# Nitin H. Vaidya

## Contact Details

NameNitin H. Vaidya |
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## Pubs By Year |
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## Pub CategoriesComputer Science - Distributed; Parallel; and Cluster Computing (41) Mathematics - Optimization and Control (9) Computer Science - Cryptography and Security (5) Mathematics - Information Theory (4) Computer Science - Information Theory (4) Computer Science - Networking and Internet Architecture (4) Computer Science - Learning (4) Computer Science - Data Structures and Algorithms (1) |

## Publications Authored By Nitin H. Vaidya

Distributed shared memory systems maintain multiple replicas of the shared memory locations. Maintaining causal consistency in such systems has received significant attention in the past. However, much of the previous literature focuses on full replication wherein each replica stores a copy of all the locations in the shared memory. Read More

Continual data collection and widespread deployment of machine learning algorithms, particularly the distributed variants, have raised new privacy challenges. In a distributed machine learning scenario, the dataset is stored among several machines and they solve a distributed optimization problem to collectively learn the underlying model. We present a secure multi-party computation inspired privacy preserving distributed algorithm for optimizing a convex function consisting of several possibly non-convex functions. Read More

Maintaining causal consistency in distributed shared memory systems using vector timestamps has received a lot of attention from both theoretical and practical prospective. However, most of the previous literature focuses on full replication where each data is stored in all replicas, which may not be scalable due to the increasing amount of data. In this report, we investigate how to achieve causal consistency in partial replicated systems, where each replica may store different set of data. Read More

We present a distributed solution to optimizing a convex function composed of several non-convex functions. Each non-convex function is privately stored with an agent while the agents communicate with neighbors to form a network. We show that coupled consensus and projected gradient descent algorithm proposed in [1] can optimize convex sum of non-convex functions under an additional assumption on gradient Lipschitzness. Read More

Availability of both massive datasets and computing resources have made machine learning and predictive analytics extremely pervasive. In this work we present a synchronous algorithm and architecture for distributed optimization motivated by privacy requirements posed by applications in machine learning. We present an algorithm for the recently proposed multi-parameter-server architecture. Read More

This paper addresses the problem of non-Bayesian learning over multi-agent networks, where agents repeatedly collect partially informative observations about an unknown state of the world, and try to collaboratively learn the true state. We focus on the impact of the adversarial agents on the performance of consensus-based non-Bayesian learning, where non-faulty agents combine local learning updates with consensus primitives. In particular, we consider the scenario where an unknown subset of agents suffer Byzantine faults -- agents suffering Byzantine faults behave arbitrarily. Read More

We study the problem of multi-agent optimization in the presence of communication failures, where agents are connected by a strongly connected communication network. Specifically, we are interested in optimizing $h(x)=\frac{1}{n}\sum_{i=1}^n h_i(x)$, where $\mathcal{V}=\{1, \ldots, n\}$ is the set of agents, and $h_i(\cdot)$ is agent $i$'s local cost function. We consider the scenario where the communication links may suffer packet-dropping failures (i. Read More

Consider an asynchronous system consisting of processes that communicate via message-passing. The processes communicate over a potentially {\em incomplete} communication network consisting of reliable bidirectional communication channels. Thus, not every pair of processes is necessarily able to communicate with each other directly. Read More

This paper addresses the problem of distributed hypothesis testing in multi-agent networks, where agents repeatedly collect local observations about an unknown state of the world, and try to collaboratively detect the true state through information exchange. We focus on the impact of failures and asynchrony (two fundamental factors in distributed systems) on the performance of consensus-based non-Bayesian learning. In particular, we consider the scenario where the networked agents may suffer crash faults, and messages delay can be arbitrarily long but finite. Read More

Exact Byzantine consensus problem requires that non-faulty processes reach agreement on a decision (or output) that is in the convex hull of the inputs at the non-faulty processes. It is well-known that exact consensus is impossible in an asynchronous system in presence of faults, and in a synchronous system, n>=3f+1 is tight on the number of processes to achieve exact Byzantine consensus with scalar inputs, in presence of up to f Byzantine faulty processes. Recent work has shown that when the inputs are d-dimensional vectors of reals, n>=max(3f+1,(d+1)f+1) is tight to achieve exact Byzantine consensus in synchronous systems, and n>= (d+2)f+1 for approximate Byzantine consensus in asynchronous systems. Read More

