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GraphBolt: Dependency-Driven Synchronous Processing of Streaming Graphs

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GraphBolt: Dependency-Driven
Synchronous Processing of Streaming Graphs
Mugilan Mariappan and Keval Vora
Simon Fraser University
EuroSys’19 – Dresden, Germany
March 27, 2019
Graph Processing
2
Dynamic Graph Processing
Real-time Processing
• Low Latency
Real-time Batch Processing
• High Throughput
Alipay payments unit of Chinese retailer Alibaba [..]
has 120 billion nodes and over 1 trillion relationships [..];
this graph has 2 billion updates each day and was running
at 250,000 transactions per second on Singles Day [..]
The Graph Database Poised to Pounce on The Mainstream. Timothy Prickett Morgan, The Next Platform. September 19, 2018.
3
Streaming Graph Processing
Incremental Processing
• Adjust results incrementally
• Reuse work that has already been done
Query
Tornado [SIGMOD’16]
GraphIn [EuroPar’16]
KineoGraph [EuroSys’12]
Graph
Mutations
KickStarter [ASPLOS’17]
..
.
..
.
Tag Propagation
upon mutation
Over 75% values get thrown out
KickStarter: Fast and Accurate Computations on Streaming Graph via Trimmed Approximations. Vora et al., ASPLOS 2017.
4
Streaming Graph Processing
Incremental Processing
• Adjust results incrementally
• Reuse work that has already been done
Query
Tornado [SIGMOD’16]
GraphIn [EuroPar’16]
KineoGraph [EuroSys’12]
Graph
Mutations
KickStarter [ASPLOS’17]
..
.
..
.
Maintain Value Dependences
Incrementally refine results
Less than 0.0005% values thrown out
KickStarter: Fast and Accurate Computations on Streaming Graph via Trimmed Approximations. Vora et al., ASPLOS 2017.
5
Streaming Graph Processing
Incremental Processing
• Adjust results incrementally
• Reuse work that has already been done
Monotonic Graph
Algorithms
Tornado [SIGMOD’16]
GraphIn [EuroPar’16]
KineoGraph [EuroSys’12]
Graph
Mutations
Query
KickStarter [ASPLOS’17]
..
.
..
.
Maintain Value Dependences
Incrementally refine results
Less than 0.0005% values thrown out
KickStarter: Fast and Accurate Computations on Streaming Graph via Trimmed Approximations. Vora et al., ASPLOS 2017.
6
• Belief Propagation
• Co-Training Expectation
Maximization
• Collaborative Filtering
Incorrect Vertices
Streaming Graph Processing
3M
2.5M
2M
1.5M
1M
500K
0
• Label Propagation
1
2
3
4
Updates
5
• …
Incorrect Vertices
• Triangle Counting
6K
5K
Error > 10%
4K
3K
2K
1K
0
1
2
3
4
Updates
5
7
RG
3M
2.5M
2M
1.5M
1M
500K
Incorrect Vertices
I
Incorrect Vertices
Streaming Graph Processing
0
1
2
3
4
Updates
5
6K
5K
Error > 10%
4K
3K
2K
1K
0
1
2
3
4
Updates
5
8
I
k
G
R
RG
3M
2.5M
2M
1.5M
1M
500K
Incorrect Vertices
G mutates at k
Incorrect Vertices
Streaming Graph Processing
0
1
2
3
4
Updates
5
6K
5K
Error > 10%
4K
3K
2K
1K
0
1
2
3
4
Updates
5
9
G mutates at k
R
RG
k+1
?
R
3M
2.5M
2M
1.5M
1M
500K
0
R? ≠ RGM
Incorrect Vertices
I
k
G
Incorrect Vertices
Streaming Graph Processing
1
2
3
4
Updates
5
6K
5K
Error > 10%
4K
3K
2K
1K
0
1
2
3
4
Updates
5
10
G mutates at k
R
RG
k+1
?
