Low-congestion shortcut and graph parameters

Distributed graph algorithms in the standard CONGEST model often exhibit the time-complexity lower bound of Ω ~ ( n + D ) rounds for several global problems, where n denotes the number of nodes and D the diameter of the input graph. Because such a lower bound is derived from special “hard-core” inst...

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Bibliographic Details
Published in:Distributed computing Vol. 34; no. 5; pp. 349 - 365
Main Authors: Kitamura, Naoki, Kitagawa, Hirotaka, Otachi, Yota, Izumi, Taisuke
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2021
Springer Nature B.V
Subjects:
Algorithms
Computer Communication Networks
Computer Hardware
Computer Science
Computer Systems Organization and Communication Networks
Congestion
Diameters
Graph theory
Lower bounds
Network topologies
Parameters
Software Engineering/Programming and Operating Systems
Theory of Computation
Upper bounds
Distributed graph algorithms
Low-congestion shortcut
Clique width
chordal graph
Minimum spanning tree
ISSN:0178-2770, 1432-0452
Online Access:Get full text
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Summary:Distributed graph algorithms in the standard CONGEST model often exhibit the time-complexity lower bound of Ω ~ ( n + D ) rounds for several global problems, where n denotes the number of nodes and D the diameter of the input graph. Because such a lower bound is derived from special “hard-core” instances, it does not necessarily apply to specific popular graph classes such as planar graphs. The concept of low-congestion shortcuts 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 C , an f -round algorithm for constructing shortcuts of quality q for any instance in C results in O ~ ( q + f ) -round algorithms for solving several fundamental graph problems such as minimum spanning tree and minimum cut, for C . The main interest on this line is to identify the graph classes allowing the shortcuts that are efficient in the sense of breaking O ~ ( n + D ) -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 , which might be of independent interest.
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ISSN:0178-2770
1432-0452
DOI:10.1007/s00446-021-00401-x