We study the problem of constrained distributed optimization in multi-agent networks when some of the computing agents may be faulty. In this problem, the system goal is to have all the non-faulty agents collectively minimize a global objective given by weighted average of local cost functions, each of which is initially known to a non-faulty agent only. In particular, we are interested in the scenario when the computing agents are connected by an arbitrary directed communication network, some of the agents may suffer from crash faults or Byzantine faults, and the estimate of each agent is restricted to lie in a common constraint set. Read More

The CAP theorem is a fundamental result that applies to distributed storage systems. In this paper, we first present and prove two CAP-like impossibility theorems. To state these theorems, we present probabilistic models to characterize the three important elements of the CAP theorem: consistency (C), availability or latency (A), and partition tolerance (P). Read More

We study fault-tolerant distributed optimization of a sum of convex (cost) functions with real-valued scalar input/output in the presence of crash faults or Byzantine faults. In particular, the goal is to optimize a global cost function $\frac{1}{n}\sum_{i\in \mathcal{V}} h_i(x)$, where $\mathcal{V}=\{1, \ldots, n\}$ is the collection of agents, and $h_i(x)$ is agent $i$'s local cost function, which is initially known only to agent $i$. Since the above global cost function cannot be optimized exactly in presence of crash faults or Byzantine faults, we define two weaker versions of the problem for crash faults and Byzantine faults, respectively. Read More

In Part I of this report, we introduced a Byzantine fault-tolerant distributed optimization problem whose goal is to optimize a sum of convex (cost) functions with real-valued scalar input/ouput. In this second part, we introduce a condition-based variant of the original problem over arbitrary directed graphs. Specifically, for a given collection of $k$ input functions $h_1(x), \ldots, h_k(x)$, we consider the scenario when the local cost function stored at agent $j$, denoted by $g_j(x)$, is formed as a convex combination of the $k$ input functions $h_1(x), \ldots, h_k(x)$. Read More

We study Byzantine fault-tolerant distributed optimization of a sum of convex (cost) functions with real-valued scalar input/ouput. In particular, the goal is to optimize a global cost function $\frac{1}{|\mathcal{N}|}\sum_{i\in \mathcal{N}} h_i(x)$, where $\mathcal{N}$ is the set of non-faulty agents, and $h_i(x)$ is agent $i$'s local cost function, which is initially known only to agent $i$. In general, when some of the agents may be Byzantine faulty, the above goal is unachievable, because the identity of the faulty agents is not necessarily known to the non-faulty agents, and the faulty agents may behave arbitrarily. Read More

This work weakens well-known consistency models using graphs that capture applications' characteristics. The weakened models not only respect application semantic, but also yield a performance benefit. We introduce a notion of dependency graphs, which specify relations between events that are important with respect to application semantic, and then weaken traditional consistency models (e. Read More

This paper explores an old problem, {\em Byzantine fault-tolerant Broadcast} (BB), under a new model, {\em selective broadcast model}. The new model "interpolates" between the two traditional models in the literature. In particular, it allows fault-free nodes to exploit the benefits of a broadcast channel (a feature from reliable broadcast model) and allows faulty nodes to send mismatching messages to different neighbors (a feature from point-to-point model) simultaneously. Read More

This work considers a point-to-point network of n nodes connected by directed links, and proves tight necessary and sufficient conditions on the underlying communication graphs for achieving consensus among these nodes under crash faults. We identify the conditions in both synchronous and asynchronous systems Read More

We address the problem of reaching consensus in the presence of Byzantine faults. In particular, we are interested in investigating the impact of messages relay on the network connectivity for a correct iterative approximate Byzantine consensus algorithm to exist. The network is modeled by a simple directed graph. Read More

This paper defines a new consensus problem, convex consensus. Similar to vector consensus [13, 20, 19], the input at each process is a d-dimensional vector of reals (or, equivalently, a point in the d-dimensional Euclidean space). However, for convex consensus, the output at each process is a convex polytope contained within the convex hull of the inputs at the fault-free processes. Read More