R
3M
2.5M
2M
1.5M
1M
500K
0
R? ≠ RGM
1
2
3
4
Updates
5
k
Zs (RG )
k
RGM
RGM
Incorrect Vertices
I
k
G
Incorrect Vertices
Streaming Graph Processing
6K
5K
Error > 10%
4K
3K
2K
1K
0
1
2
3
4
Updates
5
11
GraphBolt
G mutates at k
I
k
RG
RG
k+1
R?
R? ≠ RGM
• Dependency-Driven Incremental
Processing of Streaming Graphs
• Guarantee Bulk Synchronous
Parallel Semantics
k
Zs (RG )
k
RGM
RGM
• Lightweight dependence tracking
• Dependency-aware value refinement
upon graph mutation
12
Bulk Synchronous Processing (BSP)
Vertices
v
u
y
Iteration
x
k-1
v
u
y
x
k
v
u
y
x
Streaming Graph
13
Upon Edge Addition
Vertices
v
u
y
Iteration
x
k-1
v
u
y
x
k
v
u
y
x
Streaming Graph
14
Upon Edge Addition
Vertices
v
u
y
Iteration
x
k-1
v
u
y
x
k
v
u
y
x
k+1
v
u
y
x
Streaming Graph
15
Upon Edge Addition
Vertices
Vertices
v
u
y
Iteration
x
k-1
v
u
y
x
k-1
v
u
y
x
k
v
u
y
x
k
v
u
y
x
v
u
y
x
v
u
y
x
Streaming Graph
Ideal Scenario
16
Upon Edge Addition
Vertices
Vertices
v
u
y
Iteration
x
k-1
v
u
y
x
k-1
v
u
y
x
k
v
u
y
x
k
v
u
y
x
v
u
y
x
v
u
y
x
Streaming Graph
Ideal Scenario
17
Upon Edge Addition
Vertices
Vertices
v
u
y
Iteration
x
k-1
v
u
y
x
k-1
v
u
y
x
k
v
u
y
x
k
v
u
y
x
k+1
v
u
y
x
k+1
v
u
y
x
Streaming Graph
Ideal Scenario
18
Upon Edge Addition
Vertices
u
x
k-2
v
u
y
x
k-2
v
u
y
x
y
k-1
v
u
y
x
k-1
v
u
y
x
k
v
u
y
x
k
v
u
y
x
k+1
v
u
y
x
k+1
v
u
y
x
Iteration
v
Vertices
Streaming Graph
Ideal Scenario
19
Upon Edge Addition
Vertices
u
x
k-2
v
u
y
x
k-2
v
u
y
x
y
k-1
v
u
y
x
k-1
v
u
y
x
k
v
u
y
x
k
v
u
y
x
k+1
v
u
y
x
k+1
v
u
y
x
Iteration
v
Vertices
Streaming Graph
Ideal Scenario
20
Upon Edge Addition
Vertices
u
x
k-2
v
u
y
x
k-2
v
u
y
x
y
k-1
v
u
y
x
k-1
v
u
y
x
k
v
u
y
x
k
v
u
y
x
k+1
v
u
y
x
k+1
v
u
y
x
Iteration
v
Vertices
Streaming Graph
Ideal Scenario
21
Upon Edge Addition
Vertices
u
x
k-2
v
u
y
x
k-2
v
u
y
x
y
k-1
v
u
y
x
k-1
v
u
y
x
k
v
u
y
x
k
v
u
y
x
k+1
v
u
y
x
k+1
v
u
y
x
Iteration
v
Vertices
Streaming Graph
Ideal Scenario
22
Upon Edge Deletion
Vertices
u
x
k-2
v
u
y
x
k-2
v
u
y
x
y
k-1
v
u
y
x
k-1
v
u
y
x
k
v
u
y
x
k
v
u
y
x
k+1
v
u
y
x
k+1
v
u
y
x
Iteration
v
Vertices
Streaming Graph
Ideal Scenario
23
GraphBolt: Correcting Dependencies
Vertices
u
x
k-2
v
u
y
x
k-2
v
u
y
x
y
k-1
v
u
y
x
k-1
v
u
y
x
k
v
u
y
x
k
v
u
y
x
Iteration
v
Vertices
Streaming Graph
Ideal Scenario
24
GraphBolt: Correcting Dependencies
Vertices
u
x
k-2
v
u
y
x
k-2
v
u
y
x
y
k-1
v
u
y
x
k-1
v
u
y
x
k
v
u
y
x
k
v
u
y
x
Iteration
v
Vertices
Streaming Graph
Ideal Scenario
25
GraphBolt: Correcting Dependencies
Vertices
u
x
k-2
v
u
y
x
k-2
v
u
y
x
y
k-1
v
u
y
x
k-1
v
u
y
x
k
v
u
y
x
k
v
u
y
x
Iteration
v
Vertices
Streaming Graph
Ideal Scenario
26
GraphBolt: Correcting Dependencies
Vertices
u
x
k-2
v
u
y
x
k-2
v
u
y
x
y
k-1
v
u
y
x
k-1
v
u
y
x
k
v
u
y
x
k
v
u
y
x
Iteration
v
Vertices
Streaming Graph
Ideal Scenario
27
GraphBolt: Correcting Dependencies
Vertices
u
x
k-2
v
u
y
x
k-2
v
u
y
x
y
k-1
v
u
y
x
k-1
v
u
y
x
k
v
u
y
x
k
v
u
y
x
Iteration
v
Vertices
Streaming Graph
Ideal Scenario
28
GraphBolt: Correcting Dependencies
Vertices
u
x
k-2
v
u
y
x
k-2
v
u
y
x
y
k-1
v
u
y
x
k-1
v
u
y
x
k
v
u
y
x
k
v
u
y
x
k+1
v
u
y
x
k+1
v
u
y
x
Iteration
v
Vertices
Streaming Graph
Ideal Scenario
29
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which aggregated values won’t be track
1.0B
39.5M
dependency graph in terms of aggregation valuesŒat the end
Õ
0 )on
0, s)hand,
0) )
1.5B
41.7M
the
other
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at vertex-le
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8s
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,
s
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of
iteration
k:
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2.0B
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Vertex
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by not
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–
E A = { ( i 1 (u), i ( )) :Õ
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pute vertex value for the current iteration. This computation
can be formulated as 2 :
º
ci ( ) =
(
(c i 1 (u)) )
Iteration
Refinement: Aggregation Types
20:
_dest =e ���T������(E_update)
22:
V _updated
_chan e, �������, i)
21:
_chan
==V������M��(V
_chan e [ V _dest
21:
_chan
_chan e [ V _dest
23:
end
for e ==V������M��(V
22:
V _updated
_chan e, �������, i)
22:
V _updated
=_chan
������M��(V
_chan e, �������,
i)
24:
������M��(V
e, �������B�����,
k)
23:
end
for
23:
end
for
25:
function
24: end
������M��(V
_chan e, �������B�����, k)
24: end
������M��(V
25:
function _chan e, �������B�����, k)
25: end function
Algorithm
2 PageRank - Complex Aggregation
5:
6:
7:
oldpr [u][i]
������S��(&sum[ ][i + 1], old_de ree[u] )
end function
function ���������(e = (u, ), i)
newpr [u][i]
������A��(&sum[ ][i + 1], new_de ree[u] )
end function
function P�������( )
Direct changes
for i 2 [0...k] do
����M��(E_add, �����������, i)
����M��(E_delete, �������, i)
end for
V _updated = ���S������(E_add [ E_delete)
V _chan e = ���T������(E_add [ E_delete)
for i 2 [0...k] do
E_update = {(u, ) : u 2 V _updated }
����M��(E_update, �������, i)
����M��(E_update, ���������, i)
V _dest = ���T������(E_update)
V _chan e = V _chan e [ V _dest
V _updated = ������M��(V _chan e, �������, i)
end for
end function
GraphBolt: Programming Model
Algorithm
PageRank - Complex
1: function2�����������(e
= (u, ), Aggregation
i)
Algorithm
2
PageRank
Complex
Aggregation
oldpr
1: function �����������(e = (u, ),
i) [u][i]
2:
1:
2:
3:
2:
4:
3:
3:
4:
5:
4:
5:
6:
5:
7:
6:
6:
7:
8:
7:
8:
9:
8:
10:
9:
9:
11:
10:
10:
12:
11:
11:
13:
12:
12:
14:
13:
13:
15:
14:
14:
16:
15:
15:
17:
16:
16:
18:
17:
17:
19:
18:
18:
20:
19:
������A��(&sum[ ][i + 1],
ree[u] )
oldpr
function �����������(e = (u, old_de
),
i) [u][i]
������A��(&sum[
][i + 1], old_de
end
function
ree[u] )
oldpr [u][i]
������A��(&sum[
function
�������(e =][i
(u,+ 1],
), i)old_de ree[u] )
end
function
end
function
function
�������(e =][i(u,+ 1],
), i) oldpr [u][i] )
������S��(&sum[
old_de
ree[u]
oldpr [u][i]
function �������(e = (u, ), i)
