Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, March 25, 2021, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Yi-Jun Chang

Tight Distributed Listing of Cliques

In this talk, we will discuss my recent work with Keren Censor-Hillel, François Le Gall and Dean Leitersdorf on distributed clique listing in SODA 2021. Much progress has recently been made in understanding the complexity landscape of subgraph finding problems in the CONGEST model of distributed computing. However, so far, very few tight bounds are known in this area. For triangle (i.e., 3-clique) listing, an optimal O(n^{1/3} polylog n)-round distributed algorithm has been constructed by Chang et al. [SODA 2019, PODC 2019]. Recent works of Eden et al. [DISC 2019] and of Censor-Hillel et al. [PODC 2020] have shown sublinear algorithms for K_p-listing, for each p≥4, but still leaving a significant gap between the upper bounds and the known lower bounds of the problem. In this work, we completely close this gap. We show that for each p≥4, there is an O(n^{1−2/p} polylog n)-round distributed algorithm that lists all p-cliques K_p in the communication network. Our algorithm is optimal up to a polylogarithmic factor, due to the Ω(n^{1−2/p} / log n)-round lower bound of Fischer et al. [SPAA 2018], which holds even in the CONGESTED CLIQUE model. Together with the triangle-listing algorithm by Chang et al. [SODA 2019, PODC 2019], our result thus shows that the round complexity of Kp-listing, for all p, is the same in both the CONGEST and CONGESTED CLIQUE models, at Θ(n^{1−2/p}) rounds (up to a polylogarithmic factor). For p=4, our result additionally matches the Ω(n^{1/2} / log n) lower bound for K_4-detection by Czumaj and Konrad [DISC 2018], implying that the round complexities for detection and listing of K_4 are equivalent in the CONGEST model (again, up to a polylogarithmic factor).

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