This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each directed link of the underlying communication graph represents a communication channel between a pair of nodes. We adopt the transient Byzantine link failure model [15, 16], where an omniscient adversary controls a subset of the directed communication links, but the nodes are assumed to be fault-free. Recent work has addressed the problem of reaching approximate consen- sus in incomplete graphs with Byzantine nodes using a restricted class of iterative algorithms that maintain only a small amount of memory across iterations [22, 21, 23, 12]. Read More

Carrier Sense Multiple Access (CSMA) protocols have been shown to reach the full capacity region for data communication in wireless networks, with polynomial complexity. However, current literature achieves the throughput optimality with an exponential delay scaling with the network size, even in a simplified scenario for transmission jobs with uniform sizes. Although CSMA protocols with order-optimal average delay have been proposed for specific topologies, no existing work can provide worst-case delay guarantee for each job in general network settings, not to mention the case when the jobs have non-uniform lengths while the throughput optimality is still targeted. Read More

In distributed optimization and iterative consensus literature, a standard problem is for $N$ agents to minimize a function $f$ over a subset of Euclidean space, where the cost function is expressed as a sum $\sum f_i$. In this paper, we study the private distributed optimization (PDOP) problem with the additional requirement that the cost function of the individual agents should remain differentially private. The adversary attempts to infer information about the private cost functions from the messages that the agents exchange. Read More

This work addresses Byzantine vector consensus (BVC), wherein the input at each process is a d-dimensional vector of reals, and each process is expected to decide on a decision vector that is in the convex hull of the input vectors at the fault-free processes [3, 8]. The input vector at each process may also be viewed as a point in the d-dimensional Euclidean space R^d, where d > 0 is a finite integer. Recent work [3, 8] has addressed Byzantine vector consensus in systems that can be modeled by a complete graph. Read More

Much of the past work on asynchronous approximate Byzantine consensus has assumed scalar inputs at the nodes [4, 8]. Recent work has yielded approximate Byzantine consensus algorithms for the case when the input at each node is a d-dimensional vector, and the nodes must reach consensus on a vector in the convex hull of the input vectors at the fault-free nodes [9, 13]. The d-dimensional vectors can be equivalently viewed as points in the d-dimensional Euclidean space. Read More

Much of the past work on asynchronous approximate Byzantine consensus has assumed scalar inputs at the nodes [3, 7]. Recent work has yielded approximate Byzantine consensus algorithms for the case when the input at each node is a d-dimensional vector, and the nodes must reach consensus on a vector in the convex hull of the input vectors at the fault-free nodes [8, 12]. The d-dimensional vectors can be equivalently viewed as points in the d-dimensional Euclidean space. Read More

Consider a network of n processes each of which has a d-dimensional vector of reals as its input. Each process can communicate directly with all the processes in the system; thus the communication network is a complete graph. All the communication channels are reliable and FIFO (first-in-first-out). Read More

We explore the correctness of the Certified Propagation Algorithm (CPA) [6, 1, 8, 5] in solving broadcast with locally bounded Byzantine faults. CPA allows the nodes to use only local information regarding the network topology. We provide a tight necessary and sufficient condition on the network topology for the correctness of CPA. Read More

Consider a synchronous point-to-point network of n nodes connected by directed links, wherein each node has a binary input. This paper proves a tight necessary and sufficient condition on the underlying communication topology for achieving Byzantine consensus among these nodes in the presence of up to f Byzantine faults. We derive a necessary condition, and then we provide a constructive proof of sufficiency by presenting a Byzantine consensus algorithm for directed graphs that satisfy the necessary condition. Read More

In this work, we explore iterative approximate Byzantine consensus algorithms that do not make explicit use of the global parameter of the graph, i.e., the upper-bound on the number of faults, f. Read More

In this work, we consider a generalized fault model that can be used to represent a wide range of failure scenarios, including correlated failures and non-uniform node reliabilities. This fault model is general in the sense that fault models studied in prior related work, such as f -total and f -local models, are special cases of the generalized fault model. Under the generalized fault model, we explore iterative approximate Byzantine consensus (IABC) algorithms in arbitrary directed networks. Read More

