The DOI matches its Crossref record.
Probabilistic Analysis of Partitioning Algorithms for the Traveling-Salesman Problem in the Plane
Abstract
We consider partitioning algorithms for the approximate solution of large instances of the traveling-salesman problem in the plane. These algorithms subdivide the set of cities into small groups, construct an optimum tour through each group, and then patch the subtours together to form a tour through all the cities. If the number of cities in the problem is n, and the number of cities in each group is t, then the worst-case error is [Formula: see text]. If the cities are randomly distributed, then the relative error is O(t−1/2) (with probability one). Hybrid schemes are suggested, in which partitioning is used in conjunction with existing heuristic algorithms. These hybrid schemes may be expected to give near-optimum solutions to problems with thousands of cities.
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
Cited by
Optimization by Simulated Annealing
Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983) · Science · doi:10.1126/science.220.4598.671 · Cited by 45,134
An evolutionary approach to the traveling salesman problem
Fogel, D. B. (1988) · Biological Cybernetics · doi:10.1007/bf00202901 · Cited by 287
Stochastic and Dynamic Vehicle Routing in the Euclidean Plane with Multiple Capacitated Vehicles
Bertsimas, D. J., & van Ryzin, G. (1993) · Operations Research · doi:10.1287/opre.41.1.60 · Cited by 274
Metadata
- Authors
- Karp, R. M.
- Venue
- Mathematics of Operations Research
- Published
- 1977-08
- Volume
- 2
- Issue
- 3
- Pages
- 209-224
- ISSN
- 0364-765X (ISSN-L)
- 1526-5471
- OpenAlex
- W2143037347
- Cited by
- 439
- References
- 0
- FWCI
- 49.40
- Type
- journal article
- 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: Probabilistic Analysis of Partitioning Algorithms for the Traveling-Salesman Problem in the Plane. https://app.cochat.ai/papers/10.1287/moor.2.3.209
- The paper
- Karp, R. M. (1977). Probabilistic Analysis of Partitioning Algorithms for the Traveling-Salesman Problem in the Plane. Mathematics of Operations Research. https://doi.org/10.1287/moor.2.3.209
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.
