Abstract
Shortest paths in complex networks play key roles in many applications. Examples include routing packets in a computer network, routing traffic on a transportation network, and inferring semantic distances between concepts on the World Wide Web. An adversary with the capability to perturb the graph might make the shortest path between two nodes route traffic through advantageous portions of the graph (e.g., a toll road he owns). In this paper, we introduce the Force Path Cut problem, in which there is a specific route the adversary wants to promote by removing a low-cost set of edges in the graph. We show that Force Path Cut is NP-complete. It can be recast as an instance of the Weighted Set Cover problem, enabling the use of approximation algorithms. The size of the universe for the set cover problem is potentially factorial in the number of nodes. To overcome this hurdle, we propose the PATHATTACK algorithm, which via constraint generation considers only a small subset of paths—at most 5% of the number of edges in 99% of our experiments. Across a diverse set of synthetic and real networks, the linear programming formulation of Weighted Set Cover yields the optimal solution in over 98% of cases. We also demonstrate running time vs. cost tradeoff using two approximation algorithms and greedy baseline methods. This work expands the area of adversarial graph mining beyond recent work on node classification and embedding.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
The eigenscore of an edge is the product of the entries in the principal eigenvector of the adjacency matrix corresponding to the edge’s vertices.
- 2.
This alternative method of selecting the destination was used due to the computational expense of identifying successive shortest paths in large grid-like networks.
- 3.
Gurobi is at https://www.gurobi.com. NetworkX is at https://networkx.org. Code from the experiments is at https://github.com/bamille1/PATHATTACK.
- 4.
GreedyEigenscore only outperforms GreedyCost in COMP with uniform weights.
References
Albert, R., Jeong, H., Barabási, A.L.: Error and attack tolerance of complex networks. Nature 406(6794), 378–382 (2000)
Ben-Ameur, W., Neto, J.: A constraint generation algorithm for large scale linear programs using multiple-points separation. Math. Program. 107(3), 517–537 (2006)
Benson, A.R., Abebe, R., Schaub, M.T., Jadbabaie, A., Kleinberg, J.: Simplicial closure and higher-order link prediction. Proc. Nat. Acad. Sci. 115(48), E11221–E11230 (2018)
Bojchevski, A., Günnemann, S.: Adversarial attacks on node embeddings via graph poisoning. In: ICML, pp. 695–704 (2019)
Dahlhaus, E., Johnson, D.S., Papadimitriou, C.H., Seymour, P.D., Yannakakis, M.: The complexity of multiterminal cuts. SIAM J. Comput. 23(4), 864–894 (1994)
Jain, M., et al.: A double oracle algorithm for zero-sum security games on graphs. In: AAMAS, pp. 327–334 (2011)
Jun, M., D’Andrea, R.: Path planning for unmanned aerial vehicles in uncertain and adversarial environments. In: Butenko, S., Murphey, R., Pardalos, P.M. (eds.) Cooperative Control: Models, Applications and Algorithms, pp. 95–110. Springer, Boston (2003). https://doi.org/10.1007/978-1-4757-3758-5_6
Kegelmeyer, W.P., Wendt, J.D., Pinar, A.: An example of counter-adversarial community detection analysis. Technical report, SAND2018-12068, Sandia National Laboratories (2018). https://doi.org/10.2172/1481570
Kim, H., Olave-Rojas, D., Álvarez-Miranda, E., Son, S.W.: In-depth data on the network structure and hourly activity of the central Chilean power grid. Sci. Data 5(1), 1–10 (2018)
Leskovec, J., Kleinberg, J., Faloutsos, C.: Graphs over time: densification laws, shrinking diameters and possible explanations. In: KDD, pp. 177–187 (2005)
Leskovec, J., Lang, K.J., Dasgupta, A., Mahoney, M.W.: Community structure in large networks: natural cluster sizes and the absence of large well-defined clusters. Internet Math. 6(1), 29–123 (2009)
Letchford, J., Vorobeychik, Y.: Optimal interdiction of attack plans. In: AAMAS, pp. 199–206 (2013)
Nardelli, E., Proietti, G., Widmayer, P.: Finding the most vital node of a shortest path. Theoret. Comput. Sci. 296(1), 167–177 (2003)
Neu, G., Gyorgy, A., Szepesvari, C.: The adversarial stochastic shortest path problem with unknown transition probabilities. In: AISTATS, pp. 805–813 (2012)
Qiao, M., Cheng, H., Yu, J.X.: Querying shortest path distance with bounded errors in large graphs. In: Bayard Cushing, J., French, J., Bowers, S. (eds.) SSDBM 2011. LNCS, vol. 6809, pp. 255–273. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22351-8_16
Rayner, D.C., Bowling, M., Sturtevant, N.: Euclidean heuristic optimization. In: AAAI (2011)
Speicher, P., Steinmetz, M., Backes, M., Hoffmann, J., Künnemann, R.: Stackelberg planning: towards effective leader-follower state space search. In: AAAI, pp. 6286–6293 (2018)
Tong, H., Prakash, B.A., Eliassi-Rad, T., Faloutsos, M., Faloutsos, C.: Gelling, and melting, large graphs by edge manipulation. In: CIKM, pp. 245–254 (2012)
Vazirani, V.V.: Approximation Algorithms. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-662-04565-7
Washburn, A., Wood, K.: Two-person zero-sum games for network interdiction. Oper. Res. 43(2), 243–251 (1995)
West, R., Pineau, J., Precup, D.: Wikispeedia: an online game for inferring semantic distances between concepts. In: IJCAI (2009)
Zügner, D., Akbarnejad, A., Günnemann, S.: Adversarial attacks on neural networks for graph data. In: KDD, pp. 2847–2856 (2018)
Zügner, D., Günnemann, S.: Certifiable robustness and robust training for graph convolutional networks. In: KDD, pp. 246–256 (2019)
Acknowledgments
BAM was supported by the United States Air Force under Contract No. FA8702-15-D-0001. TER was supported in part by the Combat Capabilities Development Command Army Research Laboratory (under Cooperative Agreement No. W911NF-13-2-0045) and by the Under Secretary of Defense for Research and Engineering under Air Force Contract No. FA8702-15-D-0001. YV was supported by grants from the Army Research Office (W911NF1810208, W911NF1910241) and National Science Foundation (CAREER Award IIS-1905558). Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the funding agencies or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes not withstanding any copyright notation here on.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
1 Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Miller, B.A., Shafi, Z., Ruml, W., Vorobeychik, Y., Eliassi-Rad, T., Alfeld, S. (2021). PATHATTACK: Attacking Shortest Paths in Complex Networks. In: Oliver, N., Pérez-Cruz, F., Kramer, S., Read, J., Lozano, J.A. (eds) Machine Learning and Knowledge Discovery in Databases. Research Track. ECML PKDD 2021. Lecture Notes in Computer Science(), vol 12976. Springer, Cham. https://doi.org/10.1007/978-3-030-86520-7_33
Download citation
DOI: https://doi.org/10.1007/978-3-030-86520-7_33
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-86519-1
Online ISBN: 978-3-030-86520-7
eBook Packages: Computer ScienceComputer Science (R0)
