Abstract
We study algorithms for graph problems in which the graphs are of extremely large size N so that super-linear time \(\omega (N)\) or linear space \(\varTheta (N)\) would become impractical. We use a parameter k to characterize the computational power of a normal computer that can provide additional time and space bounded by polynomials of k. In particular, we are interested in strict linear-time algorithms using space \(O(k^{O(1)})\). In our case studies, as examples, we present a randomized algorithm of time O(N) and space \(O(k^2)\) that constructs a maximal matching of size upper bounded by k in a graph of size N, and a randomized kernelization algorithm of time O(N) and space \(O(k^3)\) for the NP-hard Edge Dominating Set problem. Our kernelization algorithm for Edge Dominating Set has its kernel size match the best kernel size by known polynomial-time kernelization algorithms for the problem with no space complexity constraints. We also show that the techniques developed in our algorithms can be used to develop improved streaming algorithms.
Supported by National Natural Science Foundation of China under grant 61872097.
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Notes
- 1.
It is known [5] that (even randomized) 1-pass streaming algorithms for the p-EDS problem require \(\varOmega (N)\) space. As a result, 1-pass streaming algorithms for the problem have become less interesting.
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Chen, J., Chu, Z., Guo, Y., Yang, W. (2022). Space Limited Graph Algorithms on Big Data. In: Zhang, Y., Miao, D., Möhring, R. (eds) Computing and Combinatorics. COCOON 2022. Lecture Notes in Computer Science, vol 13595. Springer, Cham. https://doi.org/10.1007/978-3-031-22105-7_23
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