Research

My research focuses on combinatorial optimization problems in graphs or networks. I am particularly interested in:

• solving problems with connectivity/distance constraints,
• studying operations research and mathematical programming problems using insights from parameterized complexity, and
• applications in political redistricting.

Here are links to my Google Scholar, GitHub, ORCID, and DBLP. 

Grants

• A. Buchanan (PI). CAREER: Parsimonious Models for Redistricting. National Science Foundation (CMMI-1942065). $508,000, 06/01/2020–05/31/2025. (link)
• B. Balasundaram (PI), A. Buchanan (coPI), and S. Heragu (coPI). FLAT: Freight Lane Assignment Tool. TreeHouse Foods Inc. $163,730, 01/13/2020–01/16/2021. 
• A. Buchanan (PI). Imposing connectivity constraints in large-scale network problems. National Science Foundation (CMMI-1662757). $258,586, 06/15/2017–05/31/2021. (link)
• B. Balasundaram (PI), A. Buchanan (coPI), and S. Heragu (coPI). Optimization-Based Aggregate Master Planning Tools for Bay Valley Foods, LLC. Bay Valley Foods, LLC. $250,599, 10/01/2017–01/31/2020.

Submitted Papers

• J. Zhang, L. Silveira, H. Validi, L. Smith, A. Buchanan, I.V. Hicks. Partitioning a graph into low-diameter clusters. Submitted in October 2024. (link) (code)
• E. Vercesi, A. Buchanan. The Dantzig-Fulkerson-Johnson TSP formulation is easy to solve for few subtour constraints. Submitted in September 2024. (link) (code)

