The DOI matches its Crossref record; 12 of the 12 references it cites were found in a registry or an index.
Some NP-complete geometric problems
Abstract
We show that the STEINER TREE problem and TRAVELING SALESMAN problem for points in the plane are NP-complete when distances are measured either by the rectilinear (Manhattan) metric or by a natural discretized version of the Euclidean metric. Our proofs also indicate that the problems are NP-hard if the distance measure is the (unmodified) Euclidean metric. However, for reasons we discuss, there is some question as to whether these problems, or even the well-solved MINIMUM SPANNING TREE problem, are in NP when the distance measure is the Euclidean metric.
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Cites
The Design and Analysis of Computer Algorithms
Aho, A. V., & Hopcroft, J. E. (1974) · CERN Document Server (European Organization for Nuclear Research) · Cited by 9,403
An Effective Heuristic Algorithm for the Traveling-Salesman Problem
Lin, S., & Kernighan, B. W. (1973) · Operations Research · doi:10.1287/opre.21.2.498 · Cited by 3,821
Reducibility Among Combinatorial Problems
Karp, R. M. (2010) · 50 Years of Integer Programming 1958-2008 · doi:10.1007/978-3-540-68279-0_8 · Cited by 2,490
The Rectilinear Steiner Tree Problem is $NP$-Complete
Garey, M. R., & Johnson, D. S. (1977) · SIAM Journal on Applied Mathematics · doi:10.1137/0132071 · Cited by 1,124
Self-citationShamos, M. I., & Hoey, D. (1975) · 16th Annual Symposium on Foundations of Computer Science (sfcs 1975) · doi:10.1109/sfcs.1975.8 · Cited by 1,057
The Euclidean travelling salesman problem is NP-complete
Papadimitriou, C. H. (1977) · Theoretical Computer Science · doi:10.1016/0304-3975(77)90012-3 · Cited by 776
On the Computational Complexity of Combinatorial Problems
Karp, R. M. (1975) · Networks · doi:10.1002/net.1975.5.1.45 · Cited by 711
Gilbert, E. N., & Pollak, H. O. (1968) · SIAM Journal on Applied Mathematics · doi:10.1137/0116001 · Cited by 690
On Steiner’s Problem with Rectilinear Distance
Hanan, M. (1966) · SIAM Journal on Applied Mathematics · doi:10.1137/0114025 · Cited by 623
The Complexity of Computing Steiner Minimal Trees
Garey, M. R., Graham, R. L., & Johnson, D. S. (1977) · SIAM Journal on Applied Mathematics · doi:10.1137/0132072 · Cited by 576
Self-citation
Cited by
Voronoi diagrams—a survey of a fundamental geometric data structure
Aurenhammer, F. (1991) · ACM Computing Surveys · doi:10.1145/116873.116880 · Cited by 4,340
Routing and scheduling of vehicles and crews
Raff, S. (1983) · Computers & Operations Research · doi:10.1016/0305-0548(83)90030-8 · Cited by 867
Recursive Markov chains, stochastic grammars, and monotone systems of nonlinear equations
Etessami, K., & Yannakakis, M. (2009) · Journal of the ACM · doi:10.1145/1462153.1462154 · Cited by 512
Completeness Classes in Algebra
Valiant, L. G. (1979) · ACM eBooks · doi:10.1145/3749740.3749750 · Cited by 465
Approximation algorithms for the geometric covering salesman problem
Arkin, E. M., & Hassin, R. (1994) · Discrete Applied Mathematics · doi:10.1016/0166-218x(94)90008-6 · Cited by 356
Metadata
- Authors
- Garey, M. R., Graham, R. L., & Johnson, D. S.
- Venue
- Proceedings of the eighth annual ACM symposium on Theory of computing - STOC '76
- Publisher
- ACM Press
- Published
- 1976
- Pages
- 10-22
- OpenAlex
- W2066194644
- Cited by
- 400
- References
- 12
- FWCI
- 7.02
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Garey, M. R., Graham, R. L., & Johnson, D. S. (1976). Some NP-complete geometric problems. Proceedings of the eighth annual ACM symposium on Theory of computing - STOC '76. https://doi.org/10.1145/800113.803626
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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.
