Survey of Distributed Decision

We survey the recent distributed computing literature on checking whether a given distributed system configuration satisfies a given boolean predicate, i.e., whether the configuration is legal or illegal w.r.t. that predicate. We consider classical distributed computing environments, including mostly synchronous fault-free network computing (LOCAL and CONGEST models), but also asynchronous crash-prone shared-memory computing (WAIT-FREE model), and mobile computing (FSYNC model)

Deterministic Subgraph Detection in Broadcast CONGEST

We present simple deterministic algorithms for subgraph finding and enumeration in the broadcast CONGEST model of distributed computation: - For any constant k, detecting k-paths and trees on k nodes can be done in O(1) rounds. - For any constant k, detecting k-cycles and pseudotrees on k nodes can be done in O(n) rounds. - On d-degenerate graphs, cliques and 4-cycles can be enumerated in O(d + log n) rounds, and 5-cycles in O(d2 + log n) rounds. In many cases, these bounds are tight up to logarithmic factors. Moreover, we show that the algorithms for d-degenerate graphs can be improved to O(d/logn) and O(d2/logn), respect- ively, in the supported CONGEST model, which can be seen as an intermediate model between CONGEST and the congested clique

Deterministic subgraph detection in broadcast CONGEST

We present simple deterministic algorithms for subgraph finding and enumeration in the broadcast CONGEST model of distributed computation: For any constant k, detecting k-paths and trees on k nodes can be done in O(1) rounds. For any constant k, detecting k-cycles and pseudotrees on k nodes can be done in O(n) rounds. On d-degenerate graphs, cliques and 4-cycles can be enumerated in O(d+log n) rounds, and 5-cycles in O(d2 + log n) rounds. In many cases, these bounds are tight up to logarithmic factors. Moreover, we show that the algorithms for d-degenerate graphs can be improved to O(d/ log n) and O(d2/log n), respectively, in the supported CONGEST model, which can be seen as an intermediate model between CONGEST and the congested clique. © 2017 Janne H. Korhonen and Joel Rybicki.Peer reviewe

Distance Computations in the Hybrid Network Model via Oracle Simulations

The Hybrid network model was introduced in [Augustine et al., SODA '20] for laying down a theoretical foundation for networks which combine two possible modes of communication: One mode allows high-bandwidth communication with neighboring nodes, and the other allows low-bandwidth communication over few long-range connections at a time. This fundamentally abstracts networks such as hybrid data centers, and class-based software-defined networks. Our technical contribution is a \emph{density-aware} approach that allows us to simulate a set of \emph{oracles} for an overlay skeleton graph over a Hybrid network. As applications of our oracle simulations, with additional machinery that we provide, we derive fast algorithms for fundamental distance-related tasks. One of our core contributions is an algorithm in the Hybrid model for computing \emph{exact} weighted shortest paths from $\tilde O(n^{1/3})$ sources which completes in $\tilde O(n^{1/3})$ rounds w.h.p. This improves, in both the runtime and the number of sources, upon the algorithm of [Kuhn and Schneider, PODC '20], which computes shortest paths from a single source in $\tilde O(n^{2/5})$ rounds w.h.p. We additionally show a 2-approximation for weighted diameter and a $(1+\epsilon)$-approximation for unweighted diameter, both in $\tilde O(n^{1/3})$ rounds w.h.p., which is comparable to the $\tilde \Omega(n^{1/3})$ lower bound of [Kuhn and Schneider, PODC '20] for a $(2-\epsilon)$-approximation for weighted diameter and an exact unweighted diameter. We also provide fast distance \emph{approximations} from multiple sources and fast approximations for eccentricities.Comment: To appear in STACS 202

Distributed Detection of Cliques in Dynamic Networks

This paper provides an in-depth study of the fundamental problems of finding small subgraphs in distributed dynamic networks. While some problems are trivially easy to handle, such as detecting a triangle that emerges after an edge insertion, we show that, perhaps somewhat surprisingly, other problems exhibit a wide range of complexities in terms of the trade-offs between their round and bandwidth complexities. In the case of triangles, which are only affected by the topology of the immediate neighborhood, some end results are: - The bandwidth complexity of 1-round dynamic triangle detection or listing is Theta(1). - The bandwidth complexity of 1-round dynamic triangle membership listing is Theta(1) for node/edge deletions, Theta(n^{1/2}) for edge insertions, and Theta(n) for node insertions. - The bandwidth complexity of 1-round dynamic triangle membership detection is Theta(1) for node/edge deletions, O(log n) for edge insertions, and Theta(n) for node insertions. Most of our upper and lower bounds are tight. Additionally, we provide almost always tight upper and lower bounds for larger cliques

The Hardness of Optimization Problems on the Weighted Massively Parallel Computation Model

The topology-aware Massively Parallel Computation (MPC) model is proposed and studied recently, which enhances the classical MPC model by the awareness of network topology. The work of Hu et al. on topology-aware MPC model considers only the tree topology. In this paper a more general case is considered, where the underlying network is a weighted complete graph. We then call this model as Weighted Massively Parallel Computation (WMPC) model, and study the problem of minimizing communication cost under it. Two communication cost minimization problems are defined based on different pattern of communication, which are the Data Redistribution Problem and Data Allocation Problem. We also define four kinds of objective functions for communication cost, which consider the total cost, bottleneck cost, maximum of send and receive cost, and summation of send and receive cost, respectively. Combining the two problems in different communication pattern with the four kinds of objective cost functions, 8 problems are obtained. The hardness results of the 8 problems make up the content of this paper. With rigorous proof, we prove that some of the 8 problems are in P, some FPT, some NP-complete, and some W[1]-complete