Abstract
We study the following DAG Partitioning problem: given a directed acyclic graph with arc weights, delete a set of arcs of minimum total weight so that each of the resulting connected components has exactly one sink. We prove that the problem is hard to approximate in a strong sense: If \(\mathcal P\neq \mathcal{NP}\) then for every fixed ε > 0, there is no (n 1 − ε)-approximation algorithm, even if the input graph is restricted to have unit weight arcs, maximum out-degree three, and two sinks. We also present a polynomial time algorithm for solving the DAG Partitioning problem in graphs with bounded pathwidth.
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References
Adar, E., Adamic, L.A.: Tracking information epidemics in blogspace. In: Proceedings of the 2005 IEEE/WIC/ACM International Conference on Web Intelligence, WI 2005, pp. 207–214. IEEE Computer Society, Washington, DC (2005), http://dx.doi.org/10.1109/WI.2005.151
Adar, E., Zhang, L., Adamic, L.A., Lukose, R.M.: Implicit Structure and the Dynamics of Blogspace. In: WWW 2004 Workshop on the Weblogging Ecosystem: Aggregation, Analysis and Dynamics. ACM Press, New York (2004)
Berger, B., Shor, P.W.: Approximation alogorithms for the maximum acyclic subgraph problem. In: Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990, pp. 236–243. Society for Industrial and Applied Mathematics, Philadelphia (1990), http://dl.acm.org/citation.cfm?id=320176.320203
Blei, D.M., Lafferty, J.D.: Dynamic topic models. In: Proceedings of the 23rd International Conference on Machine Learning, ICML 2006, pp. 113–120. ACM, New York (2006), http://doi.acm.org/10.1145/1143844.1143859
Courcelle, B.: The monadic second-order logic of graphs. i. recognizable sets of finite graphs. Inf. Comput. 85, 12–75 (1990), http://dl.acm.org/citation.cfm?id=81253.81255
Călinescu, G., Karloff, H., Rabani, Y.: An improved approximation algorithm for multiway cut. In: Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, STOC 1998, pp. 48–52. ACM, New York (1998), http://doi.acm.org/10.1145/276698.276711
Korach, E., Solel, N.: Tree-width, path-width, and cutwidth. Discrete Appl. Math. 43, 97–101 (1993), http://dl.acm.org/citation.cfm?id=153610.153618
Kwon, Y.S., Kim, S.W., Park, S., Lim, S.H., Lee, J.B.: The information diffusion model in the blog world. In: Proceedings of the 3rd Workshop on Social Network Mining and Analysis, SNA-KDD 2009, pp. 4:1–4:9. ACM, New York (2009), http://doi.acm.org/10.1145/1731011.1731015
Leskovec, J., Backstrom, L., Kleinberg, J.: Meme-tracking and the dynamics of the news cycle. In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2009, pp. 497–506. ACM, New York (2009), http://doi.acm.org/10.1145/1557019.1557077
Leskovec, J., McGlohon, M., Faloutsos, C., Glance, N., Hurst, M.: Cascading behavior in large blog graphs: Patterns and a model. In: Society of Applied and Industrial Mathematics: Data Mining, SDM 2007 (2007)
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Alamdari, S., Mehrabian, A. (2012). On a DAG Partitioning Problem. In: Bonato, A., Janssen, J. (eds) Algorithms and Models for the Web Graph. WAW 2012. Lecture Notes in Computer Science, vol 7323. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30541-2_2
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DOI: https://doi.org/10.1007/978-3-642-30541-2_2
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