1. Towards a Theory of Parameterized Streaming Algorithms
- Author
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Chitnis, Rajesh, Cormode, Graham, and Wagner, Michael
- Subjects
FOS: Computer and information sciences ,000 Computer science, knowledge, general works ,Computer Science ,Computer Science - Data Structures and Algorithms ,Data Structures and Algorithms (cs.DS) ,QA ,QA76 - Abstract
Parameterized complexity attempts to give a more fine-grained analysis of the complexity of problems: instead of measuring the running time as a function of only the input size, we analyze the running time with respect to additional parameters. This approach has proven to be highly successful in delineating our understanding of \NP-hard problems. Given this success with the TIME resource, it seems but natural to use this approach for dealing with the SPACE resource. First attempts in this direction have considered a few individual problems, with some success: Fafianie and Kratsch [MFCS'14] and Chitnis et al. [SODA'15] introduced the notions of streaming kernels and parameterized streaming algorithms respectively. For example, the latter shows how to refine the $\Omega(n^2)$ bit lower bound for finding a minimum Vertex Cover (VC) in the streaming setting by designing an algorithm for the parameterized $k$-VC problem which uses $O(k^{2}\log n)$ bits. In this paper, we initiate a systematic study of graph problems from the paradigm of parameterized streaming algorithms. We first define a natural hierarchy of space complexity classes of FPS, SubPS, SemiPS, SupPS and BrutePS, and then obtain tight classifications for several well-studied graph problems such as Longest Path, Feedback Vertex Set, Dominating Set, Girth, Treewidth, etc. into this hierarchy. (see paper for full abstract), Comment: Extended abstract in IPEC 2019. arXiv admin note: text overlap with arXiv:1603.05715 by other authors
- Published
- 2019