������S��(&sum[
][i
+
1],
end function
old_de
ree[u] )
oldpr [u][i]
������S��(&sum[
1], ),old_de
function
���������(e][i=+(u,
i)
end
function
ree[u] )
newpr [u][i]
end
function
function
���������(e][i
=+
(u,1],), i)
������A��(&sum[
ree[u] )
newpr [u][i]
function ���������(e = (u, ),new_de
i)
������A��(&sum[
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end
function
ree[u] )
newpr [u][i]
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function
P�������( ) ][i + 1], new_de ree[u] )
end
function
end
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i 2 [0...k]
do )
function
P�������(
function
P�������(
for����M��(E_add,
i 2 [0...k]
do )�����������, i)
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end
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V
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end
for = ���S������(E_add
end
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V
_chan
_updated
���S������(E_add [[E_delete)
E_delete)
_updated
���S������(E_add
E_delete)
for
i 2 [0...k]
do
V
_chan
e ==���T������(E_add
[[E_delete)
V
_chan
e ==
���T������(E_add
[ E_delete)
E_update
{(u, ) : u 2 V _updated
}
for
i 2 [0...k]
do
forE_update
i 2 [0...k]=do
����M��(E_update,
i) }
{(u, ) : u�������,
2 V _updated
E_update
= {(u, ) : u���������,
2 V _updated
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i) i) }
8:
9:
10:
11:
12:
13:
14:
15:
16:
17:
18:
19:
20:
21:
22:
23:
24:
25:
1
40
20:
_dest =e ���T������(E_update)
22:
V _updated
_chan e, �������, i)
21:
_chan
==V������M��(V
_chan e [ V _dest
21:
_chan
_chan e [ V _dest
23:
end
for e ==V������M��(V
22:
V _updated
_chan e, �������, i)
22:
V _updated
=_chan
������M��(V
_chan e, �������,
i)
24:
������M��(V
e, �������B�����,
k)
23:
end
for
23:
end
for
25:
function
24: end
������M��(V
_chan e, �������B�����, k)
24: end
������M��(V
25:
function _chan e, �������B�����, k)
25: end function
Algorithm
2 PageRank - Complex Aggregation
5:
6:
7:
oldpr [u][i]
������S��(&sum[ ][i + 1], old_de ree[u] )
end function
function ���������(e = (u, ), i)
newpr [u][i]
������A��(&sum[ ][i + 1], new_de ree[u] )
end function
function P�������( )
for i 2 [0...k] do
����M��(E_add, �����������, i)
����M��(E_delete, �������, i)
end for
V _updated = ���S������(E_add [ E_delete)
V _chan e = ���T������(E_add [ E_delete)
for i 2 [0...k] do
E_update = {(u, ) : u 2 V _updated } Transitive changes
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����M��(E_update, ���������, i)
V _dest = ���T������(E_update)
V _chan e = V _chan e [ V _dest
V _updated = ������M��(V _chan e, �������, i)
end for
end function
GraphBolt: Programming Model - Complex aggregations
Algorithm
PageRank - Complex
1: function2�����������(e
= (u, ), Aggregation
i)
Algorithm
2
PageRank
Complex
Aggregation
oldpr
1: function �����������(e = (u, ),
i) [u][i]
2:
1:
2:
3:
2:
4:
3:
3:
4:
5:
4:
5:
6:
5:
7:
6:
6:
7:
8:
7:
8:
9:
8:
10:
9:
9:
11:
10:
10:
12:
11:
11:
13:
12:
12:
14:
13:
13:
15:
14:
14:
16:
15:
15:
17:
16:
16:
18:
17:
17:
19:
18:
18:
20:
19:
