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Author
Title The Impact Of Locality In The Broadcast Congested Clique Model Type
Year 2020 Publication Siam Journal On Discrete Mathematics Abbreviated Journal SIAM Discret. Math.
Volume 34 Issue 1 Pages 682-700
Keywords
Abstract The broadcast congested clique model (BCLIQUE) is a message-passing model of distributed computation where n nodes communicate with each other in synchronous rounds. First, in this paper we prove that there is a one-round, deterministic algorithm that reconstructs the input graph G if the graph is d-degenerate, and rejects otherwise, using bandwidth b = O(d . log n). Then, we introduce a new parameter to the model. We study the situation where the nodes, initially, instead of knowing their immediate neighbors, know their neighborhood up to a fixed radius r. In this new framework, denoted BCLIQuE[r], we study the problem of detecting, in G, an induced cycle of length at most k (CYCLE <= k) and the problem of detecting an induced cycle of length at least k +1 (CYCLE>k). We give upper and lower bounds. We show that if each node is allowed to see up to distance r = left perpendicular k/2 right perpendicular + 1, then a polylogarithmic bandwidth is sufficient for solving CYCLE>k with only two rounds. Nevertheless, if nodes were allowed to see up to distance r = left perpendicular k/3 right perpendicular, then any one-round algorithm that solves CYCLE>k needs the bandwidth b to be at least Omega(n/ log n). We also show the existence of a one-round, deterministic BCLIQUE algorithm that solves CYCLE <= k with bandwitdh b = O(n(1/left perpendicular k/2 right perpendicular). log n). On the negative side, we prove that, if epsilon <= 1/3 and 0 < r <= k/4, then any epsilon-error, R-round, b-bandwidth algorithm in the BCLIQUE[r] model that solves problem CYCLE(<= k )satisfies R . b = Omega(n(1/left perpendicular k/2 right perpendicular)).
Address [Becker, F.; Todinca, I] Univ Orleans, INSA Ctr Val Loire, LIFO EA 4022, Orleans, France, Email: florent.becker@univ-orleans.fr;
Corporate Author Thesis
Publisher Siam Publications Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0895-4801 ISBN Medium
Area Expedition Conference
Notes WOS:000546886700033 Approved
Call Number UAI @ eduardo.moreno @ Serial 1182

Author
Title The role of randomness in the broadcast congested clique model Type
Year 2021 Publication Information and Computation Abbreviated Journal Inf. Comput.
Volume 281 Issue Pages 104669
Keywords
Abstract We study the role of randomness in the broadcast congested clique model. This is a message-passing model of distributed computation where the nodes of a network know their local neighborhoods and they broadcast, in synchronous rounds, messages that are visible to every other node.

This works aims to separate three different settings: deterministic protocols, randomized protocols with private coins, and randomized protocols with public coins. We obtain the following results:

If more than one round is allowed, public randomness is as powerful as private ran-domness.

One-round public-coin algorithms can be exponentially more powerful than determin-istic algorithms running in several rounds.

One-round public-coin algorithms can be exponentially more powerful than one-round private-coin algorithms.

One-round private-coin algorithms can be exponentially more powerful than one-round deterministic algorithms.

Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0890-5401 ISBN Medium
Area Expedition Conference
Notes WOS:000721215200042 Approved
Call Number UAI @ alexi.delcanto @ Serial 1491