Refereed Journal Articles

1. P. Belotti, A. Buchanan, S. Ezazipour. Political districting to optimize the Polsby-Popper compactness score with application to voting rights. To appear, Operations Research. (link) (pdf) (code)
2. A. Buchanan, S. Ezazipour, M. Shahmizad. A widespread belief about county splits in political districting plans is wrong. To appear, Election Law Journal. (link) (pdf) (code)
3. M. Shahmizad, A. Buchanan. Political districting to minimize county splits. Operations Research, 73(2): 752-774, 2025. (link) (pdf) (code) (slides) (poster) Honorable Mention for Best Poster at IPCO 2023
4. J. Zhang, H. Validi, A. Buchanan, I.V. Hicks. Linear-size formulations for connected planar graph partitioning and political districting. Optimization Letters, 18(1): 19-31, 2024. (link) (pdf) (code)
5. Y. Lu, H. Salemi, B. Balasundaram, A. Buchanan. On fault-tolerant low-diameter clusters in graphs. INFORMS Journal on Computing, 34(6): 3181-3199, 2022. (link) (pdf) (code)
6. H. Validi, A. Buchanan. Political districting to minimize cut edges. Mathematical Programming Computation, 14: 623-672, 2022. (link) (pdf) (code) (slides) (video)
7. M.J. Naderi, A. Buchanan, J.L. Walteros. Worst-case analysis of clique MIPs. Mathematical Programming, 195: 517-551, 2022. (link) (pdf) (code)
8. H. Salemi, A. Buchanan. Solving the distance-based critical node problem. INFORMS Journal on Computing, 34(3): 1309-1326, 2022. (link) (pdf) (code)
9. H. Validi, A. Buchanan, E. Lykhovyd. Imposing contiguity constraints in political districting models. Operations Research, 70(2): 867-892, 2022. (link) (pdf) (slides) (code) (video) (spotlight in ICS newsletter) Winner of the 2021 ICS Harvey J Greenberg Research Award
10. V. Stozhkov, A. Buchanan, S. Butenko, V. Boginski. Continuous cubic formulations for cluster detection problems in networks. Mathematical Programming, 196, 279-307, 2022. (link) (pdf)
11. B. Farmanesh, A. Pourhabib, B. Balasundaram, A. Buchanan. A Bayesian framework for functional calibration of expensive computational models through non-isometric matching. IISE Transactions, 53(3): 352-364, 2021. (link) (pdf) 
12. H. Validi, A. Buchanan. The optimal design of low-latency virtual backbones. INFORMS Journal on Computing, 32(4): 952-967, 2020. (link) (pdf) (supplement) (code)
13. J.L. Walteros, A. Buchanan. Why is maximum clique often easy in practice? Operations Research, 68(6): 1866-1895, 2020. (link) (pdf) (slides) (code)  Honorable Mention in the 2019 JFIG Paper Competition
14. H. Salemi, A. Buchanan. Parsimonious formulations for low-diameter clusters. Mathematical Programming Computation, 12(3): 493-528, 2020. (link) (pdf) (slides) (code)
15. H. Validi, A. Buchanan. A Note on “A linear-size zero-one programming model for the minimum spanning tree problem in planar graphs”. Networks, 73(1): 135-142, 2019. (link) (pdf)
16. A. Buchanan, Y. Wang, S. Butenko. Algorithms for node-weighted Steiner tree and maximum-weight connected subgraph. Networks, 72(2): 238-248, 2018. (link) (pdf) 
17. Y. Wang, A. Buchanan, S. Butenko. On imposing connectivity constraints in integer programs. Mathematical Programming, 166(1): 241-271, 2017. (link) (pdf) 
18. A. Buchanan. Extended formulations for vertex cover. Operations Research Letters, 44(3): 374-378, 2016. (link) (pdf) (slides)
19. S. Kahruman-Anderoglu, A. Buchanan, S. Butenko, O.A. Prokopyev. On provably best construction heuristics for hard combinatorial optimization problems. Networks, 67(3): 238-245, 2016. (link) (pdf)
20. A. Buchanan, J.S. Sung, S. Butenko, E.L. Pasiliao. An integer programming approach for fault-tolerant connected dominating sets. INFORMS Journal on Computing, 27(1):178-188, 2015. (link) (pdf) (testbed)
21. A. Verma, A. Buchanan, S. Butenko. Solving the maximum clique and vertex coloring problems on very large sparse networks. INFORMS Journal on Computing, 27(1):164-177, 2015. (link) (pdf)  Selected by INFORMS President L. Robin Keller as the May 2015 President’s Pick article
22. A. Buchanan, J.S. Sung, V. Boginski, S. Butenko. On connected dominating sets of restricted diameter. European Journal of Operational Research, 236(2):410-418, 2014. (link) (pdf)
23. A. Buchanan, J.L. Walteros, S. Butenko, P.M. Pardalos. Solving maximum clique in sparse graphs: an O(nm + n2^{d/4}) algorithm for d-degenerate graphs. Optimization Letters, 8(5):1611-1617, 2014. (link) (pdf)

Other

• A. Buchanan. A brief tutorial on Benders decomposition. IFORS News, pages 6-7, March 2024. (link) (pdf) (code)
• A. Buchanan. Using optimization to support minority representation in Voting Rights Act cases. ORMS Today, 50(4): 32-35, 2023. (link)
• A. Buchanan. Political Districting. In Encyclopedia of Optimization (3rd edition). Ed. by P.M. Pardalos and O.A. Prokopyev. Springer, 2023. (link) (pdf)
• A. Buchanan. New congressional districts for Alabama: SCOTUS rules on race v. geography. Montgomery Advertiser, June 19, 2023. (link1) (link2)
• A. Buchanan, M.J. Naderi. A brief tutorial on Gomory cuts. IFORS News, pages 7-9, March 2020. (link) (pdf) (code)
• A. Buchanan, S. Butenko. Tight extended formulations for independent set. 2015. (link) (pdf)
  • A main result of this paper is that there are size O(n2^k) extended formulations for independent set in graphs of treewidth at most k. Unbeknownst to us, the same bound had been obtained by Monique Laurent using different techniques. See page 134 of her paper “Sums of squares, moment matrices and optimization over polynomials.” 
• A. Buchanan, N. Chen, X. Ma. Using GRASP for the cover by s-defective independent sets problem. In Examining Robustness and Vulnerability of Critical Infrastructure Networks. Ed. by S. Butenko, E.L. Pasiliao, and V. Shylo. Amsterdam: IOS Press, 2014, pp. 17–25. (pdf)