������A��(&sum[ ][i + 1],
ree[u] )
oldpr
function �����������(e = (u, old_de
),
i) [u][i]
������A��(&sum[
][i + 1], old_de
end
function
ree[u] )
oldpr [u][i]
������A��(&sum[
function
�������(e =][i
(u,+ 1],
), i)old_de ree[u] )
end
function
end
function
function
�������(e =][i(u,+ 1],
), i) oldpr [u][i] )
������S��(&sum[
old_de
ree[u]
oldpr [u][i]
function �������(e = (u, ), i)
������S��(&sum[
][i
+
1],
end function
old_de
ree[u] )
oldpr [u][i]
������S��(&sum[
1], ),old_de
function
���������(e][i=+(u,
i)
end
function
ree[u] )
newpr [u][i]
end
function
function
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=+
(u,1],), i)
������A��(&sum[
ree[u] )
newpr [u][i]
function ���������(e = (u, ),new_de
i)
������A��(&sum[
][i + 1], new_de
end
function
ree[u] )
newpr [u][i]
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function
P�������( ) ][i + 1], new_de ree[u] )
end
function
end
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i 2 [0...k]
do )
function
P�������(
function
P�������(
for����M��(E_add,
i 2 [0...k]
do )�����������, i)
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end
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for = ���S������(E_add
end
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V
_chan
_updated
���S������(E_add [[E_delete)
E_delete)
_updated
���S������(E_add
E_delete)
for
i 2 [0...k]
do
V
_chan
e ==���T������(E_add
[[E_delete)
V
_chan
e ==
���T������(E_add
[ E_delete)
E_update
{(u, ) : u 2 V _updated
}
for
i 2 [0...k]
do
forE_update
i 2 [0...k]=do
����M��(E_update,
i) }
{(u, ) : u�������,
2 V _updated
E_update
= {(u, ) : u���������,
2 V _updated
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�������,
i) i) }
8:
9:
10:
11:
12:
13:
14:
15:
16:
17:
18:
19:
20:
21:
22:
23:
24:
25:
1
41
22:
V _updated
_chan e, �������, i)
21:
_chan e ==V������M��(V
_chan e [ V _dest
23:
end
for
22:
V _updated
= ������M��(V _chan e, �������, i)
24:
������M��(V
_chan e, �������B�����, k)
23:
end for
25:
function _chan e, �������B�����, k)
24: end
������M��(V
25: end function
5:
6:
7:
oldpr [u][i]
������S��(&sum[ ][i + 1], old_de ree[u] )
end function
function ���������D����(e = (u, ), i)
newpr [u][i]
oldpr [u][i]
������A��(&sum[ ][i + 1], new_de ree[u]
old_de ree[u] )
end function
function P�������( )
for i 2 [0...k] do
����M��(E_add, �����������, i)
����M��(E_delete, �������, i)
end for
V _updated = ���S������(E_add [ E_delete)
V _chan e = ���T������(E_add [ E_delete)
for i 2 [0...k] do
E_update = {(u, ) : u 2 V _updated } Transitive changes
����M��(E_update, ���������D����, i)
V _dest = ���T������(E_update)
V _chan e = V _chan e [ V _dest
V _updated = ������M��(V _chan e, �������, i)
end for
end function
GraphBolt: Programming Model - Simple aggregations
Algorithm 2 PageRank - Complex Aggregation
Algorithm
PageRank - Complex
1: function2�����������(e
= (u, ), Aggregation
i)
Algorithm 1 PageRank - Simple Aggregation
oldpr [u][i]
1:
2:
1:
2:
3:
2:
4:
3:
3:
4:
5:
4:
5:
6:
5:
7:
6:
6:
7:
8:
7:
8:
9:
8:
10:
9:
9:
11:
10:
10:
12:
11:
11:
