Deterministic CONGEST Algorithm for MDS on Bounded Arboricity Graphs

均匀稀疏图中的动态支配集

Dynamic Dominating Set in Uniformly Sparse Graphs

研究动态最小支配集问题，针对树宽有界的动态图，提出基于原始对偶框架的算法，能以O(α·log(Cn))更新时间维护O(α)近似MDS，改进了近似保证并摆脱对Δ的依赖，常数树宽图族可达O(1)近似和O(log(Cn))更新时间。

Distributed Approximation on Power Graphs

We investigate graph problems in the following setting: we are given a graph $G$ and we are required to solve a problem on $G^2$. While we focus mostly on exploring this theme in the distributed CONGEST model, we show new results and surprising connections to the centralized model of computation. In the CONGEST model, it is natural to expect that problems on $G^2$ 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) slo…

Distributed Symmetry-Breaking Algorithms for Congested Cliques

The {Congested Clique} is a distributed-computing model for single-hop networks with restricted bandwidth that has been very intensively studied recently. It models a network by an $n$-vertex graph in which any pair of vertices can communicate one with another by transmitting $O(\log n )$ bits in each round. Various problems have been studied in this setting, but for some of them the best-known results are those for general networks. In this paper we devise significantly improved algorithms for various symmetry-breaking problems, such as forests-decompositions, vertex-colorings, and maximal in…

Distributed Triangle Detection via Expander Decomposition

We present improved distributed algorithms for triangle detection and its variants in the CONGEST model. We show that Triangle Detection, Counting, and Enumeration can be solved in $\tilde{O}(n^{1/2})$ rounds. In contrast, the previous state-of-the-art bounds for Triangle Detection and Enumeration were $\tilde{O}(n^{2/3})$ and $\tilde{O}(n^{3/4})$, respectively, due to Izumi and LeGall (PODC 2017). The main technical novelty in this work is a distributed graph partitioning algorithm. We show that in $\tilde{O}(n^{1-δ})$ rounds we can partition the edge set of the network $G=(V,E)$ into three p…

Algorithms for the Minimum Dominating Set Problem in Bounded Arboricity Graphs: Simpler, Faster, and Combinatorial

We revisit the minimum dominating set problem on graphs with arboricity bounded by $α$. Bansal and Umboh [BU17] gave an $O(α)$-approximation LP rounding algorithm, which also translates into a near-linear time algorithm using general-purpose approximation results for explicit mixed packing and covering or pure covering LPs [KY14, You14, AZO19, Qua10]. Moreover, [BU17] showed that it is NP-hard to achieve an asymptotic improvement for the approximation factor. On the other hand, the previous two non-LP-based algorithms, by Lenzen and Wattenhofer [LW10], and Jones et al. [JLR+13], achieve an app…

A local constant-factor approximation algorithm for MDS problem in anonymous network

In research on distributed local algorithms it is commonly assumed that each vertex has a unique identifier in the entire graph. However, it turns out that in case of certain classes of graphs (for example not lift-closed bounded degree graphs) identifiers are unnecessary and only a port ordering is needed. One of the open issues was whether identifiers are essential in planar graphs. In this paper, we answer this question and we propose an algorithm which returns constant approximation of the MDS problem in CONGEST model. The algorithm doesn't use any additional information about the structur…