The DOI matches its Crossref record.
A dual algorithm for the constrained shortest path problem
Abstract
In this paper we develop a Lagrangian relaxation algorithm for the problem of finding a shortest path between two nodes in a network, subject to a knapsack‐type constraint. For example, we may wish to find a minimum cost route subject to a total time constraint in a multimode transportation network. Furthermore, the problem, which is shown to be at least as hard as NP‐complete problems, is generic to a class of problems that arise in the solution of integer linear programs and discrete state/stage deterministic dynamic programs. One approach to solving the problem is to utilize a k th shortest path algorithm, terminating with the first path that satisfies the constraint. This approach is impractical when the terminal value of k is large. Using Lagrangian relaxation we propose a method that is designed to reduce this value of k. Computational results indicate orders of magnitude savings when the approach is applied to large networks.
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
A survey of resource constrained shortest path problems: Exact solution approaches
Pugliese, L. D. P., & Guerriero, F. (2013) · Networks · doi:10.1002/net.21511 · Cited by 147
Resource Constrained Shortest Paths
Mehlhorn, K., & Ziegelmann, M. (2000) · Lecture Notes in Computer Science · doi:10.1007/3-540-45253-2_30 · Cited by 124
A technical review of column generation in integer programming
Wilhelm, W. E. (2001) · Optimization and Engineering · doi:10.1023/a:1013141227104 · Cited by 108
Metadata
- Authors
- Handler, G. Y., & Zang, I.
- Venue
- Networks
- Publisher
- Wiley
- Published
- 1980-12
- Volume
- 10
- Issue
- 4
- Pages
- 293-309
- ISSN
- 0028-3045 (ISSN-L)
- 1097-0037
- OpenAlex
- W1964443412
- Cited by
- 457
- References
- 0
- FWCI
- 2.81
- 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: A dual algorithm for the constrained shortest path problem. https://app.cochat.ai/papers/10.1002/net.3230100403
- The paper
- Handler, G. Y., & Zang, I. (1980). A dual algorithm for the constrained shortest path problem. Networks. https://doi.org/10.1002/net.3230100403
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.
