John Augustine

Fast byzantine agreement in dynamic networks

We study Byzantine agreement in dynamic networks where topology can change from round to round and nodes can also experience heavy churn (i.e., nodes can join and leave the network continuously over time). Our main contributions are randomized distributed algorithms that achieve almost-everywhere Byzantine agreement with high probability even under a large number of adaptively chosen Byzantine nodes and continuous adversarial churn in a number of rounds that is polylogarithmic in n (where n is the stable network size). We show that our algorithms are essentially optimal (up to polylogarithmic factors) with respect to the amount of Byzantine nodes and churn rate that they can tolerate by showing a lower bound. In particular, we present the following results: 1. An O(log3 n) round randomized algorithmto achieve almost everywhere Byzantine agreement with high probability under a presence of up to O(√n/polylog(n)) Byzantine nodes and up to a churn of O(√n/polylog(n)) nodes per round. We assume that the Byzantine nodes have knowledge about the entire state of network at every round (including random choices made by all the nodes) and can behave arbitrarily. We also assume that an adversary controls the churn - it has complete knowledge and control of what nodes join and leave and at what time and has unlimited computational power (but is oblivious to the topology changes from round to round). Our algorithm requires only polylogarithmic in n bits to be processed and sent (per round) by each node. 2. We also present an O(log3 n) round randomized algorithm that has same guarantees as the above algorithm, but works even when the connectivity of the network is controlled by an adaptive adversary (that can choose the topology based on the current states of the nodes). However, this algorithm requires up to polynomial in n bits to be processed and sent (per round) by each node. 3. We show that the above bounds are essentially the best possible, if one wants fast (i.e., polylogarithmic run time) algorithms, by showing that any (randomized) algorithm to achieve agreement in a dynamic network controlled by an adversary that can churn up to Θ(√n log n) nodes per round should take at least a polynomial number of rounds. Our algorithms are the first-known, fully distributed, Byzantine agreement algorithms in highly dynamic networks. We view our results as a step towards understanding the possibilities and limitations of highly dynamic networks that are subject to malicious behavior by a large number of nodes.

Minimax regret 1-sink location problem in dynamic path networks

This paper considers the minimax regret 1-sink location problem in dynamic path networks. In our model, a dynamic path network consists of an undirected path with positive edge lengths and uniform edge capacity, and each vertex supply which is nonnegative value is unknown but only the interval of supply is known. A particular assignment of supply to each vertex is called a scenario. Under any scenario, the cost of a sink location is defined as the minimum time to complete the evacuation for all supplies (evacuees), and the regret of a sink location x is defined as the cost of x minus the cost of the optimal sink location. Then, the problem is to find a point as a sink such that the maximum regret for all possible scenarios is minimized. We propose an O ( n log ? n ) time algorithm for the minimax regret 1-sink location problem in dynamic path networks with uniform capacity, where n is the number of vertices in the network.

Opportunities for energy efficient computing: a study of inexact general purpose processors for high-performance and big-data applications

In this paper, we demonstrate that disproportionate gains are possible through a simple devise for injecting inexactness or approximation into the hardware architecture of a computing system with a general purpose template including a complete memory hierarchy. The focus of the study is on energy savings possible through this approach in the context of large and challenging applications. We choose two such from different ends of the computing spectrum-the IGCM model for weather and climate modeling which embodies significant features of a high-performance computing workload, and the ubiquitous PageRank algorithm used in Internet search. In both cases, we are able to show in the affirmative that an inexact system outperforms its exact counterpart in terms of its efficiency quantified through the relative metric of operations per virtual Joule (OPVJ)-a relative metric that is not tied to particular hardware technology. As one example, the IGCM application can be used to achieve savings through inexactness of (almost) a factor of 3 in energy without compromising the quality of the forecast, quantified through the forecast error metric, in a noticeable manner. As another example finding, we show that in the case of PageRank, an inexact system is able to outperform its exact counterpart by close to a factor of 1.5 using the OPVJ metric.

Storage and search in dynamic peer-to-peer networks

We study robust and efficient distributed algorithms for searching, storing, and maintaining data in dynamic Peer-to-Peer (P2P) networks. P2P networks are highly dynamic networks that experience heavy node churn (i.e., nodes join and leave the network continuously over time). Our goal is to guarantee, despite high node churn rate, that a large number of nodes in the network can store, retrieve, and maintain a large number of data items. Our main contributions are fast randomized distributed algorithms that guarantee the above with high probability even under high adversarial churn. In particular, we present the following main results: 1. A randomized distributed search algorithm that with high probability guarantees that searches from as many as n - o(n) nodes (n is the stable network size) succeed in O(log n )-rounds despite O(n/log1+δn) churn, for any small constant δ > 0, per round. We assume that the churn is controlled by an oblivious adversary (that has complete knowledge and control of what nodes join and leave and at what time and has unlimited computational power, but is oblivious to the random choices made by the algorithm). 2. A storage and maintenance algorithm that guarantees, with high probability, data items can be efficiently stored (with only θ(log n) copies of each data item) and maintained in a dynamic P2P network with churn rate up to O(n/log1+δn) per round. Our search algorithm together with our storage and maintenance algorithm guarantees that as many as n - o(n) nodes can efficiently store, maintain, and search even under O(n/log1+δn) churn per round. Our algorithms require only polylogarithmic in n bits to be processed and sent (per round) by each node. To the best of our knowledge, our algorithms are the first-known, fully-distributed storage and search algorithms that provably work under highly dynamic settings (i.e., high churn rates per step). Furthermore, they are localized (i.e., do not require any global topological knowledge) and scalable. A technical contribution of this paper, which may be of independent interest, is showing how random walks can be provably used to derive scalable distributed algorithms in dynamic networks with adversarial node churn.

