AWGR-Based Optical Topologies for Scalable and Efficient Global Communications in Large-Scale Multi-Processor Systems

Xiaohui Ye; S. J. B. Yoo; Venkatesh Akella

doi:10.1364/JOCN.4.000651

Journal of Optical Communications and Networking
Vol. 4,
Issue 9,
pp. 651-662
(2012)
•https://doi.org/10.1364/JOCN.4.000651

AWGR-Based Optical Topologies for Scalable and Efficient Global Communications in Large-Scale Multi-Processor Systems

Xiaohui Ye, S. J. B. Yoo, and Venkatesh Akella

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Xiaohui Ye, S. J. B. Yoo, and Venkatesh Akella, "AWGR-Based Optical Topologies for Scalable and Efficient Global Communications in Large-Scale Multi-Processor Systems," J. Opt. Commun. Netw. 4, 651-662 (2012)

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Abstract

In large-scale multi-processor computing systems, global communications are typically supported by an auxiliary network (e.g., IBM Blue Gene) or with hardware support in the network (e.g., NEC Earth Simulator). We explore the potential for realizing efficient global communications that can scale beyond a million processors by harnessing the unique parallelism and wavelength routing properties of optical devices. Specifically, we use an arrayed waveguide grating router (AWGR) device as the basic building block in realizing scalable global communication. The AWGR is a passive switch fabric (wavelength router) that uses multiple wavelengths to interconnect outputs and inputs by following a specific cyclic wavelength routing (permutation) pattern. We analyze different network topologies using AWGR devices for barrier synchronization and propose techniques to pick parameters of the network for a given number of processors. We compare the performance and energy consumption for barrier synchronization with what is achievable with state-of-the-art electrical networks.

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Equations (13)

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(a) $k = 8$
s	3	4	5	6	7	8	10	14
$h_{1}$	0	1	2	3	4	0	2	4
$h_{2}$	1	1	1	1	1	2	2	0
n	7	6	5	4	3	6	4	4
N	56	84	120	160	192	588	800	10,000
(b) $k = 16$
s	3	4	5	6	7	8	9	10
$h_{1}$	0	1	2	3	4	0	1	2
$h_{2}$	1	1	1	1	1	2	2	2
n	15	10	9	6	5	14	9	8
N	240	660	1440	2688	3840	6300	10,800	20,736

s	11	12	13	14	17	20	26
$h_{1}$	3	4	5	0	3	0	0
$h_{2}$	2	2	2	4	4	6	8
n	5	8	9	12	9	10	8
N	23,040	41,472	57,600	1.3 × 10 $^{6}$	2.8 × 10 $^{6}$	1.0 × 10 $^{8}$	2.7 × 10 $^{9}$
$k = 32$
s	4	5	6	7	8	9	10
$h_{1}$	1	2	3	4	5	6	7
$h_{2}$	1	1	1	1	1	1	1
n	18	13	10	11	10	9	10
N	4788	18,200	56,320	1.7 × 10 $^{5}$	3.8 × 10 $^{5}$	8.3 × 10 $^{5}$	1.8 × 10 $^{6}$
s	11	12	13	14	17	20
$h_{1}$	8	9	10	0	3	0
$h_{2}$	1	1	1	4	4	6
n	7	6	5	28	13	26
N	3.6 × 10 $^{6}$	5.5 × 10 $^{6}$	7.8 × 10 $^{6}$	7.9 × 10 $^{7}$	4.3 × 10 $^{8}$	6.0 × 10 $^{10}$

N	100	10,000	1,000,000
G-AGCNet ( $k = 16$ )	3 ( $h_{1} = 2$ , $h_{2} = 0$ )	9 ( $h_{1} = 1$ , $h_{2} = 2$ )	14 ( $h_{1} = 0$ , $h_{2} = 4$ )
Flattened Butterfly (k-ary n-fly)	17 ( $k = 5$ , $n = 3$ )	34 ( $k = 4$ , $n = 7$ )	49 ( $k = 4$ , $n = 10$ )
Dragonfly	23 ( $p = h = 3$ , $a = 6$ )	43 ( $p = h = 8$ , $a = 16$ )	103 ( $p = h = 23$ , $a = 46$ )
DCell	15 ( $n = 3$ , $k = 2$ )	31 ( $n = 3$ , $k = 3$ )	55 ( $n = 6$ , $k = 3$ )

(a) $k = 8$
s	3	4	5	6	7	8	10	14
$h_{1}$	0	1	2	3	4	0	2	4
$h_{2}$	1	1	1	1	1	2	2	0
n	7	6	5	4	3	6	4	4
N	56	84	120	160	192	588	800	10,000
(b) $k = 16$
s	3	4	5	6	7	8	9	10
$h_{1}$	0	1	2	3	4	0	1	2
$h_{2}$	1	1	1	1	1	2	2	2
n	15	10	9	6	5	14	9	8
N	240	660	1440	2688	3840	6300	10,800	20,736

s	11	12	13	14	17	20	26
$h_{1}$	3	4	5	0	3	0	0
$h_{2}$	2	2	2	4	4	6	8
n	5	8	9	12	9	10	8
N	23,040	41,472	57,600	1.3 × 10 $^{6}$	2.8 × 10 $^{6}$	1.0 × 10 $^{8}$	2.7 × 10 $^{9}$
$k = 32$
s	4	5	6	7	8	9	10
$h_{1}$	1	2	3	4	5	6	7
$h_{2}$	1	1	1	1	1	1	1
n	18	13	10	11	10	9	10
N	4788	18,200	56,320	1.7 × 10 $^{5}$	3.8 × 10 $^{5}$	8.3 × 10 $^{5}$	1.8 × 10 $^{6}$
s	11	12	13	14	17	20
$h_{1}$	8	9	10	0	3	0
$h_{2}$	1	1	1	4	4	6
n	7	6	5	28	13	26
N	3.6 × 10 $^{6}$	5.5 × 10 $^{6}$	7.8 × 10 $^{6}$	7.9 × 10 $^{7}$	4.3 × 10 $^{8}$	6.0 × 10 $^{10}$

Abstract

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Figures (14)

Tables (2)

Equations (13)

Journal of Optical Communications and Networking