Constant Round Distributed Domination on Graph Classes with Bounded Expansion

Kublenz, Simeon; Siebertz, Sebastian; Vigny, Alexandre

doi:10.1007/978-3-030-79527-6_19

Cited by 5 publications

(2 citation statements)

References 28 publications

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“…Later, Amiri et al [4,5] provided a new analysis method to extend the result of Lenzen et al to bounded genus graphs. This has been gradually generalized to excluded minor graphs [15] and bounded expansion [19].…”

Section: Related Workmentioning

confidence: 99%

Distributed Distance-r Covering Problems on Sparse High-Girth Graphs

Amiri

Wiederhake

2021

Lecture Notes in Computer Science

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We prove that the distance-r dominating set, distance-r connected dominating set, distance-r vertex cover, and distance-r connected vertex cover problems admit constant factor approximations in the CONGEST model of distributed computing in a constant number of rounds on classes of sparse high-girth graphs. In this paper, sparse means bounded expansion, and high-girth means girth at least 4r + 2. Our algorithm is quite simple; however, the proof of its approximation guarantee is non-trivial. To complement the algorithmic results, we show tightness of our approximation by providing a loosely matching lower bound on rings. Our result is the first to show the existence of constant-factor approximations in a constant number of rounds in non-trivial classes of graphs for distance-r covering problems.

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Section: Related Workmentioning

confidence: 99%

Distributed Distance-r Covering Problems on Sparse High-Girth Graphs

Amiri

Wiederhake

2021

Lecture Notes in Computer Science

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“…Amiri et al [2], additionally provided a constant factor approximation on bounded expansion graphs in logarithmic rounds for a generalized version of the problem: the distance-r MDS. The latter recently has been improved in two directions: Kublenz et al [17], reduced the number of rounds to a constant but only for the standard MDS-problem, Amiri and Wiederhake [6] showed that for high girth graphs the approximation algorithm for distance r-MDS can be obtained by O(r) rounds. The minimum girth requirement showed to be useful in a recent work of Alipour and Jafari [1], where they showed that in C 4 -free planar graphs there is a better approximation guarantee for the MDS problem.…”

Section: Introductionmentioning

confidence: 99%