This paper presents a proof of correctness of an iterative approximate Byzantine consensus (IABC) algorithm for directed graphs. The iterative algorithm allows fault- free nodes to reach approximate conensus despite the presence of up to f Byzantine faults. Necessary conditions on the underlying network graph for the existence of a correct IABC algorithm were shown in our recent work [15, 16]. Read More

This report contains two related sets of results with different assumptions on synchrony. The first part is about iterative algorithms in synchronous systems. Following our previous work on synchronous iterative approximate Byzantine consensus (IABC) algorithms, we provide a more intuitive tight necessary and sufficient condition for the existence of such algorithms in synchronous networks1. Read More

IEEE 802.11 DCF is the MAC protocol currently used in wireless LANs. 802. Read More

In this paper, we explore the problem of iterative approximate Byzantine consensus in arbitrary directed graphs. In particular, we prove a necessary and sufficient condition for the existence of iterative byzantine consensus algorithms. Additionally, we use our sufficient condition to examine whether such algorithms exist for some specific graphs. Read More

This two-part paper discusses robustification methodologies for linear-iterative distributed algorithms for consensus and coordination problems in multicomponent systems, in which unreliable communication links may drop packets. We consider a setup where communication links between components can be asymmetric (i.e. Read More

In this two-part paper, we consider multicomponent systems in which each component can iteratively exchange information with other components in its neighborhood in order to compute, in a distributed fashion, the average of the components' initial values or some other quantity of interest (i.e., some function of these initial values). Read More

The goal of Byzantine Broadcast (BB) is to allow a set of fault-free nodes to agree on information that a source node wants to broadcast to them, in the presence of Byzantine faulty nodes. We consider design of efficient algorithms for BB in {\em synchronous} point-to-point networks, where the rate of transmission over each communication link is limited by its "link capacity". The throughput of a particular BB algorithm is defined as the average number of bits that can be reliably broadcast to all fault-free nodes per unit time using the algorithm without violating the link capacity constraints. Read More

In this report, we investigate the multi-valued Byzantine consensus problem. We introduce two algorithms: the first one achieves traditional validity requirement for consensus, and the second one achieves a stronger "q-validity" requirement. Both algorithms are more efficient than the ones introduces in our recent PODC 2011 paper titled "Error-Free Multi-Valued Consensus with Byzantine Failures". Read More

We consider the problem of maximizing the throughput of Byzantine consensus, when communication links have finite capacity. Byzantine consensus is a classical problem in distributed computing. In existing literature, the communication links are implicitly assumed to have infinite capacity. Read More

In this paper, we present an efficient deterministic algorithm for consensus
in presence of Byzantine failures. Our algorithm achieves consensus on an
$L$-bit value with communication complexity $O(nL + n^4 L^{0.5} + n^6)$ bits,
in a network consisting of $n$ processors with up to $t$ Byzantine failures,
such that $t

In this report, we study the multiparty communication complexity problem of the multiparty equality function (MEQ): EQ(x_1,... Read More

In this report, building on the deterministic multi-valued one-to-many Byzantine agreement (broadcast) algorithm in our recent technical report [2], we introduce a deterministic multi-valued all-to-all Byzantine agreement algorithm (consensus), with linear complexity per bit agreed upon. The discussion in this note is not self-contained, and relies heavily on the material in [2] - please refer to [2] for the necessary background. Read More

Randomized algorithm that achieves multi-valued Byzantine agreement with high probability, and achieves optimal complexity. Read More

In this paper, we consider the problem of maximizing the throughput of Byzantine agreement, given that the sum capacity of all links in between nodes in the system is finite. We have proposed a highly efficient Byzantine agreement algorithm on values of length l>1 bits. This algorithm uses error detecting network codes to ensure that fault-free nodes will never disagree, and routing scheme that is adaptive to the result of error detection. Read More

In this work we study the problem of misbehavior detection in wireless networks. A commonly adopted approach is to utilize the broadcasting nature of the wireless medium and have nodes monitor their neighborhood. We call such nodes the Watchdogs. Read More