Space Limited Graph Algorithms on Big Data

• Published in: Computing and Combinatorics Vol. 13595; pp. 255 - 267
• Main Authors: Chen, Jianer, Chu, Zirui, Guo, Ying, Yang, Wei
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2023; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Big data; Edge dominating set; Maximal matching
• ISBN: 3031221044; 9783031221040
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-031-22105-7_23

We study algorithms for graph problems in which the graphs are of extremely large size N so that super-linear time ω(N) $$\omega (N)$$ or linear space Θ(N) $$\varTheta (N)$$ 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(kO(1)) $$O(k^{O(1)})$$ . In our case studies, as examples, we present a randomized algorithm of time O(N) and space O(k2) $$O(k^2)$$ 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(k3) $$O(k^3)$$ 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.