https://dl.acm.org/doi/10.1145/3340531.3411878

1. Incremental and Parallel Computation of
Structural Graph Summaries
for Evolving Graphs
Till Blume1
, David Richerby2
, and Ansgar Scherp3
CIKM 2020, Virtual Event
1
Kiel University, Germany
2
University of Essex, United Kingdom
3
Ulm University, Germany

2. Structural Graph Summaries
Structural graph summaries are a condensed representation of graphs such that a
set of chosen (structural) features in the graph summary are equivalent to the
original graph.
Structural Features (f1
,..., fx
)
Input Graph
Structural Graph Summary
2

3. G2
G1
G2
G1 vs1
Evolving Structural Graph Summaries for LPGs
SGGDB
{Person}
v2
{Book}
v1
{Subject}
v3
{author}
{topic}Source X
{Person}
v8
{Book}
v7
{Subject}
v9
{author}
{topic}Source Y
{Person}
s2
{Book}
r1
{Subject}
s3
{author}
{topic}
{Person}
v2
{Book}
v1
{Subject}
v3
{author}
{topic}Source X
{Agent}
v8
{Book}
v7
{Subject}
v9
{author}
{topic}
{Person}
s2
{Book}
r1 {author}
{topic}
vs1
time
t
t+1 {Subject}
s3
{Book}
r2
{Agent}
s4
{topic}
{author}
vs2Source Y
3

4. Problem Definition
● there are various different structural features that can be used to summarize
● when the input graph changes, it is often prohibitively expensive to recompute
the structural graph summary from scratch
● existing incremental algorithms are often not designed for evolving graphs or
require an explicit change log
4

5. Contribution
1. generic, parallel algorithm to incrementally compute and update structural
graph summaries and as well as a generic data structure following our formal
language
2. theoretical complexity analysis: all graph summaries defined in the formal
language can be updated in O(∆·dk
), with ∆ changes the input graph, d is the
maximum degree of the input graph, and k is the maximum distance in the
subgraphs considered for the equivalence
3. empirical analyses on benchmark and real-world datasets: our
incremental algorithm outperforms a batch computation even with about 50%
of the graph changed
5

6. Parallel Algorithm
Phase 2: Find and
Merge
Phase 1:
Make-set
v1
v3
Signal &
Collectv2
v91
v93
v92
v1
v3
v2
v3
Phase 0: Partitioning
(Random Vertex Cut)
v2
v91
v93
v92
v93v92
r1
r2
r3
r4
r5
r6
r1
r2
r3
r4
r6
r5
r1 s3
r2
vs1
vs2
r3
vs3
s3
O(n · dk
) O(m · dk
)
6

7. Vertex Update Hash Index
hash(v1)
hash(vs1)
hash(pe1)
hash(v2) hash(v3)
hash(vs1)
hash(pe2)
L1
L2
L3
7

8. Experimental Evaluation
Datasets
● LUBM100 (~2.1 M vertices and ~13 M edges)
● BSBM (up to 1.3 M vertices and 13 M edges)
● DyLDO-core (2.1–3.5 M vertices and 7–13 M edges)
● DyLDO-ext (7–10 M vertices and 84–106 M edges)
Summary Models
● Attribute Collection
● Type Collection
● SchemEX
In total, 312 experiments for incremental and for batch each
8

9. Compression
DyLDO-core datasets
9
Graph Summaries: Attribute Collection, Type Collection, and SchemEX

10. Run Time Performance
Graph Summaries: Attribute Collection, Type Collection, and SchemEX
DyLDO-core datasets
10

11. Run Time Performance
LUBM100 dataset
11

12. Conclusion
1. generic, parallel algorithm to incrementally compute and update structural graph
summaries and as well as a generic data structure following our formal language
2. theoretical complexity analysis: all graph summaries defined in the formal
language can be updated in O(∆·dk
), with ∆ changes the input graph, d is the
maximum degree of the input graph, and k is the maximum distance in the
subgraphs considered for the equivalence
3. empirical analyses on benchmark and real-world datasets: our incremental
algorithm outperforms a batch computation even with about 50% of the graph
changed
Source Code and all resources available on GitHub:
https://github.com/t-blume/fluid-spark 12