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Comput."],"published-print":{"date-parts":[[2021,10]]},"abstract":"Abstract<\/jats:title>Distributed graph algorithms in the standard CONGEST model often exhibit the time-complexity lower bound of $${\\tilde{\\Omega }}(\\sqrt{n} + D)$$<\/jats:tex-math>\n \n \n \u03a9<\/mml:mi>\n ~<\/mml:mo>\n <\/mml:mover>\n \n (<\/mml:mo>\n \n n<\/mml:mi>\n <\/mml:msqrt>\n +<\/mml:mo>\n D<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> rounds for several global problems, where n<\/jats:italic> denotes the number of nodes and D<\/jats:italic> the diameter of the input graph. Because such a lower bound is derived from special \u201chard-core\u201d instances, it does not necessarily apply to specific popular graph classes such as planar graphs. The concept of low-congestion shortcuts<\/jats:italic> was initiated by Ghaffari and Haeupler [SODA2016] for addressing the design of CONGEST algorithms running fast in restricted network topologies. In particular, given a graph class $${\\mathcal {C}}$$<\/jats:tex-math>\n C<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, an f<\/jats:italic>-round algorithm for constructing shortcuts of quality q<\/jats:italic> for any instance in $${\\mathcal {C}}$$<\/jats:tex-math>\n C<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> results in $${\\tilde{O}}(q + f)$$<\/jats:tex-math>\n \n \n O<\/mml:mi>\n ~<\/mml:mo>\n <\/mml:mover>\n \n (<\/mml:mo>\n q<\/mml:mi>\n +<\/mml:mo>\n f<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-round algorithms for solving several fundamental graph problems such as minimum spanning tree and minimum cut, for $${\\mathcal {C}}$$<\/jats:tex-math>\n C<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. The main interest on this line is to identify the graph classes allowing the shortcuts that are efficient in the sense of breaking $${\\tilde{O}}(\\sqrt{n}+D)$$<\/jats:tex-math>\n \n \n O<\/mml:mi>\n ~<\/mml:mo>\n <\/mml:mover>\n \n (<\/mml:mo>\n \n n<\/mml:mi>\n <\/mml:msqrt>\n +<\/mml:mo>\n D<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-round general lower bounds. In this study, we consider the relationship between the quality of low-congestion shortcuts and the following four major graph parameters: doubling dimension, chordality, diameter, and clique-width. The key ingredient of the upper-bound side is a novel shortcut construction technique known as short-hop extension<\/jats:italic>, which might be of independent interest.<\/jats:p>","DOI":"10.1007\/s00446-021-00401-x","type":"journal-article","created":{"date-parts":[[2021,8,28]],"date-time":"2021-08-28T18:04:39Z","timestamp":1630173879000},"page":"349-365","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Low-congestion shortcut and graph parameters"],"prefix":"10.1007","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3143-7200","authenticated-orcid":false,"given":"Naoki","family":"Kitamura","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hirotaka","family":"Kitagawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yota","family":"Otachi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Taisuke","family":"Izumi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,8,28]]},"reference":[{"key":"401_CR1","doi-asserted-by":"publisher","unstructured":"Abboud, A., Censor-Hillel, K., Khoury, S.: Near-linear lower bounds for distributed distance computations, even in sparse networks. 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