On Approximating Target Set Selection

Authors Moses Charikar, Yonatan Naamad, Anthony Wirth



PDF
Thumbnail PDF

File

LIPIcs.APPROX-RANDOM.2016.4.pdf
  • Filesize: 0.6 MB
  • 16 pages

Document Identifiers

Author Details

Moses Charikar
Yonatan Naamad
Anthony Wirth

Cite AsGet BibTex

Moses Charikar, Yonatan Naamad, and Anthony Wirth. On Approximating Target Set Selection. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 60, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2016.4

Abstract

We study the Target Set Selection (TSS) problem introduced by Kempe, Kleinberg, and Tardos (2003). This problem models the propagation of influence in a network, in a sequence of rounds. A set of nodes is made "active" initially. In each subsequent round, a vertex is activated if at least a certain number of its neighbors are (already) active. In the minimization version, the goal is to activate a small set of vertices initially - a seed, or target, set - so that activation spreads to the entire graph. In the absence of a sublinear-factor algorithm for the general version, we provide a (sublinear) approximation algorithm for the bounded-round version, where the goal is to activate all the vertices in r rounds. Assuming a known conjecture on the hardness of Planted Dense Subgraph, we establish hardness-of-approximation results for the bounded-round version. We show that they translate to general Target Set Selection, leading to a hardness factor of n^(1/2-epsilon) for all epsilon > 0. This is the first polynomial hardness result for Target Set Selection, and the strongest conditional result known for a large class of monotone satisfiability problems. In the maximization version of TSS, the goal is to pick a target set of size k so as to maximize the number of nodes eventually active. We show an n^(1-epsilon) hardness result for the undirected maximization version of the problem, thus establishing that the undirected case is as hard as the directed case. Finally, we demonstrate an SETH lower bound for the exact computation of the optimal seed set.
Keywords
  • target set selection
  • influence propagation
  • approximation algorithms
  • hardness of approximation
  • planted dense subgraph

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Michael Alekhnovich, Sam Buss, Shlomo Moran, and Toniann Pitassi. Minimum propositional proof length is NP-hard to linearly approximate. The Journal of Symbolic Logic, 66(01):171-191, 2001. Google Scholar
  2. Benny Applebaum, Boaz Barak, and Avi Wigderson. Public-key cryptography from different assumptions. In Proceedings of the 42nd ACM Symposium on Theory of Computing (STOC), pages 171-180. ACM, 2010. Google Scholar
  3. Sanjeev Arora, Boaz Barak, Markus Brunnermeier, and Rong Ge. Computational complexity and information asymmetry in financial products. In Proceedings of the Innovations in (Theoretical) Computer Science Conference (ICS), pages 49-65, 2010. Google Scholar
  4. Pranjal Awasthi, Moses Charikar, Kevin A. Lai, and Andrej Risteski. Label optimal regret bounds for online local learning. In Proceedings of the 28th Conference on Learning Theory (COLT), pages 150-166, 2015. Google Scholar
  5. Oren Ben-Zwi, Danny Hermelin, Daniel Lokshtanov, and Ilan Newman. Treewidth governs the complexity of target set selection. Discrete Optimization, 8(1):87-96, 2011. Google Scholar
  6. Aditya Bhaskara, Moses Charikar, Eden Chlamtac, Uriel Feige, and Aravindan Vijayaraghavan. Detecting high log-densities: an O(n^1/4) approximation for densest k-subgraph. In Proceedings of the 42nd ACM Symposium on Theory of Computing (STOC), pages 201-210. ACM, 2010. Google Scholar
  7. Ning Chen. On the approximability of influence in social networks. SIAM Journal on Discrete Mathematics, 23(3):1400-1415, 2009. Google Scholar
  8. Ramkumar Chinchani, Duc Ha, Anusha Iyer, Hung Q Ngo, and Shambhu Upadhyaya. On the hardness of approximating the min-hack problem. Journal of Combinatorial Optimization, 9(3):295-311, 2005. Google Scholar
  9. Eden Chlamtac, Michael Dinitz, and Robert Krauthgamer. Everywhere-sparse spanners via dense subgraphs. In Proceedings of the 53rd Annual Symposium on Foundations of Computer Science (FOCS), pages 758-767. IEEE, 2012. Google Scholar
  10. Ferdinando Cicalese, Gennaro Cordasco, Luisa Gargano, Martin Milanič, Joseph Peters, and Ugo Vaccaro. Spread of influence in weighted networks under time and budget constraints. Theoretical Computer Science, 586:40-58, 2015. Google Scholar
  11. Ferdinando Cicalese, Gennaro Cordasco, Luisa Gargano, Martin Milanič, and Ugo Vaccaro. Latency-bounded target set selection in social networks. Theoretical Computer Science, 535:1-15, 2014. Google Scholar
  12. Amin Coja-Oghlan, Uriel Feige, Michael Krivelevich, and Daniel Reichman. Contagious sets in expanders. In Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1953-1987. SIAM, 2015. Google Scholar
  13. Irit Dinur and Shmuel Safra. On the hardness of approximating label-cover. Information Processing Letters, 89(5):247-254, 2004. Google Scholar
  14. Pedro Domingos and Matt Richardson. Mining the network value of customers. In Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 57-66. ACM, 2001. Google Scholar
  15. Joel Friedman. Constructing O(n log n) size monotone formulae for the kth threshold function of n Boolean variables. SIAM Journal on Computing, 15(3):641-654, 1986. Google Scholar
  16. Oded Goldreich and Shafi Goldwasser. On the possibility of basing cryptography on the assumption that P≠NP., 1998. Google Scholar
  17. Michael Goldwasser and Rajeev Motwani. Intractability of assembly sequencing: Unit disks in the plane. Springer, 1997. Google Scholar
  18. David Kempe, Jon Kleinberg, and Éva Tardos. Maximizing the spread of influence through a social network. In Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 137-146. ACM, 2003. Google Scholar
  19. Mihai Pătraşcu and Ryan Williams. On the possibility of faster sat algorithms. In Proceedings of the 21st Annual ACM-SIAM symposium on Discrete Algorithms (SODA), pages 1065-1075. Society for Industrial and Applied Mathematics, 2010. Google Scholar
  20. Matthew Richardson and Pedro Domingos. Mining knowledge-sharing sites for viral marketing. In Proceedings of the Eighth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 61-70. ACM, 2002. Google Scholar
  21. Christopher Umans. Hardness of approximating Σ₂^p minimization problems. In Proceedings of the 40th Annual Symposium on Foundations of Computer Science (FOCS), pages 465-474. IEEE, 1999. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail