Abstract
Communication complexity theory is a powerful tool to show time complexity lower bounds of distributed algorithms for global problems such as minimum spanning tree (MST) and shortest path. While it often leads to nearly-tight lower bounds for many problems, polylogarithmic complexity gaps still lie between the currently best upper and lower bounds. In this paper, we propose a new approach for filling the gaps. Using this approach, we achieve tighter deterministic lower bounds for MST and shortest paths. Specifically, for those problems, we show the deterministic \(\Omega(\sqrt{n})\)-round lower bound for graphs of O(n ε) hop-count diameter, and the deterministic \(\Omega(\sqrt{n/\log n})\) lower bound for graphs of O(logn) hop-count diameter. The main idea of our approach is to utilize the two-party communication complexity lower bound for a function we call permutation identity, which is newly introduced in this paper.
This work is supported in part by KAKENHI No. 25106507 and No. 25289114.
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Ookawa, H., Izumi, T. (2015). Filling Logarithmic Gaps in Distributed Complexity for Global Problems. In: Italiano, G.F., Margaria-Steffen, T., Pokorný, J., Quisquater, JJ., Wattenhofer, R. (eds) SOFSEM 2015: Theory and Practice of Computer Science. SOFSEM 2015. Lecture Notes in Computer Science, vol 8939. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46078-8_31
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DOI: https://doi.org/10.1007/978-3-662-46078-8_31
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