Distributed Verification and Hardness of Distributed Approximation
Atish Das Sarma,Stephan Holzer,Liah Kor,Amos Korman,Danupon Nanongkai,Gopal Pandurangan,David Peleg,Roger Wattenhofer +7 more
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The verification problem in distributed networks is studied, stated as follows: let H be a subgraph of a network G where each vertex of G knows which edges incident on it are in H.Abstract:
We study the verification problem in distributed networks, stated as follows. Let $H$ be a subgraph of a network $G$ where each vertex of $G$ knows which edges incident on it are in $H$. We would l...read more
Citations
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Proceedings ArticleDOI
On the power of the congested clique model
TL;DR: It is shown that the unicast congested clique can simulate powerful classes of bounded-depth circuits, implying that even slightly super-constant lower bounds for the congestedClique would give new lower bounds in circuit complexity.
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What graph neural networks cannot learn: depth vs width
TL;DR: GNNmp are shown to be Turing universal under sufficient conditions on their depth, width, node attributes, and layer expressiveness, and it is discovered that GNNmp can lose a significant portion of their power when their depth and width is restricted.
Proceedings ArticleDOI
Networks cannot compute their diameter in sublinear time
TL;DR: A new technique is used to prove an Ω (√n + D) lower bound on approximating the girth of a graph by a factor 2 − e, which is valid even if the diameter of the network is a small constant.
Proceedings ArticleDOI
Optimal distributed all pairs shortest paths and applications
Stephan Holzer,Roger Wattenhofer +1 more
TL;DR: A new lower bound for approximating the diameter D of a graph is presented: being allowed to answer D+1 or D can speed up the computation by at most a factor D, and an algorithm is provided that achieves such a speedup of D and computes an (1+εepsilon) multiplicative approximation of the diameter.
Journal ArticleDOI
Local Computation: Lower and Upper Bounds
TL;DR: The first polylogarithmic lower bound on such local computation for (optimization) problems including minimum vertex cover, minimum (connected) dominating set, maximum matching, maximal independent set, and maximal matching is given.
References
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