TY - GEN

T1 - Distributed Construction of Light Networks

AU - Elkin, Michael

AU - Filtser, Arnold

AU - Neiman, Ofer

N1 - Funding Information:
∗The reader is encouraged to read the full version of the paper, found here. †This research was supported by the ISF grant No. (724/15). ‡Supported by the Simons Foundation. The work was done while the author was affiliated with Ben-Gurion University of the Negev. §Supported in part by ISF grant 1817/17, and by BSF Grant 2015813.
Publisher Copyright:
© 2020 ACM.

PY - 2020/7/31

Y1 - 2020/7/31

N2 - A t-spanner H of a weighted graph G = (V, E, w) is a subgraph that approximates all pairwise distances up to a factor of t. The lightness of H is defined as the ratio between the weight of H to that of the minimum spanning tree. An (α, β)-Shallow Light Tree (SLT) is a tree of lightness β, that approximates all distances from a designated root vertex up to a factor of α. A long line of works resulted in efficient algorithms that produce (nearly) optimal light spanners and SLTs. Some of the most notable algorithmic applications of light spanners and SLTs are in distributed settings. Surprisingly, so far there are no known efficient distributed algorithms for constructing these objects in general graphs. In this paper we devise efficient distributed algorithms in the CONGEST model for constructing light spanners and SLTs, with near optimal parameters. Specifically, for any k ≥ 1 and 0 < ∈ < 1, we show a (2k - 1) · (1 + ∈)-spanner with lightness O(k·n1/k) can be built in [EQUATION] rounds (where n = |V| and D is the hop-diameter of G). In addition, for any α > 1 we provide an [EQUATION] rounds. The running times of our algorithms cannot be substantially improved. We also consider spanners for the family of doubling graphs, and devise a [EQUATION] rounds algorithm in the CONGEST model that computes a (1 + ∈)-spanner with lightness (log n)/∈O(1). As a stepping stone, which is interesting in its own right, we first develop a distributed algorithm for constructing nets (for arbitrary weighted graphs), generalizing previous algorithms that worked only for unweighted graphs.

AB - A t-spanner H of a weighted graph G = (V, E, w) is a subgraph that approximates all pairwise distances up to a factor of t. The lightness of H is defined as the ratio between the weight of H to that of the minimum spanning tree. An (α, β)-Shallow Light Tree (SLT) is a tree of lightness β, that approximates all distances from a designated root vertex up to a factor of α. A long line of works resulted in efficient algorithms that produce (nearly) optimal light spanners and SLTs. Some of the most notable algorithmic applications of light spanners and SLTs are in distributed settings. Surprisingly, so far there are no known efficient distributed algorithms for constructing these objects in general graphs. In this paper we devise efficient distributed algorithms in the CONGEST model for constructing light spanners and SLTs, with near optimal parameters. Specifically, for any k ≥ 1 and 0 < ∈ < 1, we show a (2k - 1) · (1 + ∈)-spanner with lightness O(k·n1/k) can be built in [EQUATION] rounds (where n = |V| and D is the hop-diameter of G). In addition, for any α > 1 we provide an [EQUATION] rounds. The running times of our algorithms cannot be substantially improved. We also consider spanners for the family of doubling graphs, and devise a [EQUATION] rounds algorithm in the CONGEST model that computes a (1 + ∈)-spanner with lightness (log n)/∈O(1). As a stepping stone, which is interesting in its own right, we first develop a distributed algorithm for constructing nets (for arbitrary weighted graphs), generalizing previous algorithms that worked only for unweighted graphs.

KW - CONGEST

KW - doubling dimension

KW - light spanners

KW - shallow light tree

UR - http://www.scopus.com/inward/record.url?scp=85090355441&partnerID=8YFLogxK

U2 - 10.1145/3382734.3405701

DO - 10.1145/3382734.3405701

M3 - Conference contribution

AN - SCOPUS:85090355441

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 483

EP - 492

BT - PODC 2020 - Proceedings of the 39th Symposium on Principles of Distributed Computing

PB - Association for Computing Machinery

T2 - 39th Symposium on Principles of Distributed Computing, PODC 2020

Y2 - 3 August 2020 through 7 August 2020

ER -