The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
A multilevel algorithm for partitioning graphs
Abstract
The graph partitioning problem is that of dividing the vertices of a graph into sets of specified sizes such that few edges cross between sets. This NP-complete problem arises in many important scientific and engineering problems. Prominent examples include the decomposition of data structures for parallel computation, the placement of circuit elements and the ordering of sparse matrix computations. We present a multilevel algorithm for graph partitioning in which the graph is approximated by a sequence of increasingly smaller graphs. The smallest graph is then partitioned using a spectral method, and this partition is propagated back through the hierarchy of graphs. A variant of the Kernighan-Lin algorithm is applied periodically to refine the partition. The entire algorithm can be implemented to execute in time proportional to the size of the original graph. Experiments indicate that, relative to other advanced methods, the multilevel algorithm produces high quality partitions at low cost.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
An Efficient Heuristic Procedure for Partitioning Graphs
Kernighan, B. W., & Lin, S. (1970) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1970.tb01770.x · Cited by 5,305
Some simplified NP-complete graph problems
Garey, M. R., Johnson, D. S., & Stockmeyer, L. (1976) · Theoretical Computer Science · doi:10.1016/0304-3975(76)90059-1 · Cited by 2,059
Partitioning Sparse Matrices with Eigenvectors of Graphs
Pothen, A., Simon, H. D., & Liou, K.-P. (1990) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/0611030 · Cited by 1,684
The Chaco user`s guide. Version 1.0
Hendrickson, B., & Leland, R. (1993) · doi:10.2172/10106339 · Cited by 655
Self-citationA Procedure for Placement of Standard-Cell VLSI Circuits
Dunlop, A. E., & Kernighan, B. W. (1985) · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · doi:10.1109/tcad.1985.1270101 · Cited by 505
Barnard, S. T., & Simon, H. D. (1994) · Concurrency: Practice and Experience · doi:10.1002/cpe.4330060203 · Cited by 488
An Improved Spectral Graph Partitioning Algorithm for Mapping Parallel Computations
Hendrickson, B., & Leland, R. (1995) · SIAM Journal on Scientific Computing · doi:10.1137/0916028 · Cited by 480
Self-citationPerformance of dynamic load balancing algorithms for unstructured mesh calculations
Williams, R. D. (1991) · Concurrency: Practice and Experience · doi:10.1002/cpe.4330030502 · Cited by 345
An algorithm for quadrisection and its application to standard cell placement
Suaris, P., & Kedem, G. (1988) · IEEE Transactions on Circuits and Systems · doi:10.1109/31.1742 · Cited by 106
Cited by
Leskovec, J., Lang, K. J., Dasgupta, A., & Mahoney, M. W. (2009) · Internet Mathematics · doi:10.1080/15427951.2009.10129177 · Cited by 1,872
Multilevel hypergraph partitioning: applications in VLSI domain
Karypis, G., Aggarwal, R., Kumar, V., & Shekhar, S. (1999) · IEEE Transactions on Very Large Scale Integration (VLSI) Systems · doi:10.1109/92.748202 · Cited by 800
Bootstrapping Entity Alignment with Knowledge Graph Embedding
Sun, Z., Hu, W., Zhang, Q., & Qu, Y. (2018) · Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2018/611 · Cited by 521
Graph partitioning models for parallel computing
Hendrickson, B., & Kolda, T. G. (2000) · Parallel Computing · doi:10.1016/s0167-8191(00)00048-x · Cited by 461
Self-citationStreaming graph partitioning for large distributed graphs
Stanton, I., & Kliot, G. (2012) · Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining · doi:10.1145/2339530.2339722 · Cited by 446
Metadata
- Authors
- Hendrickson, B., & Leland, R.
- Venue
- Proceedings of the 1995 ACM/IEEE conference on Supercomputing (CDROM) - Supercomputing '95
- Publisher
- ACM Press
- Published
- 1995
- Pages
- 28-es
- ISSN
- 1063-9535 (ISSN-L)
- OpenAlex
- W2118953734
- Cited by
- 1,069
- References
- 9
- FWCI
- 127.66
- Type
- conference paper
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: A multilevel algorithm for partitioning graphs. https://app.cochat.ai/papers/10.1145/224170.224228
- The paper
- Hendrickson, B., & Leland, R. (1995). A multilevel algorithm for partitioning graphs. Proceedings of the 1995 ACM/IEEE conference on Supercomputing (CDROM) - Supercomputing '95. https://doi.org/10.1145/224170.224228
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
