Showing papers by "John Augustine published in 2016"

Distributed Algorithmic Foundations of Dynamic Networks

Abstract: Much of the well-established theory of distributed algorithms focuses on static networks, where nodes do not crash and edges maintain operational status forever. On the other hand, large real-world networks are inherently dynamic: the participants in peer-to-peer networks and social networks change over time, mobile nodes in wireless networks move in and out of each other’s transmission range, and, in distributed data center networks, faulty machines need to be replaced by new machines without interrupting the operation of the remaining network. Dynamic network models, where the communication topology varies over time but where the set of nodes is fixed, have been studied extensively in literature.

Information Spreading in Dynamic Networks Under Oblivious Adversaries

Abstract: We study the problem of gossip in dynamic networks controlled by an adversary that can modify the network arbitrarily from one round to another, provided that the network is always connected. In the gossip problem, there are n tokens arbitrarily distributed among the n network nodes, and the goal is to disseminate all the n tokens to every node. Our focus is on token-forwarding algorithms, which do not manipulate tokens in any way other than storing, copying, and forwarding them. An important open question is whether gossip can be realized by a distributed protocol that can do significantly better than an easily achievable bound of \(O(n^2)\) rounds.

Information Spreading in Dynamic Networks under Oblivious Adversaries

Abstract: We study the problem of gossip in dynamic networks controlled by an adversary that can modify the network arbitrarily from one round to another, provided that the network is always connected. In the gossip problem, $n$ tokens are arbitrarily distributed among the $n$ network nodes, and the goal is to disseminate all the $n$ tokens to every node. Our focus is on token-forwarding algorithms, which do not manipulate tokens in any way other than storing, copying, and forwarding them. Gossip can be completed in linear time in any static network, but a basic open question for dynamic networks is the existence of a distributed protocol that can do significantly better than an easily achievable bound of $O(n^2)$ rounds. In previous work, it has been shown that under adaptive adversaries, every token forwarding algorithm requires $\Omega(n^2/\log n)$ rounds. In this paper, we study oblivious adversaries, which differ from adaptive adversaries in one crucial aspect--- they are oblivious to random choices made by the protocol. We present an $\tilde{\Omega}(n^{3/2})$ lower bound under an oblivious adversary for RANDDIFF, a natural algorithm in which neighbors exchange a token chosen uniformly at random from the difference of their token sets. We also present an $\tilde{\Omega}(n^{4/3})$ bound under a stronger notion of oblivious adversary for symmetric knowledge-based algorithms. On the positive side, we present a centralized algorithm that completes gossip in $\tilde{O}(n^{3/2})$ rounds. We also show an $\tilde{O}(n^{5/3})$ upper bound for RANDDIFF in a restricted class of oblivious adversaries, which we call paths-respecting.

Leader Election in Sparse Dynamic Networks with Churn

Abstract: We investigate the problem of electing a leader in a sparse but well-connected synchronous dynamic network in which up to a fraction of the nodes chosen adversarially can leave/join the network per time step. At this churn rate, all nodes in the network can be replaced by new nodes in a constant number of rounds. Moreover, the adversary can shield a fraction of the nodes (which may include the leader) by repeatedly churning their neighborhood and, thus, hindering, their communication with the rest of the network. However, empirical studies in peer-to-peer networks have shown that a significant fraction of the nodes are usually stable and well connected. It is, therefore, natural to take advantage of such stability to establish a leader that can maintain good communication with the rest of the nodes. Because the dynamics could change eventually, it is also essential to reelect a new leader whenever the current leader either has left the network or is not well-connected with rest of the nodes. In su...

Optimal Evacuation Flows on Dynamic Paths with General Edge Capacities

Abstract: A Dynamic Graph Network is a graph in which each edge has an associated travel time and a capacity (width) that limits the number of items that can travel in parallel along that edge. Each vertex in this dynamic graph network begins with the number of items that must be evacuated into designated sink vertices. A $k$-sink evacuation protocol finds the location of $k$ sinks and associated evacuation movement protocol that allows evacuating all the items to a sink in minimum time. The associated evacuation movement must impose a confluent flow, i.e, all items passing through a particular vertex exit that vertex using the same edge. In this paper we address the $k$-sink evacuation problem on a dynamic path network. We provide solutions that run in $O(n \log n)$ time for $k=1$ and $O(k n \log^2 n)$ for $k >1$ and work for arbitrary edge capacities.

Balanced Allocation: Patience is not a Virtue

Abstract: Load balancing is a well-studied problem, with balls-in-bins being the primary framework. The greedy algorithm $\mathsf{Greedy}[d]$ of Azar et al. places each ball by probing $d > 1$ random bins and placing the ball in the least loaded of them. With high probability, the maximum load under $\mathsf{Greedy}[d]$ is exponentially lower than the result when balls are placed uniformly randomly. Vocking showed that a slightly asymmetric variant, $\mathsf{Left}[d]$, provides a further significant improvement. However, this improvement comes at an additional computational cost of imposing structure on the bins. Here, we present a fully decentralized and easy-to-implement algorithm called $\mathsf{FirstDiff}[d]$ that combines the simplicity of $\mathsf{Greedy}[d]$ and the improved balance of $\mathsf{Left}[d]$. The key idea in $\mathsf{FirstDiff}[d]$ is to probe until a different bin size from the first observation is located, then place the ball. Although the number of probes could be quite large for some of the balls, we show that $\mathsf{FirstDiff}[d]$ requires only at most $d$ probes on average per ball (in both the standard and the heavily-loaded settings). Thus the number of probes is no greater than either that of $\mathsf{Greedy}[d]$ or $\mathsf{Left}[d]$. More importantly, we show that $\mathsf{FirstDiff}[d]$ closely matches the improved maximum load ensured by $\mathsf{Left}[d]$ in both the standard and heavily-loaded settings. We further provide a tight lower bound on the maximum load up to $O(\log \log \log n)$ terms. We additionally give experimental data that $\mathsf{FirstDiff}[d]$ is indeed as good as $\mathsf{Left}[d]$, if not better, in practice.

Balanced allocation: patience is not a virtue

Abstract: Load balancing is a well-studied problem, with balls-in-bins being the primary framework. The greedy algorithm Greedy[d] of Azar et al. places each ball by probing d > 1 random bins and placing the ball in the least loaded of them. It ensures a maximum load that is exponentially better than the strategy of placing each ball uniformly at random. Vocking showed that a slightly asymmetric variant, Left[d], provides a further significant improvement. However, this improvement comes at an additional computational cost of imposing structure on the bins.Here, we present a fully decentralized and easy-to-implement algorithm called FirstDiff[d] that combines the simplicity of Greedy[d] and the improved balance of Left[d]. The key idea in FirstDiff[d] is to probe until a different bin size from the first observation is located, then place the ball. Although the number of probes could be quite large for some of the balls, we show that FirstDiff[d] requires only d probes on average per ball (in both the standard and the heavily-loaded settings). Thus the number of probes is no greater than either that of Greedy[d] or Left[d]. More importantly, we show that FirstDiff[d] closely matches the improved maximum load ensured by Left[d] in both the standard and heavily-loaded settings. We additionally give experimental data that FirstDiff[d] is indeed as good as Left[d], if not better, in practice.