Linear time approximation schemes for vehicle scheduling problems

We consider makespan minimization for vehicle scheduling problems on trees with job requests that have release and handling times. 2-approximation algorithms were known for several variants of the single vehicle problem on a path. A 3/2-approximation algorithm was known for the single vehicle problem on a path where there is a fixed starting point and the vehicle must return to the starting point upon completion. Karuno, Nagamochi and Ibaraki give a 2-approximation algorithm for the single vehicle problem on trees. We develop a polynomial time approximation scheme (PTAS) that runs in time linear in the number of job requests for the single vehicle scheduling problem on trees that have a constant number of leaves. This PTAS can be easily adapted to accommodate various starting/ending constraints. We then extended this to a PTAS for the multiple vehicle problem where vehicles operate in disjoint subtrees.

Enabling Robust and Efficient Distributed Computation in Dynamic Peer-to-Peer Networks

Motivated by the need for designing efficient and robust fully-distributed computation in highly dynamic networks such as Peer-to-Peer (P2P) networks, we study distributed protocols for constructing and maintaining dynamic network topologies with good expansion properties. Our goal is to maintain a sparse (bounded degree) expander topology despite heavy churn (i.e., Nodes joining and leaving the network continuously over time). We assume that the churn is controlled by an adversary that has complete knowledge and control of what nodes join and leave and at what time and has unlimited computational power, but is oblivious to the random choices made by the algorithm. Our main contribution is a randomized distributed protocol that guarantees with high probability the maintenance of a constant degree graph with high expansion even under continuous high adversarial churn. Our protocol can tolerate a churn rate of up to O(n/polylog(n)) per round (where n is the stable network size). Our protocol is efficient, lightweight, and scalable, and it incurs only O(polylog(n)) overhead for topology maintenance: only polylogarithmic(in n) bits needs to be processed and sent by each node per round and any nodes computation cost per round is also polylogarithmic. The given protocol is a fundamental ingredient that is needed for the design of efficient fully-distributed algorithms for solving fundamental distributed computing problems such as agreement, leader election, search, and storage in highly dynamic P2P networks and enables fast and scalable algorithms for these problems that can tolerate a large amount of churn.

Dynamics of profit-sharing games

An important task in the analysis of multiagent systems is to understand how groups of selfish players can form coalitions, i.e., work together in teams. In this paper, we study the dynamics of coalition formation under bounded rationality. We consider settings where each teams profit is given by a concave function, and propose three profit-sharing schemes, each of which is based on the concept of marginal utility. The agents are assumed to be myopic, i.e., they keep changing teams as long as they can increase their payoff by doing so. We study the properties (such as closeness to Nash equilibrium or total profit) of the states that result after a polynomial number of such moves, and prove bounds on the price of anarchy and the price of stability of the corresponding games.

Probe station selection algorithms for fault management in computer networks

In this paper, we address the problem of probe station selection. Probe station nodes are the nodes that are instrumented with the functionality of sending probes and analyzing probe results. The placement of probe stations affects the diagnosis capability of the probes sent by the probe stations. The probe station placement also involves the overhead of instrumentation. Thus it is important to minimize the required number of probe stations without compromising on the required diagnosis capability of the probes. In this paper, we address the problem of selection of probe stations to detect failures in the network. We present an algorithm for probe station selection using a reduction of the probe station selection problem to the Minimum Hitting Set problem. We address several issues involved while selecting probe stations such as link failures and probe station failures. We present experimental evaluation to show the effectiveness of the proposed approach.

Dynamics of Profit-Sharing Games

Abstract An important task in the analysis of multiagent systems is to understand how groups of selfish players can form coalitions, i.e., work together in teams. In this paper, we study the dynamics of coalition formation under bounded rationality. We consider settings whereby each team’s profit is given by a submodular function and propose three profit-sharing schemes, each of which is based on the concept of marginal utility. The agents are assumed to be myopic, i.e., they keep changing teams as long as they can increase their payoff by doing so. We study the properties (such as closeness to Nash equilibrium or total profit) of the states that result after a polynomial number of such moves, and prove bounds on the price of anarchy and the price of stability of the corresponding games.

Localized geometric query problems

A new class of geometric query problems are studied in this paper. We are required to preprocess a set of geometric objects P in the plane, so that for any arbitrary query point q, the largest circle that contains q but does not contain any member of P, can be reported efficiently. The geometric sets that we consider are point sets and boundaries of simple polygons.