Abstract
The study of parameterized streaming complexity on graph problems was initiated by Fafianie et al. (MFCS’14) and Chitnis et al. (SODA’15 and SODA’16). In this work, we initiate a systematic study of parameterized streaming complexity of graph deletion problems – \(\mathcal {F}\) -Subgraph deletion, \(\mathcal {F}\) -Minor deletion in the four most well-studied streaming models: the \(\textsc {Ea}\) (edge arrival), \(\textsc {Dea}\) (dynamic edge arrival), \(\textsc {Va}\) (vertex arrival) and Al (adjacency list) models. Our main conceptual contribution is to overcome the obstacles to efficient parameterized streaming algorithms by utilizing the power of parameterization. We focus on the vertex cover size K as the parameter for the parameterized graph deletion problems we consider. At the same time, most of the previous work in parameterized streaming complexity was restricted to the Ea (edge arrival) or Dea (dynamic edge arrival) models. In this work, we consider the four most well-studied streaming models: the Ea, Dea, Va (vertex arrival) and Al (adjacency list) models.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
It is usual in streaming that the lower bound results are in bits, and the upper bound results are in words.
- 2.
V(M) denotes the set of all vertices present in the matching M.
- 3.
By enough, we mean \(\mathcal {O}(K)\) in this case.
References
Assadi, S., Khanna, S., Li, Y.: Tight bounds for single-pass streaming complexity of the set cover problem. In: STOC, pp. 698–711 (2016)
Bishnu, A., Ghosh, A., Kolay, S., Mishra, G., Saurabh, S.: Fixed-parameter tractability of graph deletion problems over data streams. CoRR, abs/1906.05458 (2019)
Bury, M., et al.: Structural results on matching estimation with applications to streaming. Algorithmica 81(1), 367–392 (2019)
Chitnis, R., Cormode, G.: Towards a theory of parameterized streaming algorithms. In: IPEC, vol. 148, pp. 7:1–7:15 (2019)
Chitnis, R., et al.: Kernelization via sampling with applications to finding matchings and related problems in dynamic graph streams. In: SODA, pp. 1326–1344 (2016)
Chitnis, R.H., Cormode, G., Esfandiari, H., Hajiaghayi, M., Monemizadeh, M.: Brief announcement: new streaming algorithms for parameterized maximal matching & beyond. In: SPAA, pp. 56–58 (2015)
Chitnis, R.H., Cormode, G., Hajiaghayi, M.T., Monemizadeh, M.: Parameterized streaming: maximal matching and vertex cover. In: SODA, pp. 1234–1251 (2015)
Cormode, G., Dark, J., Konrad, C.: Independent sets in vertex-arrival streams. In: ICALP, pp. 45:1–45:14 (2019)
Cormode, G., Jowhari, H., Monemizadeh, M., Muthukrishnan, S.: The sparse awakens: streaming algorithms for matching size estimation in sparse graphs. In: 25th Annual European Symposium on Algorithms, ESA 2017. LIPIcs, vol. 87, pp. 29:1–29:15 (2017)
Cygan, M., et al.: Parameterized Algorithms, 1st edn. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-319-21275-3
Esfandiari, H., Hajiaghayi, M., Liaghat, V., Monemizadeh, M., Onak, K.: Streaming algorithms for estimating the matching size in planar graphs and beyond. ACM Trans. Algorithms 14(4), 1–23 (2018)
Fafianie, S., Kratsch, S.: Streaming kernelization. In: MFCS, pp. 275–286 (2014)
Fomin, F.V., Jansen, B.M.P., Pilipczuk, M.: Preprocessing subgraph and minor problems: When does a small vertex cover help? JCSS 80(2), 468–495 (2014)
Guruswami, V., Velingker, A., Velusamy, S.: Streaming complexity of approximating max 2CSP and max acyclic subgraph. In: APPROX/RANDOM, pp. 8:1–8:19 (2017)
Kapralov, M., Khanna, S., Sudan, M., Velingker, A.: \(1+\omega (1)\) approximation to MAX-CUT requires linear space. In: SODA, pp. 1703–1722 (2017)
McGregor, A.: Graph stream algorithms: a survey. SIGMOD Rec. 43(1), 9–20 (2014)
McGregor, A., Vorotnikova, S.: Planar matching in streams revisited. In: APPROX/RANDOM, Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2016)
McGregor, A., Vorotnikova, S.: A simple, space-efficient, streaming algorithm for matchings in low arboricity graphs. In: SOSA (2018)
McGregor, A., Vorotnikova, S., Vu, H.T.: Better algorithms for counting triangles in data streams. In: PODS, pp. 401–411 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Bishnu, A., Ghosh, A., Kolay, S., Mishra, G., Saurabh, S. (2020). Fixed Parameter Tractability of Graph Deletion Problems over Data Streams. In: Kim, D., Uma, R., Cai, Z., Lee, D. (eds) Computing and Combinatorics. COCOON 2020. Lecture Notes in Computer Science(), vol 12273. Springer, Cham. https://doi.org/10.1007/978-3-030-58150-3_53
Download citation
DOI: https://doi.org/10.1007/978-3-030-58150-3_53
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-58149-7
Online ISBN: 978-3-030-58150-3
eBook Packages: Computer ScienceComputer Science (R0)