13:
12:
12:
14:
13:
13:
15:
14:
16:
14:
15:
17:
15:
16:
18:
16:
17:
19:
18:
17:
20:
19:
18:
function
�����������(e
= 1],
(u, ), i)
������A��(&sum[
][i +
ree[u] )
function �����������(e = (u, old_de
),
i) [u][i]
oldpr
������A��(&sum[
][i + 1], old_de
end
function
oldpr [u][i]
ree[u] )
������A��(&sum[
][i
+
1],
function
�������(e = (u, ), i)old_de ree[u] )
end function
end function
function
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), i) oldpr [u][i] )
������S��(&sum[
old_de
ree[u]
oldpr [u][i]
function �������(e = (u, ), i)
������S��(&sum[
][i
+
1],
end function
oldpr [u][i]
old_de
ree[u] )
������S��(&sum[
1], ),old_de
function
���������(e][i=+(u,
i)
ree[u] )
end
function
newpr [u][i]
end function
function
���������(e][i
=+
(u,1],), i)
������A��(&sum[
ree[u] )
newpr
[u][i]
function ���������D����(e =new_de
(u,
), i)
������A��(&sum[
][i + 1], new_de
end
function
newpr [u][i]
ree[u] )
������A��(&sum[
function
P�������( ) ][i + 1], new_de ree[u]
end
function
end
forfunction
i 2 [0...k]
do )
function
P�������(
function
P�������(
for����M��(E_add,
i 2 [0...k]
do )�����������, i)
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end
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�������, i) [ E_delete)
V
_updated
end
for = ���S������(E_add
V
_chan
end
for e ==���T������(E_add
_updated
���S������(E_add [[E_delete)
E_delete)
for
i 2 [0...k]
do
_updated
���S������(E_add
E_delete)
V
_chan
e ==���T������(E_add
[[E_delete)
E_update
{(u, ) : u 2 V _updated
}
V
_chan
e ==
���T������(E_add
[ E_delete)
for
i 2 [0...k]
do
����M��(E_update,
i) }
{(u, ) : u�������,
2 V _updated
forE_update
i 2 [0...k]= do
����M��(E_update,
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i) i)
E_update = {(u, ) : u���������,
2 V _updated}
8:
9:
10:
11:
12:
13:
14:
15:
16:
17:
18:
19:
oldpr [u][i] 20:
old_de ree[u] ) 21:
22:
23:
24:
Algorithm 2 PageRank - Complex Aggregation
1: function �����������(e = (u, ), i)
oldpr [u][i]
������A��(&sum[ ][i + 1], old_de ree[u] )
3: end function
4: function �������(e = (u, ), i)
2:
42
GraphBolt Details …
•
Aggregation properties & non-decomposable aggregations
•
Pruning dependencies for light-weight tracking
•
•
Vertical pruning
•
Horizontal pruning
Hybrid incremental execution
•
With & without dependency information
• Graph data structure & parallelization model
43
ces
M
M
M
M
M
B
uation.
mB
48)
Hz
GB
B/sec
ion.
Experimental Setup
Algorithm
Aggregation (
PageRank (PR)
Belief Propagation (BP)
8s 2 S :
Label Propagation (LP)
Œ
8f 2 F :
Collaborative Filtering (CF)
Triangle Counting (TC)
h
Õ
(
Õ
8s 0 2S
Õ
8e =(u, )2E
8e =(u,
8e =(u, )2E
c(u, f ) ⇥ wei ht (u, )
c (u)⇥w
ei ht (u, )
Õ
w ei ht (w, )
8e =(w, )2E
tr
)2E c i (u).c i (u) ,
Õ
(u, s 0 ) ⇥ (u, , s 0, s) ⇥ c(u, s 0 ) )
8e =(u, )2E
Õ
)
c (u)
out _d e r e e (u)
8e =(u, )2E
8e =(u, )2E
Co-Training Expectation
Maximization (CoEM)
Õ
…
Õ
8e =(u,
)2E c i (u).wei ht (u, ) i
|in_nei hbor s(u) \ out _nei hbor s( )|
Table 4. Graph algorithms used in evaluation and their aggregation functions.
ining Expectation Maxpervised learning algoCollaborative Filtering
ach to identify related
Triangle Counting (TC)
iangles.
aphs used in our evalued an initial �xed point
To ensure a fair comparison among the above versions, experiments were run such that each algorithm version had
the same number of pending edge mutations to be processed
(similar to methodology in [44]). Unless otherwise stated,
100K edge mutations were applied before the processing of
each version. While Theorem 4.1 guarantees correctness of
results via synchronous processing semantics, we validated
correctness for each run by comparing �nal results.
Graphs
Wiki (WK) [47]
UKDomain (UK) [7]
Twitter (TW) [21]
TwitterMPI (TT) [8]
Friendster (FT) [14]
Yahoo (YH) [49]
Edges
378M
1.0B
1.5B
2.0B
2.5B
6.6B
Vertices
12M
39.5M
41.7M
52.6M
68.3M
1.4B
Table 2. Input graphs used in evaluation.
System A
System B
Core
Count 32-core
32 (1
(2 ⇥ GB
48)
Server:
/ ⇥2 32)
GHz 96
/ 231
Core Speed
2GHz
2.5GHz
Memory Capacity
231GB
748GB
Memory Speed
9.75 GB/sec 7.94 GB/sec
Table 3. Systems used in evaluation.
Be
La
Co
M
Coll
Tr
Tab
is a learning algorithm while Co-Training Expect
imization (CoEM) [28] is a semi-supervised lea
44
rithm for named entity recognition. Collaborativ
Computation
time
Execution time
(seconds)
0
0
PR on TT(
30
20
10
1K
200
1K
10K
10K
100K
COEM on FT
150
100
50
100K
200
0
0
150
100
50
1K
300
1K
10K
10K
100K
225
150
75
100K
Normalized
Computation
time time
Execution
time
computation
(seconds)
CF on TT
Computation
time
Execution time
(seconds)
40
Execution time
Computation
time
(seconds)
50
Computation
time
Execution time
(seconds)
Computation
time
Execution time
(seconds)
GraphBolt Performance
Ligra
GraphBolt-Reset
GraphBolt
500
0
LP on FT
0
BP on TT
400
1
300
200
100
1K
80
1K
10K
10K
100K
0
TC on FT
60
40
20
100K
45
50
25
50
1K
10K
COEM on FT (28.5x to 32.3x)
40
30
20
10
0
20
100
15
10
5
0
1K
10K
100K
14
7
0
20
100
0
10
5
100
1K
10K
BP on TT (8.6x to 23.1x)
60
1
40
20
LP on FT (5.9x to 24.7x)
50
25
0
20
100
15
10
5
1K
10K
100K
75
500
25
0
100K
75
0
80
0
100
15
0
100K
1
% Edge
Computations
75
Execution time
Computation
time
(seconds)
Computation
time
Execution time
(seconds)
% Edge
Computations
0
100
21
Computation
time
Execution time
(seconds)
4
CF on TT (3.8x to 8.6x)
% Edge
Computations
8
28
GB-Reset
GraphBolt-Reset
GraphBolt
GraphBolt
Normalized
computation time
Execution time
Computation
time
Normalized
(seconds)
computation time
12
0
% Edge
Computations
PR on TT(1.4x to 1.6x)
Computation
time
Execution time
(seconds)
16
% Edge
Computations
% Edge
Computations
Computation
time
Execution time
(seconds)
GraphBolt Performance
2
1K
10K
100K
TC on FT (279x to 722.5x)
1.5
1
0.5
0
0.1
100
0.075
0.05
0.025
0
1K
10K
100K
46
50
25
50
1K
10K
COEM on FT (28.5x to 32.3x)
40
30
20
10
0
20
100
15
10
5
0
1K
10K
100K
14
7
0
20
100
0
10
5
100
1K
10K
BP on TT (8.6x to 23.1x)
60
1
40
20
LP on FT (5.9x to 24.7x)
