硕,王博. 交换交叉立方网络在MM模型下的条件诊断度研究[J]. 通信学报, 2017, 38(9): 106-124.
[2]	梁家荣,陈秒江. 基于比较模型的扩展立方体网络的（t，k）-诊断度研究[J]. 通信学报, 2017, 38(8): 9-18.
[3]	熊茜,梁家荣,马强. 交换超立方网络的(t,k)故障诊断度研究[J]. 通信学报, 2016, 37(3): 190-198.

序号																节点编号
序号	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31
1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0
4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0
5	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0
#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#
5 178	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#	#
35 959	1	1	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
35 960	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0