TY - GEN
T1 - Distributed Approximation on Power Graphs
AU - Bar-Yehuda, Reuven
AU - Censor-Hillel, Keren
AU - Maus, Yannic
AU - Pai, Shreyas
AU - Pemmaraju, Sriram V.
N1 - Funding Information: This work was supported in part by the European Union’s Horizon 2020 Research And Innovation Programme under grant agreement no. 755839 (Keren Censor-Hillel, Yannic Maus). Publisher Copyright: © 2020 ACM.
PY - 2020/7/31
Y1 - 2020/7/31
N2 - We investigate graph problems in the following setting: we are given a graph G and we are required to solve a problem on G2. While we focus mostly on exploring this theme in the distributed CONGEST model, we also show new results and surprising connections to the centralized model of computation. In the CONGEST model, it is natural to expect that problems on G2 would be quite difficult to solve efficiently on G, due to congestion. However, we show that the picture is both more complicated and more interesting. Specifically, we encounter two phenomena acting in opposing directions: (i) slowdown due to congestion and (ii) speedup due to structural properties of G2. We demonstrate these two phenomena via two fundamental graph problems, namely, Minimum Vertex Cover (MVC) and Minimum Dominating Set (MDS). Among our many contributions, the highlights are the following. (1) In the CONGEST model, we show an O(n/∈)-round (1 + ∈)-approximation algorithm for MVC on G2, whereas no o(n2)-round algorithm is known for any better-than-2 approximation for MVC on G. (2) We show a centralized polynomial time 5/3-approximation algorithm for MVC on G2, whereas a better-than-2 approximation is UGC-hard for G. (3) In contrast, for MDS, in the CONGEST model, we show an [EQUATION] lower bound for a constant approximation factor for MDS on G2, whereas an Ω(n2) lower bound for MDS on G is known only for exact computation.
AB - We investigate graph problems in the following setting: we are given a graph G and we are required to solve a problem on G2. While we focus mostly on exploring this theme in the distributed CONGEST model, we also show new results and surprising connections to the centralized model of computation. In the CONGEST model, it is natural to expect that problems on G2 would be quite difficult to solve efficiently on G, due to congestion. However, we show that the picture is both more complicated and more interesting. Specifically, we encounter two phenomena acting in opposing directions: (i) slowdown due to congestion and (ii) speedup due to structural properties of G2. We demonstrate these two phenomena via two fundamental graph problems, namely, Minimum Vertex Cover (MVC) and Minimum Dominating Set (MDS). Among our many contributions, the highlights are the following. (1) In the CONGEST model, we show an O(n/∈)-round (1 + ∈)-approximation algorithm for MVC on G2, whereas no o(n2)-round algorithm is known for any better-than-2 approximation for MVC on G. (2) We show a centralized polynomial time 5/3-approximation algorithm for MVC on G2, whereas a better-than-2 approximation is UGC-hard for G. (3) In contrast, for MDS, in the CONGEST model, we show an [EQUATION] lower bound for a constant approximation factor for MDS on G2, whereas an Ω(n2) lower bound for MDS on G is known only for exact computation.
UR - https://www.scopus.com/pages/publications/85090347569
U2 - 10.1145/3382734.3405750
DO - 10.1145/3382734.3405750
M3 - Conference contribution
T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing
SP - 501
EP - 510
BT - PODC 2020 - Proceedings of the 39th Symposium on Principles of Distributed Computing
T2 - 39th Symposium on Principles of Distributed Computing, PODC 2020
Y2 - 3 August 2020 through 7 August 2020
ER -