50
25
0
20
100
15
9.3%
10
3.6%
5
0.2%
1K
10K
100K
75
500
25
0
100K
75
0
80
0
100
15
0
100K
1
% Edge
Computations
75
Execution time
Computation
time
(seconds)
Computation
time
Execution time
(seconds)
% Edge
Computations
0
100
21
Computation
time
Execution time
(seconds)
4
CF on TT (3.8x to 8.6x)
% Edge
Computations
8
28
GB-Reset
GraphBolt-Reset
GraphBolt
GraphBolt
Normalized
computation time
Execution time
Computation
time
Normalized
(seconds)
computation time
12
0
% Edge
Computations
PR on TT(1.4x to 1.6x)
Computation
time
Execution time
(seconds)
16
% Edge
Computations
% Edge
Computations
Computation
time
Execution time
(seconds)
GraphBolt Performance
2
1K
10K
100K
TC on FT (279x to 722.5x)
1.5
1
0.5
0
0.1
100
0.075
0.05
0.025
0
1K
10K
100K
47
50
25
50
1K
10K
COEM on FT (28.5x to 32.3x)
40
30
20
10
0
20
100
15
10
5
0
1K
10K
100K
14
7
0
20
100
100
0
10
5
100
1K
10K
BP on TT (8.6x to 23.1x)
60
1
40
20
LP on FT (5.9x to 24.7x)
50
25
0
20
100
15
10
5
1K
10K
100K
75
500
25
0
100K
75
0
80
0
100
15
0
100K
1
% Edge
Computations
75
Execution time
Computation
time
(seconds)
Computation
time
Execution time
(seconds)
% Edge
Computations
0
100
21
Computation
time
Execution time
(seconds)
4
CF on TT (3.8x to 8.6x)
% Edge
Computations
8
28
GB-Reset
GraphBolt-Reset
GraphBolt
GraphBolt
Normalized
computation time
Execution time
Computation
time
Normalized
(seconds)
computation time
12
0
% Edge
Computations
PR on TT(1.4x to 1.6x)
Computation
time
Execution time
(seconds)
16
% Edge
Computations
% Edge
Computations
Computation
time
Execution time
(seconds)
GraphBolt Performance
2
0.4%
1K
2.1%
10K
7.8%
100K
TC on FT (279x to 722.5x)
1.5
1
0.5
0
0.1
100
0.075
0.05
0.025
0
1K
10K
100K
48
Detailed Experiments …
• Varying workload type
• Mutations affecting majority of the values v/s affecting small values
• Varying graph mutation rate
• Single edge update (reactiveness) v/s 1 million edge updates (throughput)
• Scaling to large graph (Yahoo) over large system (96 core/748 GB)
49
375
175
375
250
125
0
250
1
10
100
Batch Size
1K
125
1
10
100
Batch Size
1K
PR on TT
10K
41.7x
10K
150
125
100
Execution Time (sec)
500
625 Diferential Dataow
GraphBolt
500
Execution Time
(seconds)
625
0
7.6x
Execution Time
(seconds)
Execution Time
(seconds)
GraphBolt v/s Differential Dataflow
175
150
125
100
PR on TT
Dierential Dataow
GraphBolt
75
50
25
0
75
20
40
60
80
Single Edge Mutations
100
50
25
0
20
40
60
80
Single Edge Mutations
100
PR on TT
(100 single edge mutations)
Differential Dataflow. McSherry et al., CIDR 2013.
50
Summary
• Efficient incremental processing of streaming graphs
• Guarantee Bulk Synchronous Parallel semantics
• Lightweight dependence tracking at aggregation level
• Dependency-aware value refinement upon graph mutation
•
Programming model to support incremental complex aggregation types
Acknowledgements
51
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