# A Multithreaded Algorithm for Network Alignment Via Approximate Matching

## Abstract

Network alignment is an optimization problem to find the best one-to-one map between the vertices of a pair of graphs that overlaps in as many edges as possible. It is a relaxation of the graph isomorphism problem and is closely related to the subgraph isomorphism problem. The best current approaches are entirely heuristic, and are iterative in nature. They generate real-valued heuristic approximations that must be rounded to find integer solutions. This rounding requires solving a bipartite maximum weight matching problem at each step in order to avoid missing high quality solutions. We investigate substituting a parallel, half-approximation for maximum weight matching instead of an exact computation. Our experiments show that the resulting difference in solution quality is negligible. We demonstrate almost a 20-fold speedup using 40 threads on an 8 processor Intel Xeon E7-8870 system (from 10 minutes to 36 seconds).

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1089096

- Report Number(s):
- PNNL-SA-87964

400470000

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Conference

- Resource Relation:
- Conference: International Conference for High Performance Computing, Networking, Storage and Analysis (SC), November 10-16, 2012, Salt Lake City, Utah

- Country of Publication:
- United States

- Language:
- English

- Subject:
- network alignment, matching, multicore

### Citation Formats

```
Khan, Arif, Gleich, David F., Pothen, Alex, and Halappanavar, Mahantesh.
```*A Multithreaded Algorithm for Network Alignment Via Approximate Matching*. United States: N. p., 2012.
Web. doi:10.1109/SC.2012.8.

```
Khan, Arif, Gleich, David F., Pothen, Alex, & Halappanavar, Mahantesh.
```*A Multithreaded Algorithm for Network Alignment Via Approximate Matching*. United States. doi:10.1109/SC.2012.8.

```
Khan, Arif, Gleich, David F., Pothen, Alex, and Halappanavar, Mahantesh. Fri .
"A Multithreaded Algorithm for Network Alignment Via Approximate Matching". United States. doi:10.1109/SC.2012.8.
```

```
@article{osti_1089096,
```

title = {A Multithreaded Algorithm for Network Alignment Via Approximate Matching},

author = {Khan, Arif and Gleich, David F. and Pothen, Alex and Halappanavar, Mahantesh},

abstractNote = {Network alignment is an optimization problem to find the best one-to-one map between the vertices of a pair of graphs that overlaps in as many edges as possible. It is a relaxation of the graph isomorphism problem and is closely related to the subgraph isomorphism problem. The best current approaches are entirely heuristic, and are iterative in nature. They generate real-valued heuristic approximations that must be rounded to find integer solutions. This rounding requires solving a bipartite maximum weight matching problem at each step in order to avoid missing high quality solutions. We investigate substituting a parallel, half-approximation for maximum weight matching instead of an exact computation. Our experiments show that the resulting difference in solution quality is negligible. We demonstrate almost a 20-fold speedup using 40 threads on an 8 processor Intel Xeon E7-8870 system (from 10 minutes to 36 seconds).},

doi = {10.1109/SC.2012.8},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2012},

month = {11}

}