Low-congestion shortcut and graph parameters

Abstract Distributed graph algorithms in the standard CONGEST model often exhibit time-complexity lower bound of $${\tilde{\Omega }}(\sqrt{n} + D)$$ ? ~ ( n + D ) rounds for several global problems, where n denotes number nodes and D diameter input graph. Because such a is derived from special “hard-core” instances, it does not necessarily apply to specific popular classes as planar graphs. The concept low-congestion shortcuts was initiated by Ghaffari Haeupler [SODA2016] addressing design running fast restricted network topologies. In particular, given class $${\mathcal {C}}$$ C , an f -round algorithm constructing quality q any instance results $${\tilde{O}}(q f)$$ O q f solving fundamental problems minimum spanning tree cut, . main interest on this line identify allowing that are efficient sense breaking $${\tilde{O}}(\sqrt{n}+D)$$ general bounds. study, we consider relationship between following four major parameters: doubling dimension, chordality, diameter, clique-width. key ingredient upper-bound side novel shortcut construction technique known short-hop extension which might be independent interest.